diff --git a/bayesian/bayesian_network.py b/bayesian/bayesian_network.py new file mode 100644 index 0000000..108d645 --- /dev/null +++ b/bayesian/bayesian_network.py @@ -0,0 +1,132 @@ +import random + +# CPTs +# P(C) +P_C = {True: 0.5, False: 0.5} + +# P(S | C) +P_S_given_C = { + True: {True: 0.10, False: 0.90}, # C=T + False: {True: 0.50, False: 0.50} # C=F +} + +# P(R | C) +P_R_given_C = { + True: {True: 0.80, False: 0.20}, # C=T + False: {True: 0.20, False: 0.80} # C=F +} + +# P(W | S, R) +P_W_given_SR = { + (True, True): {True: 0.99, False: 0.01}, + (True, False): {True: 0.90, False: 0.10}, + (False, True): {True: 0.90, False: 0.10}, + (False, False): {True: 0.00, False: 1.00} +} + +def sample_variable(prob_true): + """Returns True with probability prob_true, else False""" + return random.random() < prob_true + +def get_prior_sample(): + """Generates a sample from the joint distribution P(C, S, R, W)""" + c = sample_variable(P_C[True]) + s = sample_variable(P_S_given_C[c][True]) + r = sample_variable(P_R_given_C[c][True]) + w = sample_variable(P_W_given_SR[(s, r)][True]) + return {'C': c, 'S': s, 'R': r, 'W': w} + +def rejection_sampling(query_var, query_val, evidence, num_samples): + """ + Estimates P(query_var = query_val | evidence) using Rejection Sampling. + evidence is a dict, e.g., {'S': True, 'W': True} + """ + consistent_count = 0 + query_match_count = 0 + + for _ in range(num_samples): + sample = get_prior_sample() + + # Check if sample is consistent with evidence + is_consistent = True + for var, val in evidence.items(): + if sample[var] != val: + is_consistent = False + break + + if is_consistent: + consistent_count += 1 + if sample[query_var] == query_val: + query_match_count += 1 + + if consistent_count == 0: + return 0.0 # Avoid division by zero + + return query_match_count / consistent_count + +def likelihood_weighting(query_var, query_val, evidence, num_samples): + """ + Estimates P(query_var = query_val | evidence) using Likelihood Weighting. + evidence is a dict, e.g., {'S': True, 'W': True} + """ + weighted_counts = {True: 0.0, False: 0.0} + + for _ in range(num_samples): + weight = 1.0 + sample = {} + + # C + if 'C' in evidence: + sample['C'] = evidence['C'] + weight *= P_C[sample['C']] + else: + sample['C'] = sample_variable(P_C[True]) + + # S + if 'S' in evidence: + sample['S'] = evidence['S'] + weight *= P_S_given_C[sample['C']][sample['S']] + else: + sample['S'] = sample_variable(P_S_given_C[sample['C']][True]) + + # R + if 'R' in evidence: + sample['R'] = evidence['R'] + weight *= P_R_given_C[sample['C']][sample['R']] + else: + sample['R'] = sample_variable(P_R_given_C[sample['C']][True]) + + # W + if 'W' in evidence: + sample['W'] = evidence['W'] + weight *= P_W_given_SR[(sample['S'], sample['R'])][sample['W']] + else: + sample['W'] = sample_variable(P_W_given_SR[(sample['S'], sample['R'])][True]) + + # Accumulate weight for the value of the query variable in this sample + weighted_counts[sample[query_var]] += weight + + total_weight = sum(weighted_counts.values()) + if total_weight == 0: + return 0.0 + + return weighted_counts[query_val] / total_weight + +if __name__ == "__main__": + evidence = {'S': True, 'W': True} + query_var = 'R' + query_val = True + + # Exact Calculation (calculated manually in thought process) + # Numerator: 0.0891 + # Denominator: 0.2781 + exact_prob = 0.0891 / 0.2781 + print(f"Exact Probability P(R=T | S=T, W=T): {exact_prob:.6f}") + print("-" * 60) + print(f"{'Samples':<10} | {'Rejection Sampling':<20} | {'Likelihood Weighting':<20}") + print("-" * 60) + + for N in [100, 1000, 10000, 100000, 1000000]: + rs_result = rejection_sampling(query_var, query_val, evidence, N) + lw_result = likelihood_weighting(query_var, query_val, evidence, N) + print(f"{N:<10} | {rs_result:<20.6f} | {lw_result:<20.6f}") diff --git a/bayesian/generate_data.py b/bayesian/generate_data.py new file mode 100644 index 0000000..6bd3e36 --- /dev/null +++ b/bayesian/generate_data.py @@ -0,0 +1,57 @@ +import pandas as pd +import numpy as np + +# 定义真实的条件概率表 (Ground Truth CPTs) +# 学生需要从生成的数据中“反向学习”出这些概率 +PROBS = { + 'IsSmoker': 0.2, + 'VisitAsia': 0.05, + 'HasLungCancer': { # Given IsSmoker + (1,): 0.1, + (0,): 0.01 + }, + 'HasTuberculosis': { # Given VisitAsia + (1,): 0.08, + (0,): 0.001 + }, + 'XRayPositive': { # Given HasLungCancer, HasTuberculosis + (1, 1): 0.98, + (1, 0): 0.95, + (0, 1): 0.90, + (0, 0): 0.05 + }, + 'HasDyspnea': { # Given HasLungCancer + (1,): 0.7, + (0,): 0.2 + } +} + +def generate_data(num_samples=1000): + data = [] + for _ in range(num_samples): + # Sample from parent nodes + is_smoker = np.random.binomial(1, PROBS['IsSmoker']) + visit_asia = np.random.binomial(1, PROBS['VisitAsia']) + + # Sample from children nodes based on parents + p_lc = PROBS['HasLungCancer'][(is_smoker,)] + has_lc = np.random.binomial(1, p_lc) + + p_tb = PROBS['HasTuberculosis'][(visit_asia,)] + has_tb = np.random.binomial(1, p_tb) + + p_xray = PROBS['XRayPositive'][(has_lc, has_tb)] + xray_pos = np.random.binomial(1, p_xray) + + p_dys = PROBS['HasDyspnea'][(has_lc,)] + has_dys = np.random.binomial(1, p_dys) + + data.append([is_smoker, visit_asia, has_lc, has_tb, xray_pos, has_dys]) + + df = pd.DataFrame(data, columns=['IsSmoker', 'VisitAsia', 'HasLungCancer', + 'HasTuberculosis', 'XRayPositive', 'HasDyspnea']) + df.to_csv('data.csv', index=False) + print(f"Generated data.csv with {num_samples} samples.") + +if __name__ == '__main__': + generate_data(num_samples=2000) \ No newline at end of file diff --git a/bayesian/homework.pdf b/bayesian/homework.pdf new file mode 100644 index 0000000..65b20a2 --- /dev/null +++ b/bayesian/homework.pdf @@ -0,0 +1,6702 @@ +%PDF-1.7 +% + +1 0 obj +<< + /Type /Pages + /Count 5 + /Kids [454 0 R 456 0 R 458 0 R 460 0 R 462 0 R] +>> +endobj + +2 0 obj +<< + /Type /Outlines + /First 3 0 R + /Last 9 0 R + /Count 7 +>> +endobj + +3 0 obj +<< + /Parent 2 0 R + /Next 4 0 R + /Title + /Dest 447 0 R +>> +endobj + +4 0 obj +<< + /Parent 2 0 R + 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33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 30 0 R 29 0 R 29 0 R 29 0 R 29 0 R 29 0 R 29 0 R 29 0 R 27 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 22 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 21 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 18 0 R] +endobj + +16 0 obj +<< + /Type /StructElem + /S /Document + /P 10 0 R + /K [412 0 R 411 0 R 404 0 R 402 0 R 401 0 R 397 0 R 395 0 R 394 0 R 388 0 R 387 0 R 386 0 R 385 0 R 384 0 R 382 0 R 381 0 R 379 0 R 355 0 R 351 0 R 345 0 R 344 0 R 343 0 R 339 0 R 336 0 R 335 0 R 334 0 R 327 0 R 324 0 R 281 0 R 278 0 R 276 0 R 275 0 R 271 0 R 270 0 R 260 0 R 258 0 R 247 0 R 196 0 R 195 0 R 190 0 R 186 0 R 185 0 R 184 0 R 183 0 R 182 0 R 178 0 R 177 0 R 176 0 R 175 0 R 174 0 R 172 0 R 168 0 R 167 0 R 164 0 R 162 0 R 160 0 R 159 0 R 157 0 R 136 0 R 134 0 R 131 0 R 129 0 R 128 0 R 127 0 R 106 0 R 105 0 R 103 0 R 102 0 R 101 0 R 99 0 R 97 0 R 96 0 R 93 0 R 91 0 R 90 0 R 86 0 R 81 0 R 80 0 R 75 0 R 54 0 R 51 0 R 46 0 R 25 0 R 22 0 R 20 0 R 19 0 R 17 0 R] +>> +endobj + +17 0 obj +<< + /Type /StructElem + /S /P + /P 16 0 R + /K [18 0 R] +>> +endobj + +18 0 obj +<< + /Type /StructElem + /S /Strong + /P 17 0 R + /K [794] + /Pg 462 0 R +>> +endobj + +19 0 obj +<< + /Type /StructElem + /S /Formula + /P 16 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793] + /Pg 462 0 R +>> +endobj + +20 0 obj +<< + /Type /StructElem + /S /P + /P 16 0 R + /K [21 0 R] +>> +endobj + +21 0 obj +<< + /Type /StructElem + /S /Strong + /P 20 0 R + /K [740] + /Pg 462 0 R +>> +endobj + +22 0 obj +<< + /Type /StructElem + /S /P + /P 16 0 R + /K [24 0 R 706 23 0 R] + /Pg 462 0 R +>> +endobj + +23 0 obj +<< + /Type /StructElem + /S /Formula + /P 22 0 R + /K [707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739] + /Pg 462 0 R +>> +endobj + +24 0 obj +<< + /Type /StructElem + /S /Formula + /P 22 0 R + /K [667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705] + /Pg 462 0 R +>> +endobj + +25 0 obj +<< + /Type /StructElem + /S /L + /P 16 0 R + /A [<< + /O /List + /ListNumbering /Circle + >>] + /K [41 0 R 36 0 R 31 0 R 26 0 R] +>> +endobj + +26 0 obj +<< + /Type /StructElem + /S /LI + /P 25 0 R + /K [30 0 R 27 0 R] +>> +endobj + +27 0 obj +<< + /Type /StructElem + /S /LBody + /P 26 0 R + /K [29 0 R 644 28 0 R] + /Pg 462 0 R +>> +endobj + +28 0 obj +<< + /Type /StructElem + /S /Formula + /P 27 0 R + /K [645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666] + /Pg 462 0 R +>> +endobj + +29 0 obj +<< + /Type /StructElem + /S /Formula + /P 27 0 R + /K [637 638 639 640 641 642 643] + /Pg 462 0 R +>> +endobj + +30 0 obj +<< + /Type /StructElem + /S /Lbl + /P 26 0 R + /K [636] + /Pg 462 0 R +>> +endobj + +31 0 obj +<< + /Type /StructElem + /S /LI + /P 25 0 R + /K [35 0 R 32 0 R] +>> +endobj + +32 0 obj +<< + /Type /StructElem + /S /LBody + /P 31 0 R + /K [34 0 R 572 33 0 R] + /Pg 462 0 R +>> +endobj + +33 0 obj +<< + /Type /StructElem + /S /Formula + /P 32 0 R + /K [573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635] + /Pg 462 0 R +>> +endobj + +34 0 obj +<< + /Type /StructElem + /S /Formula + /P 32 0 R + /K [565 566 567 568 569 570 571] + /Pg 462 0 R +>> +endobj + +35 0 obj +<< + /Type /StructElem + /S /Lbl + /P 31 0 R + /K [564] + /Pg 462 0 R +>> +endobj + +36 0 obj +<< + /Type /StructElem + /S /LI + /P 25 0 R + /K [40 0 R 37 0 R] +>> +endobj + +37 0 obj +<< + /Type /StructElem + /S /LBody + /P 36 0 R + /K [39 0 R 541 38 0 R] + /Pg 462 0 R +>> +endobj + +38 0 obj +<< + /Type /StructElem + /S /Formula + /P 37 0 R + /K [542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563] + /Pg 462 0 R +>> +endobj + +39 0 obj +<< + /Type /StructElem + /S /Formula + /P 37 0 R + /K [534 535 536 537 538 539 540] + /Pg 462 0 R +>> +endobj + +40 0 obj +<< + /Type /StructElem + /S /Lbl + /P 36 0 R + /K [533] + /Pg 462 0 R +>> +endobj + +41 0 obj +<< + /Type /StructElem + /S /LI + /P 25 0 R + /K [45 0 R 42 0 R] +>> +endobj + +42 0 obj +<< + /Type /StructElem + /S /LBody + /P 41 0 R + /K [44 0 R 469 43 0 R] + /Pg 462 0 R +>> +endobj + +43 0 obj +<< + /Type /StructElem + /S /Formula + /P 42 0 R + /K [470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532] + /Pg 462 0 R +>> +endobj + +44 0 obj +<< + /Type /StructElem + /S /Formula + /P 42 0 R + /K [462 463 464 465 466 467 468] + /Pg 462 0 R +>> +endobj + +45 0 obj +<< + /Type /StructElem + /S /Lbl + /P 41 0 R + /K [461] + /Pg 462 0 R +>> +endobj + +46 0 obj +<< + /Type /StructElem + /S /P + /P 16 0 R + /K [50 0 R 432 49 0 R 440 48 0 R 455 47 0 R 460] + /Pg 462 0 R +>> +endobj + +47 0 obj +<< + /Type /StructElem + /S /Formula + /P 46 0 R + /K [456 457 458 459] + /Pg 462 0 R +>> +endobj + +48 0 obj +<< + /Type /StructElem + /S /Formula + /P 46 0 R + /K [441 442 443 444 445 446 447 448 449 450 451 452 453 454] + /Pg 462 0 R +>> +endobj + +49 0 obj +<< + /Type /StructElem + /S /Formula + /P 46 0 R + /K [433 434 435 436 437 438 439] + /Pg 462 0 R +>> +endobj + +50 0 obj +<< + /Type /StructElem + /S /Strong + /P 46 0 R + /K [431] + /Pg 462 0 R +>> +endobj + +51 0 obj +<< + /Type /StructElem + /S /P + /P 16 0 R + /K [53 0 R 397 52 0 R] + /Pg 462 0 R +>> +endobj + +52 0 obj +<< + /Type /StructElem + /S /Formula + /P 51 0 R + /K [398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430] + /Pg 462 0 R +>> +endobj + +53 0 obj +<< + /Type /StructElem + /S /Formula + /P 51 0 R + /K [358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396] + /Pg 462 0 R +>> +endobj + +54 0 obj +<< + /Type /StructElem + /S /L + /P 16 0 R + /A [<< + /O /List + /ListNumbering /Circle + >>] + /K [70 0 R 65 0 R 60 0 R 55 0 R] +>> +endobj + +55 0 obj +<< + /Type /StructElem + /S /LI + /P 54 0 R + /K [59 0 R 56 0 R] +>> +endobj + +56 0 obj +<< + /Type /StructElem + /S /LBody + /P 55 0 R + /K [58 0 R 335 57 0 R] + /Pg 462 0 R +>> +endobj + +57 0 obj +<< + /Type /StructElem + /S /Formula + /P 56 0 R + /K [336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357] + /Pg 462 0 R +>> +endobj + +58 0 obj +<< + /Type /StructElem + /S /Formula + /P 56 0 R + /K [328 329 330 331 332 333 334] + /Pg 462 0 R +>> +endobj + +59 0 obj +<< + /Type /StructElem + /S /Lbl + /P 55 0 R + /K [327] + /Pg 462 0 R +>> +endobj + +60 0 obj +<< + /Type /StructElem + /S /LI + /P 54 0 R + /K [64 0 R 61 0 R] +>> +endobj + +61 0 obj +<< + /Type /StructElem + /S /LBody + /P 60 0 R + /K [63 0 R 263 62 0 R] + /Pg 462 0 R +>> +endobj + +62 0 obj +<< + /Type /StructElem + /S /Formula + /P 61 0 R + /K [264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326] + /Pg 462 0 R +>> +endobj + +63 0 obj +<< + /Type /StructElem + /S /Formula + /P 61 0 R + /K [256 257 258 259 260 261 262] + /Pg 462 0 R +>> +endobj + +64 0 obj +<< + /Type /StructElem + /S /Lbl + /P 60 0 R + /K [255] + /Pg 462 0 R +>> +endobj + +65 0 obj +<< + /Type /StructElem + /S /LI + /P 54 0 R + /K [69 0 R 66 0 R] +>> +endobj + +66 0 obj +<< + /Type /StructElem + /S /LBody + /P 65 0 R + /K [68 0 R 232 67 0 R] + /Pg 462 0 R +>> +endobj + +67 0 obj +<< + /Type /StructElem + /S /Formula + /P 66 0 R + /K [233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254] + /Pg 462 0 R +>> +endobj + +68 0 obj +<< + /Type /StructElem + /S /Formula + /P 66 0 R + /K [225 226 227 228 229 230 231] + /Pg 462 0 R +>> +endobj + +69 0 obj +<< + /Type /StructElem + /S /Lbl + /P 65 0 R + /K [224] + /Pg 462 0 R +>> +endobj + +70 0 obj +<< + /Type /StructElem + /S /LI + /P 54 0 R + /K [74 0 R 71 0 R] +>> +endobj + +71 0 obj +<< + /Type /StructElem + /S /LBody + /P 70 0 R + /K [73 0 R 160 72 0 R] + /Pg 462 0 R +>> +endobj + +72 0 obj +<< + /Type /StructElem + /S /Formula + /P 71 0 R + /K [161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223] + /Pg 462 0 R +>> +endobj + +73 0 obj +<< + /Type /StructElem + /S /Formula + /P 71 0 R + /K [153 154 155 156 157 158 159] + /Pg 462 0 R +>> +endobj + +74 0 obj +<< + /Type /StructElem + /S /Lbl + /P 70 0 R + /K [152] + /Pg 462 0 R +>> +endobj + +75 0 obj +<< + /Type /StructElem + /S /P + /P 16 0 R + /K [79 0 R 123 78 0 R 131 77 0 R 146 76 0 R 151] + /Pg 462 0 R +>> +endobj + +76 0 obj +<< + /Type /StructElem + /S /Formula + /P 75 0 R + /K [147 148 149 150] + /Pg 462 0 R +>> +endobj + +77 0 obj +<< + /Type /StructElem + /S /Formula + /P 75 0 R + /K [132 133 134 135 136 137 138 139 140 141 142 143 144 145] + /Pg 462 0 R +>> +endobj + +78 0 obj +<< + /Type /StructElem + /S /Formula + /P 75 0 R + /K [124 125 126 127 128 129 130] + /Pg 462 0 R +>> +endobj + +79 0 obj +<< + /Type /StructElem + /S /Strong + /P 75 0 R + /K [122] + /Pg 462 0 R +>> +endobj + +80 0 obj +<< + /Type /StructElem + /S /Formula + /P 16 0 R + /A [<< + /O /Layout + 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87 0 R] +>> +endobj + +87 0 obj +<< + /Type /StructElem + /S /Formula + /P 86 0 R + /K [88 0 R] +>> +endobj + +88 0 obj +<< + /Type /StructElem + /S /Strong + /P 87 0 R + /K [391 392 393 394 395 396 397 398 399 400 401 402 403 404] + /Pg 460 0 R +>> +endobj + +89 0 obj +<< + /Type /StructElem + /S /Strong + /P 86 0 R + /K [390] + /Pg 460 0 R +>> +endobj + +90 0 obj +<< + /Type /StructElem + /S /Span + /P 16 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [385 386 387 388 389] + /Pg 460 0 R +>> +endobj + +91 0 obj +<< + /Type /StructElem + /S /P + /P 16 0 R + /K [92 0 R] +>> +endobj + +92 0 obj +<< + /Type /StructElem + /S /Strong + /P 91 0 R + /K [384] + /Pg 460 0 R +>> +endobj + +93 0 obj +<< + /Type /StructElem + /S /P + /P 16 0 R + /K [95 0 R 353 354 355 356 357 358 359 360 361 362 363 94 0 R 383] + /Pg 460 0 R +>> +endobj + +94 0 obj +<< + /Type /StructElem + /S /Formula + /P 93 0 R + /K [364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382] + /Pg 460 0 R +>> +endobj + +95 0 obj +<< + /Type /StructElem + /S /Strong + /P 93 0 R + /K [352] + /Pg 460 0 R +>> +endobj + +96 0 obj +<< + /Type /StructElem + /S /H1 + /P 16 0 R + /T + /K [350 351] + /Pg 460 0 R +>> +endobj + +97 0 obj +<< + /Type /StructElem + /S /P + /P 16 0 R + /K [98 0 R] +>> +endobj + +98 0 obj +<< + /Type /StructElem + /S /Strong + /P 97 0 R + /K [349] + /Pg 460 0 R +>> +endobj + +99 0 obj +<< + /Type /StructElem + /S /P + /P 16 0 R + /K [314 100 0 R 348] + /Pg 460 0 R +>> +endobj + +100 0 obj +<< + /Type /StructElem + /S /Formula + /P 99 0 R + /K [315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347] + /Pg 460 0 R +>> +endobj + +101 0 obj +<< + /Type /StructElem + /S /Formula + /P 16 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313] + /Pg 460 0 R +>> +endobj + +102 0 obj 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163 164] + /Pg 460 0 R +>> +endobj + +116 0 obj +<< + /Type /StructElem + /S /Lbl + /P 112 0 R + /K [157] + /Pg 460 0 R +>> +endobj + +117 0 obj +<< + /Type /StructElem + /S /LI + /P 106 0 R + /K [121 0 R 118 0 R] +>> +endobj + +118 0 obj +<< + /Type /StructElem + /S /LBody + /P 117 0 R + /K [120 0 R 139 119 0 R] + /Pg 460 0 R +>> +endobj + +119 0 obj +<< + /Type /StructElem + /S /Formula + /P 118 0 R + /K [140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156] + /Pg 460 0 R +>> +endobj + +120 0 obj +<< + /Type /StructElem + /S /Formula + /P 118 0 R + /K [132 133 134 135 136 137 138] + /Pg 460 0 R +>> +endobj + +121 0 obj +<< + /Type /StructElem + /S /Lbl + /P 117 0 R + /K [131] + /Pg 460 0 R +>> +endobj + +122 0 obj +<< + /Type /StructElem + /S /LI + /P 106 0 R + /K [126 0 R 123 0 R] +>> +endobj + +123 0 obj +<< + /Type /StructElem + /S /LBody + /P 122 0 R + /K [125 0 R 113 124 0 R] + /Pg 460 0 R +>> +endobj + +124 0 obj +<< + /Type /StructElem + /S /Formula + /P 123 0 R 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[208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355] + /Pg 458 0 R +>> +endobj + +175 0 obj +<< + /Type /StructElem + /S /Formula + /P 16 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207] + /Pg 458 0 R +>> +endobj + +176 0 obj +<< + /Type /StructElem + /S /Formula + /P 16 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180] + /Pg 458 0 R +>> +endobj + +177 0 obj +<< + /Type /StructElem + /S /P + /P 16 0 R + /K [152 153 154] + /Pg 458 0 R +>> +endobj + +178 0 obj +<< + /Type /StructElem + /S /P + /P 16 0 R + /K [181 0 R 179 0 R] +>> +endobj + +179 0 obj +<< + /Type /StructElem + /S /Formula + /P 178 0 R + /K [180 0 R] +>> +endobj + +180 0 obj +<< + /Type /StructElem + /S /Strong + /P 179 0 R + /K [142 143 144 145 146 147 148 149 150 151] + /Pg 458 0 R +>> +endobj + +181 0 obj +<< + /Type /StructElem + /S /Strong + /P 178 0 R + /K [136 137 138 139 140 141] + /Pg 458 0 R +>> +endobj + +182 0 obj +<< + /Type /StructElem + /S /Formula + /P 16 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135] + /Pg 458 0 R +>> +endobj + +183 0 obj +<< + /Type /StructElem + /S /Formula + /P 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312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346] + /Pg 456 0 R +>> +endobj + +276 0 obj +<< + /Type /StructElem + /S /P + /P 16 0 R + /K [277 0 R] +>> +endobj + +277 0 obj +<< + /Type /StructElem + /S /Strong + /P 276 0 R + /K [255 256 257 258 259] + /Pg 456 0 R +>> +endobj + +278 0 obj +<< + /Type /StructElem + /S /P + /P 16 0 R + /K [192 280 0 R 216 279 0 R 251 252 253 254] + /Pg 456 0 R +>> +endobj + +279 0 obj +<< + /Type /StructElem + /S /Formula + /P 278 0 R + /K [217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250] + /Pg 456 0 R +>> +endobj + +280 0 obj +<< + /Type /StructElem + /S /Formula + /P 278 0 R + /K [193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215] + /Pg 456 0 R +>> +endobj + +281 0 obj +<< + /Type /StructElem + /S /L + /P 16 0 R + /A [<< + /O /List + 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318 0 R] + /Pg 456 0 R +>> +endobj + +318 0 obj +<< + /Type /StructElem + /S /Formula + /P 317 0 R + /K [65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113] + /Pg 456 0 R +>> +endobj + +319 0 obj +<< + /Type /StructElem + /S /Formula + /P 317 0 R + /K [63] + /Pg 456 0 R +>> +endobj + +320 0 obj +<< + /Type /StructElem + /S /Formula + /P 317 0 R + /K [321 0 R] +>> +endobj + +321 0 obj +<< + /Type /StructElem + /S /Strong + /P 320 0 R + /K [58 59 60 61] + /Pg 456 0 R +>> +endobj + +322 0 obj +<< + /Type /StructElem + /S /Strong + /P 317 0 R + /K [57] + /Pg 456 0 R +>> +endobj + +323 0 obj +<< + /Type /StructElem + /S /Lbl + /P 316 0 R + /K [56] + /Pg 456 0 R +>> +endobj + +324 0 obj +<< + /Type /StructElem + /S /P + /P 16 0 R + /K [43 326 0 R 50 325 0 R 55] + /Pg 456 0 R +>> +endobj + +325 0 obj +<< + /Type /StructElem + /S /Formula + /P 324 0 R + /K [51 52 53 54] + /Pg 456 0 R 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8 9 10 11 12 13 14 15 16 17 18 19 20] + /Pg 456 0 R +>> +endobj + +335 0 obj +<< + /Type /StructElem + /S /Formula + /P 16 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417] + /Pg 454 0 R +>> +endobj + +336 0 obj +<< + /Type /StructElem + /S /P + /P 16 0 R + /K [376 338 0 R 381 382 337 0 R 384 385] + /Pg 454 0 R +>> +endobj + +337 0 obj +<< + /Type /StructElem + /S /Formula + /P 336 0 R + /K [383] + /Pg 454 0 R +>> +endobj + +338 0 obj +<< + /Type /StructElem + /S /Formula + /P 336 0 R + /K [377 378 379 380] + /Pg 454 0 R +>> +endobj + +339 0 obj +<< + /Type /StructElem + /S /P + /P 16 0 R + /K [342 0 R 340 0 R] +>> +endobj + +340 0 obj +<< + /Type /StructElem + /S /Formula + /P 339 0 R + /K [341 0 R] +>> +endobj + +341 0 obj +<< + /Type /StructElem + /S /Strong + /P 340 0 R + /K [369 370 371 372 373 374 375] + /Pg 454 0 R +>> +endobj + +342 0 obj +<< 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0 R + /ID [(56cDPmhV9s3zbCLrJhRD3g==) (56cDPmhV9s3zbCLrJhRD3g==)] +>> +startxref +213490 +%%EOF \ No newline at end of file diff --git a/bayesian/homework.typ b/bayesian/homework.typ new file mode 100644 index 0000000..e9f5b1d --- /dev/null +++ b/bayesian/homework.typ @@ -0,0 +1,289 @@ +#import "@preview/cetz:0.3.3" + +#set text(font: ("Noto Sans CJK SC", "Noto Serif CJK SC"), lang: "zh") +#set page(paper: "a4", margin: (x: 2cm, y: 2cm)) +#set heading(numbering: "1.") + +#let answer(body) = block( + fill: luma(240), + stroke: (left: 2pt + blue), + inset: 10pt, + radius: 2pt, + width: 100%, + body +) + +#align(center)[ + #text(size: 18pt, weight: "bold")[第13-14章 概率与贝叶斯网络 习题解答] + + #v(1em) + // *生成时间:* #datetime.today().display() +] + += 题目 1 +*题意:* 已知 $P(a) = 0.3$, $P(b | a) = 0.2$, $P(c | a) = 0.5$。比较 $P(a and b)$ 与 $P(a and c)$。 + +#answer[ + 根据乘法公式 $P(x and y) = P(x)P(y|x)$: + $ P(a and b) &= P(a) dot P(b | a) = 0.3 times 0.2 = 0.06 \ + P(a and c) &= P(a) dot P(c | a) = 0.3 times 0.5 = 0.15 $ + 因为 $0.06 < 0.15$,所以 *$P(a and b) < P(a and c)$*。 + + *答案:B* +] + += 题目 2 +*题意:* $P(a or b)=0.7$, $P(a)=0.4$, $P(b)=0.5$,求 $P(a and b)$。 + +#answer[ + 根据概率加法公式(容斥原理): + $ P(a or b) = P(a) + P(b) - P(a and b) $ + 代入已知数值: + $ 0.7 = 0.4 + 0.5 - P(a and b) \ + P(a and b) = 0.9 - 0.7 = 0.2 $ + + *答案:0.2* +] + += 题目 3 +*数据:* 全联合概率分布表如下(Cavity, Toothache, Catch): + +#table( + columns: (auto, auto, auto, auto, auto), + inset: 8pt, + align: center, + [], [T, Catch], [T, $not$ Catch], [$not$ T, Catch], [$not$ T, $not$ Catch], + [Cavity], [0.108], [0.012], [0.072], [0.008], + [$not$ Cavity], [0.016], [0.064], [0.144], [0.576] +) + +#answer[ + *1. 计算 $P("Toothache" or not "Cavity")$* + + 利用补集思想:$P(A) = 1 - P(not A)$。 + 事件的补集是 $not "Toothache" and "Cavity"$。 + 对应表格中的项为:(Cavity, $not$ T, Catch) 和 (Cavity, $not$ T, $not$ Catch)。 + $ P(not T and "Cav") = 0.072 + 0.008 = 0.080 $ + $ P(T or not "Cav") = 1 - 0.080 = 0.92 $ + + *2. 计算 $P(not "toothache" or "catch")$* + + 补集是 $"toothache" and not "catch"$。 + 对应表格列为 (T, $not$ Catch),即第 2 列。 + $ P(T and not "Catch") = 0.012 ("Cav") + 0.064 (not "Cav") = 0.076 $ + $ P(not T or "Catch") = 1 - 0.076 = 0.924 $ + + *3. 计算 $P("Toothache" or not "Cavity" | not "catch")$ 和 $P(not "catch" | "Toothache" or not "Cavity")$* + + 令 $A = "Toothache" or not "Cavity"$, $B = not "catch"$。 + + - *计算 $P(B)$*: Sum of all $not$ Catch columns (Col 2, Col 4). + $P(B) = (0.012 + 0.064) + (0.008 + 0.576) = 0.076 + 0.584 = 0.66$ + - *计算 $P(A and B)$*: 在 $not$ Catch 列中满足 $T or not "Cav"$ 的项。 + - (Cav, T, $not$ C): 0.012 (满足 T) + - ($not$ Cav, T, $not$ C): 0.064 (满足 T) + - ($not$ Cav, $not$ T, $not$ C): 0.576 (满足 $not$ Cav) + - (Cav, $not$ T, $not$ C): 0.008 (不满足,既无T也无$not$Cav) + Sum $= 0.012 + 0.064 + 0.576 = 0.652$ + + 结果 1: $P(A | B) = 0.652 / 0.66 approx 0.9879$ + 结果 2: $P(B | A) = P(A and B) / P(A) = 0.652 / 0.92 approx 0.7087$ (其中 P(A) 来自第1小问) + + *4. 判断 Cavity 与 Toothache 是否独立* + + $ P("Cav") &= 0.108+0.012+0.072+0.008 = 0.2 \ + P("Toothache") &= 0.108+0.012+0.016+0.064 = 0.2 \ + P("Cav" and "T") &= 0.108 + 0.012 = 0.12 $ + 检验:$P("Cav") times P("T") = 0.2 times 0.2 = 0.04$。 + 因为 $0.12 != 0.04$,所以两者 *不独立*。 +] + += 题目 4 +*题意:* 设 $X, Y$ 条件独立于 $Z$(即 $X perp Y | Z$),$Y, W$ 条件独立于 $Z$(即 $Y perp W | Z$)。问 $X, W$ 是否条件独立于 $Z$? + +#answer[ + *结论:不能。* 条件独立性不具备传递性。 + + *反例证明:* + 假设 $Z$ 是一个公平的硬币投掷(0 或 1)。 + 令 $X = Z$($X$ 完全依赖于 $Z$)。 + 令 $W = Z$($W$ 完全依赖于 $Z$)。 + 令 $Y$ 是一个与 $X, W, Z$ 都完全独立的随机变量(例如掷骰子)。 + + 1. *检查 $X, Y$ 关于 $Z$ 的独立性*:给定 $Z$, $X$ 变为常数。常数与任何变量独立,故成立。 + 2. *检查 $Y, W$ 关于 $Z$ 的独立性*:同理,给定 $Z$,$W$ 变为常数,故成立。 + 3. *检查 $X, W$ 关于 $Z$ 的独立性*: + 给定 $Z$,$X$ 和 $W$ 的值完全确定且相同(例如若 $Z=1$,则 $X=1, W=1$)。虽然在 $Z$ 固定的情况下它们的方差为0(技术上可视作独立),但如果我们考虑一种因果结构: + 令 $X$ 和 $W$ 为同一变量的两个副本。显然它们是强相关的。 + + 更直观的例子:$X$ 和 $W$ 互为因果或由共同隐变量控制,而它们都与 $Y$ 独立。仅仅知道它们分别与 $Y$ 独立,无法切断 $X$ 和 $W$ 之间的联系。 +] + += 题目 5 +*题意:* 罕见病检测。$P(D)=0.001$。 +检测A:$P(+|D)=0.95, P(+|not D)=0.05$。 +检测B:$P(+|D)=0.90, P(+|not D)=0.10$。 + +#answer[ + *a. 单次检测 A 为阳性,求 $P(D|A+)$* + + 使用贝叶斯公式: + $ P(D|A+) = (P(A+|D)P(D)) / P(A+) $ + $ P(A+) &= P(A+|D)P(D) + P(A+|not D)P(not D) \ + &= 0.95 times 0.001 + 0.05 times 0.999 \ + &= 0.00095 + 0.04995 = 0.0509 $ + $ P(D|A+) &= 0.00095 / 0.0509 approx 0.0187 (1.87%) $ + + *b. 两次检测 A 和 B 均为阳性,求 $P(D|A+, B+)$* + + 由于检测独立(Naive Bayes 假设): + $ P(A+, B+ | D) = 0.95 times 0.90 = 0.855 $ + $ P(A+, B+ | not D) = 0.05 times 0.10 = 0.005 $ + + $ P(D | A+, B+) &= (P(A+, B+ | D)P(D)) / (P(A+, B+ | D)P(D) + P(A+, B+ | not D)P(not D)) \ + &= (0.855 times 0.001) / (0.855 times 0.001 + 0.005 times 0.999) \ + &= 0.000855 / (0.000855 + 0.004995) \ + &= 0.000855 / 0.00585 approx 0.1462 (14.62%) $ + + *c. 解释* + + 联合检测通过引入第二次独立测试,极大地降低了*假阳性率*(从 0.05 降至 $0.05 times 0.10 = 0.005$)。虽然真阳性率也略有下降,但分母中占主导地位的假阳性项(由 $P(not D)$ 权重放大)被大幅削减,从而显著提升了后验概率。 +] + += 题目 6 +*场景:* 骑车(B) 取决于 天气(W) 和 熬夜(S)。 +$P(W="Sun")=0.7, P(S="Yes")=0.4$。 +CPT 已知。 + +#answer[ + *a. 贝叶斯网络与 CPT* + + 结构:$W -> B <- S$ (V-structure) + + #cetz.canvas({ + import cetz.draw: * + + let r = 0.8 + // Nodes + circle((0, 0), radius: r, name: "B") + content("B", "B (骑车)") + + circle((-2, 3), radius: r, name: "W") + content("W", "W (天气)") + + circle((2, 3), radius: r, name: "S") + content("S", "S (熬夜)") + + // Edges + line("W", "B", mark: (end: ">")) + line("S", "B", mark: (end: ">")) + }) + + *条件概率表 (CPT) for B:* + #table( + columns: 3, + align: center, + [W (天气)], [S (熬夜)], [P(B=是 | W, S)], + [晴 (Sun)], [否 (No)], [0.9], + [晴 (Sun)], [是 (Yes)], [0.6], + [雨 (Rain)], [否 (No)], [0.2], + [雨 (Rain)], [是 (Yes)], [0.1] + ) + + *b. 推理:已知骑车(B=Yes),求天气概率* + + 我们需要计算 $P(W | B="Yes")$。根据贝叶斯法则:$P(W|B) = P(B|W)P(W) / P(B)$。 + + 首先计算边缘概率 $P(B="Yes")$。 + $ P(B=y) = sum_(w, s) P(B=y|w,s)P(w)P(s) $ + 因 W 和 S 独立,联合概率直接相乘。 + + 1. $W="Sun", S="No"$: $0.9 times 0.7 times 0.6 = 0.378$ + 2. $W="Sun", S="Yes"$: $0.6 times 0.7 times 0.4 = 0.168$ + 3. $W="Rain", S="No"$: $0.2 times 0.3 times 0.6 = 0.036$ + 4. $W="Rain", S="Yes"$: $0.1 times 0.3 times 0.4 = 0.012$ + + $ P(B="Yes") = 0.378 + 0.168 + 0.036 + 0.012 = 0.594 $ + + 计算 $P(W="Sun" | B="Yes")$: + 分子为 W=Sun 的所有情况之和(项1 + 项2): + $ P(B=y, W="Sun") = 0.378 + 0.168 = 0.546 $ + $ P(W="Sun" | B="Yes") = 0.546 / 0.594 approx 0.919 $ + + 同理,$P(W="Rain" | B="Yes") = (0.036 + 0.012) / 0.594 approx 0.081$。 + + *结论:这天最可能是晴天。* +] + += 题目 7 +*智能健康助手:* 变量 S(吸烟), G(基因), L(肺癌), C(咳嗽), X(胸片)。 +关系:$S->L, G->L, S->C, L->C, L->X$。 + +#answer[ + *问题 1:贝叶斯网络图* + + #align(center)[ + #cetz.canvas({ + import cetz.draw: * + // Manually positioning nodes for clarity + let r = 0.5 + circle((0, 0), radius: r, name: "L") + content("L", "L") + + circle((-2, 2), radius: r, name: "S") + content("S", "S") + + circle((2, 2), radius: r, name: "G") + content("G", "G") + + circle((-1, -2), radius: r, name: "C") + content("C", "C") + + circle((1, -2), radius: r, name: "X") + content("X", "X") + + line("S", "L", mark: (end: ">")) + line("G", "L", mark: (end: ">")) + line("L", "X", mark: (end: ">")) + line("L", "C", mark: (end: ">")) + + // S -> C 直接边 + line("S", "C", mark: (end: ">")) + }) + ] + + *问题 2:概率推理 $P(L="Yes" | C="No", X="Yes")$* + + 令 $alpha$ 为归一化常数。我们需要计算 $P(L=y, C=n, X=y)$ 和 $P(L=n, C=n, X=y)$。 + 公式分解:$P(S,G,L,C,X) = P(S)P(G)P(L|S,G)P(C|L,S)P(X|L)$。 + 求和消除 S, G: + $ P(L, C, X) = P(X|L) sum_S sum_G P(C|L,S) P(L|S,G) P(S) P(G) $ + + *Case 1: L = Yes* (且 $C=n, X=y$) + 因子 $P(X=y|L=y) = 0.9$。 + 内部求和 $Sigma_(L=y)$: + - $S=y, G=h$: $P(C=n|L=y,S=y)P(L=y|S=y,G=h)P(S=y)P(G=h) = 0.2 times 0.6 times 0.3 times 0.2 = 0.0072$ + - $S=y, G=l$: $0.2 times 0.3 times 0.3 times 0.8 = 0.0144$ + - $S=n, G=h$: $P(C=n|L=y,S=n)P(L=y|S=n,G=h)P(S=n)P(G=h) = 0.4 times 0.4 times 0.7 times 0.2 = 0.0224$ + - $S=n, G=l$: $0.4 times 0.1 times 0.7 times 0.8 = 0.0224$ + + $Sigma_(L=y) = 0.0072 + 0.0144 + 0.0224 + 0.0224 = 0.0664$ + $P(L=y, C=n, X=y) = 0.9 times 0.0664 = 0.05976$ + + *Case 2: L = No* (且 $C=n, X=y$) + 因子 $P(X=y|L=n) = 0.1$。 + 内部求和 $Sigma_(L=n)$: + - $S=y, G=h$: $P(C=n|L=n,S=y)P(L=n|S=y,G=h)P(S=y)P(G=h) = 0.7 times 0.4 times 0.3 times 0.2 = 0.0168$ + - $S=y, G=l$: $0.7 times 0.7 times 0.3 times 0.8 = 0.1176$ + - $S=n, G=h$: $P(C=n|L=n,S=n)P(L=n|S=n,G=h)P(S=n)P(G=h) = 0.9 times 0.6 times 0.7 times 0.2 = 0.0756$ + - $S=n, G=l$: $0.9 times 0.9 times 0.7 times 0.8 = 0.4536$ + + $Sigma_(L=n) = 0.0168 + 0.1176 + 0.0756 + 0.4536 = 0.6636$ + $P(L=n, C=n, X=y) = 0.1 times 0.6636 = 0.06636$ + + *最终归一化:* + $ P(L="Yes" | ...) &= 0.05976 / (0.05976 + 0.06636) \ + &= 0.05976 / 0.12612 approx 0.4738 $ + + *答案:47.38%* +] diff --git a/bayesian/labtemplate.typ b/bayesian/labtemplate.typ new file mode 100755 index 0000000..a43048b --- /dev/null +++ b/bayesian/labtemplate.typ @@ -0,0 +1,177 @@ +#let times = "Times LT Pro" +#let times = "Times New Roman" +#let song = (times, "Noto Serif CJK SC") +#let hei = (times, "Noto Sans CJK SC") +#let kai = (times, "Noto Serif CJK SC") +#let xbsong = (times, "Noto Serif CJK SC") +#let fsong = (times, "Noto Serif CJK SC") +#let code = (times, "JetBrains Mono") +#let nudtlabpaper(title: "", + author: "", + id: "", + training_type:"", + grade: "", + major: "", + department: "", + advisor: "", + jobtitle: "", + lab: "", + date: "", + header_str: "", + simple_cover: "", + body) = { + // Set the document's basic properties. + set document(author: author, title: title) + set page( + + margin: (left: 30mm, right: 30mm, top: 30mm, bottom: 30mm), + ) + + // Title row. + v(158pt) + align(center)[ + #block(text(weight: 700, size: 30pt, font: hei, tracking: 15pt, "人工智能实验报告")) + ] + // align(center)[ + // #block(text(weight: 700, size: 30pt, font: song, tracking: 15pt, "本科实验报告")) + // ] + + v(83pt) + pad( + left: 1em, + right: 1em, + grid( + columns: (80pt, 1fr), + rows: (17pt, auto), + text(weight: 700, size: 16pt, font: song, "实验名称:"), + align(center, text(weight: "regular", size: 16pt, font: song, title)), + text(""), + line(length: 100%) + ) + // #block(text(weight: 700, 1.75em, title)) + // underline(text(weight: 700, size: 16pt, font: song, title)) + ) + + // Author information. + + v(82.5pt) + + if simple_cover { + pad( + 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text(""), + line(length: 100%), + text(""), + line(length: 100%), + ) + } + + v(50.5pt) + align(center, text(font: hei, size: 15pt, "国防科技大学教育训练部制")) + + pagebreak() + + set page( + margin: (left: 30mm, right: 30mm, top: 30mm, bottom: 30mm), + numbering: "i", + number-align: center, + ) + + v(14pt) + align(center)[ + #block(text(font: hei, size: 14pt, "《本科实验报告》填写说明")) + ] + + v(14pt) + text("") + par(first-line-indent: 2em, text(font: song, size: 12pt, "实验报告内容编排应符合以下要求:")) + + par(first-line-indent: 2em, text(font: fsong, size: 12pt, "(1)采用A4(21cm×29.7cm)白色复印纸,单面黑字。上下左右各侧的页边距均为3cm;缺省文档网格:字号为小4号,中文为宋体,英文和阿拉伯数字为Times New Roman,每页30行,每行36字;页脚距边界为2.5cm,页码置于页脚、居中,采用小5号阿拉伯数字从1开始连续编排,封面不编页码。")) + + par(first-line-indent: 2em, text(font: fsong, size: 12pt, "(2)报告正文最多可设四级标题,字体均为黑体,第一级标题字号为4号,其余各级标题为小4号;标题序号第一级用“一、”、“二、”……,第二级用“(一)”、“(二)” ……,第三级用“1.”、“2.” ……,第四级用“(1)”、“(2)” ……,分别按序连续编排。")) + + par(first-line-indent: 2em, text(font: fsong, size: 12pt, "(3)正文插图、表格中的文字字号均为5号。")) + + pagebreak() + + 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0 R 72 0 R 72 0 R 72 0 R 72 0 R 72 0 R 72 0 R 72 0 R 72 0 R 72 0 R 72 0 R 72 0 R 72 0 R 72 0 R 72 0 R 72 0 R 72 0 R 69 0 R 68 0 R 68 0 R 68 0 R 68 0 R 68 0 R 68 0 R 68 0 R 66 0 R 67 0 R 67 0 R 67 0 R 67 0 R 67 0 R 67 0 R 67 0 R 67 0 R 67 0 R 67 0 R 67 0 R 67 0 R 67 0 R 67 0 R 67 0 R 67 0 R 67 0 R 67 0 R 67 0 R 67 0 R 67 0 R 67 0 R 64 0 R 63 0 R 63 0 R 63 0 R 63 0 R 63 0 R 63 0 R 63 0 R 61 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 62 0 R 59 0 R 58 0 R 58 0 R 58 0 R 58 0 R 58 0 R 58 0 R 58 0 R 56 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 57 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 53 0 R 51 0 R 52 0 R 52 0 R 52 0 R 52 0 R 52 0 R 52 0 R 52 0 R 52 0 R 52 0 R 52 0 R 52 0 R 52 0 R 52 0 R 52 0 R 52 0 R 52 0 R 52 0 R 52 0 R 52 0 R 52 0 R 52 0 R 52 0 R 52 0 R 52 0 R 52 0 R 52 0 R 52 0 R 52 0 R 52 0 R 52 0 R 52 0 R 52 0 R 52 0 R 50 0 R 46 0 R 49 0 R 49 0 R 49 0 R 49 0 R 49 0 R 49 0 R 49 0 R 46 0 R 48 0 R 48 0 R 48 0 R 48 0 R 48 0 R 48 0 R 48 0 R 48 0 R 48 0 R 48 0 R 48 0 R 48 0 R 48 0 R 48 0 R 46 0 R 47 0 R 47 0 R 47 0 R 47 0 R 46 0 R 45 0 R 44 0 R 44 0 R 44 0 R 44 0 R 44 0 R 44 0 R 44 0 R 42 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 43 0 R 40 0 R 39 0 R 39 0 R 39 0 R 39 0 R 39 0 R 39 0 R 39 0 R 37 0 R 38 0 R 38 0 R 38 0 R 38 0 R 38 0 R 38 0 R 38 0 R 38 0 R 38 0 R 38 0 R 38 0 R 38 0 R 38 0 R 38 0 R 38 0 R 38 0 R 38 0 R 38 0 R 38 0 R 38 0 R 38 0 R 38 0 R 35 0 R 34 0 R 34 0 R 34 0 R 34 0 R 34 0 R 34 0 R 34 0 R 32 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 30 0 R 29 0 R 29 0 R 29 0 R 29 0 R 29 0 R 29 0 R 29 0 R 27 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 24 0 R 22 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 23 0 R 21 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 19 0 R 18 0 R] +[237 0 R 236 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 235 0 R 234 0 R 234 0 R 234 0 R 234 0 R 234 0 R 234 0 R 234 0 R 234 0 R 234 0 R 234 0 R 234 0 R 234 0 R 234 0 R 234 0 R 234 0 R 234 0 R 234 0 R 234 0 R 234 0 R 234 0 R 234 0 R 234 0 R 234 0 R 234 0 R 234 0 R 234 0 R 234 0 R 234 0 R 234 0 R 234 0 R 234 0 R 234 0 R 234 0 R 234 0 R 234 0 R 234 0 R 234 0 R 234 0 R 234 0 R 234 0 R 234 0 R 234 0 R 233 0 R 233 0 R 233 0 R 233 0 R 233 0 R] endobj 16 0 obj -<< - /Type /StructElem - /S /Document - /P 10 0 R - /K [412 0 R 411 0 R 404 0 R 402 0 R 401 0 R 397 0 R 395 0 R 394 0 R 388 0 R 387 0 R 386 0 R 385 0 R 384 0 R 382 0 R 381 0 R 379 0 R 355 0 R 351 0 R 345 0 R 344 0 R 343 0 R 339 0 R 336 0 R 335 0 R 334 0 R 327 0 R 324 0 R 281 0 R 278 0 R 276 0 R 275 0 R 271 0 R 270 0 R 260 0 R 258 0 R 247 0 R 196 0 R 195 0 R 190 0 R 186 0 R 185 0 R 184 0 R 183 0 R 182 0 R 178 0 R 177 0 R 176 0 R 175 0 R 174 0 R 172 0 R 168 0 R 167 0 R 164 0 R 162 0 R 160 0 R 159 0 R 157 0 R 136 0 R 134 0 R 131 0 R 129 0 R 128 0 R 127 0 R 106 0 R 105 0 R 103 0 R 102 0 R 101 0 R 99 0 R 97 0 R 96 0 R 93 0 R 91 0 R 90 0 R 86 0 R 81 0 R 80 0 R 75 0 R 54 0 R 51 0 R 46 0 R 25 0 R 22 0 R 20 0 R 19 0 R 17 0 R] ->> +[232 0 R 230 0 R 230 0 R 230 0 R 227 0 R 227 0 R 227 0 R 224 0 R 224 0 R 224 0 R 221 0 R 221 0 R 221 0 R 218 0 R 218 0 R 218 0 R 215 0 R 215 0 R 215 0 R 215 0 R 212 0 R 212 0 R 212 0 R 212 0 R 208 0 R 208 0 R 208 0 R 205 0 R 205 0 R 205 0 R] endobj 17 0 obj -<< - /Type /StructElem - /S /P - /P 16 0 R - /K [18 0 R] ->> +[201 0 R 194 0 R 194 0 R 194 0 R 194 0 R 194 0 R 194 0 R 194 0 R 194 0 R 194 0 R 194 0 R 194 0 R 194 0 R 194 0 R 194 0 R 199 0 R 199 0 R 199 0 R 199 0 R 199 0 R 199 0 R 199 0 R 199 0 R 199 0 R 199 0 R 199 0 R 199 0 R 199 0 R 199 0 R 199 0 R 199 0 R 199 0 R 199 0 R 199 0 R 194 0 R 194 0 R 194 0 R 194 0 R 194 0 R 194 0 R 194 0 R 194 0 R 198 0 R 198 0 R 198 0 R 194 0 R 194 0 R 194 0 R 197 0 R 197 0 R 197 0 R 194 0 R 194 0 R 194 0 R 196 0 R 196 0 R 196 0 R 194 0 R 194 0 R 194 0 R 194 0 R 195 0 R 195 0 R 195 0 R 195 0 R 195 0 R 195 0 R 195 0 R 195 0 R 195 0 R 195 0 R 195 0 R 195 0 R 195 0 R 195 0 R 194 0 R 193 0 R 191 0 R 190 0 R 189 0 R 187 0 R 186 0 R 186 0 R 184 0 R 183 0 R 183 0 R 181 0 R 180 0 R 180 0 R 180 0 R 180 0 R 180 0 R 177 0 R 175 0 R 174 0 R 174 0 R 174 0 R 174 0 R 172 0 R 171 0 R 169 0 R 167 0 R 167 0 R 168 0 R 168 0 R 168 0 R 168 0 R 168 0 R 168 0 R 168 0 R 168 0 R 168 0 R 168 0 R 168 0 R 168 0 R 168 0 R 168 0 R 167 0 R 167 0 R 165 0 R 164 0 R 161 0 R 159 0 R 157 0 R 157 0 R 157 0 R 156 0 R 156 0 R 155 0 R 155 0 R 155 0 R 155 0 R 155 0 R 155 0 R 155 0 R 155 0 R 155 0 R 155 0 R 155 0 R 155 0 R 155 0 R 155 0 R 155 0 R 155 0 R 155 0 R 155 0 R 155 0 R 155 0 R 153 0 R 153 0 R 152 0 R 152 0 R 152 0 R 152 0 R 152 0 R 151 0 R 151 0 R 151 0 R 151 0 R 151 0 R 151 0 R 151 0 R 151 0 R 151 0 R 151 0 R 151 0 R 151 0 R 151 0 R 151 0 R 151 0 R 151 0 R 151 0 R 151 0 R 151 0 R 151 0 R 151 0 R 151 0 R 151 0 R 151 0 R 150 0 R 150 0 R 150 0 R 150 0 R 150 0 R 150 0 R 150 0 R 150 0 R 150 0 R 150 0 R 150 0 R 150 0 R 150 0 R 150 0 R 150 0 R 150 0 R 150 0 R 150 0 R 150 0 R 150 0 R 150 0 R 150 0 R 150 0 R 149 0 R] endobj 18 0 obj -<< - /Type /StructElem - /S /Strong - /P 17 0 R - /K [794] - /Pg 462 0 R ->> +[147 0 R 147 0 R 146 0 R 146 0 R 146 0 R 146 0 R 146 0 R 145 0 R 145 0 R 145 0 R 145 0 R 145 0 R 145 0 R 145 0 R 145 0 R 145 0 R 145 0 R 145 0 R 145 0 R 145 0 R 145 0 R 145 0 R 145 0 R 145 0 R 145 0 R 145 0 R 145 0 R 145 0 R 145 0 R 145 0 R 145 0 R 144 0 R 144 0 R 144 0 R 144 0 R 144 0 R 144 0 R 144 0 R 144 0 R 144 0 R 144 0 R 144 0 R 144 0 R 144 0 R 144 0 R 144 0 R 144 0 R 144 0 R 144 0 R 144 0 R 144 0 R 144 0 R 144 0 R 144 0 R 143 0 R 141 0 R 141 0 R 140 0 R 140 0 R 140 0 R 140 0 R 140 0 R 139 0 R 139 0 R 139 0 R 139 0 R 139 0 R 139 0 R 139 0 R 139 0 R 139 0 R 139 0 R 139 0 R 139 0 R 139 0 R 139 0 R 139 0 R 139 0 R 139 0 R 139 0 R 139 0 R 139 0 R 139 0 R 139 0 R 139 0 R 139 0 R 139 0 R 139 0 R 138 0 R 138 0 R 138 0 R 138 0 R 138 0 R 138 0 R 138 0 R 138 0 R 138 0 R 138 0 R 138 0 R 138 0 R 138 0 R 138 0 R 138 0 R 138 0 R 138 0 R 138 0 R 138 0 R 138 0 R 138 0 R 138 0 R 138 0 R 138 0 R 138 0 R 138 0 R 137 0 R 137 0 R 137 0 R 137 0 R 137 0 R 137 0 R 137 0 R 137 0 R 137 0 R 137 0 R 137 0 R 137 0 R 137 0 R 137 0 R 137 0 R 137 0 R 137 0 R 137 0 R 137 0 R 137 0 R 137 0 R 137 0 R 137 0 R 137 0 R 137 0 R 137 0 R 136 0 R 136 0 R 136 0 R 136 0 R 136 0 R 136 0 R 136 0 R 136 0 R 136 0 R 136 0 R 136 0 R 136 0 R 136 0 R 136 0 R 136 0 R 136 0 R 136 0 R 136 0 R 136 0 R 136 0 R 136 0 R 136 0 R 136 0 R 136 0 R 136 0 R 135 0 R 133 0 R 133 0 R 133 0 R 131 0 R 130 0 R 130 0 R 130 0 R 130 0 R 130 0 R 130 0 R 130 0 R 130 0 R 130 0 R 130 0 R 130 0 R 130 0 R 130 0 R 130 0 R 130 0 R 130 0 R 129 0 R 129 0 R 129 0 R 129 0 R 129 0 R 129 0 R 128 0 R 128 0 R 128 0 R 128 0 R 128 0 R 128 0 R 127 0 R 126 0 R 126 0 R 126 0 R 126 0 R 126 0 R 126 0 R 126 0 R 126 0 R 126 0 R 126 0 R 126 0 R 126 0 R 125 0 R 125 0 R 125 0 R 125 0 R 125 0 R 125 0 R 125 0 R 125 0 R 125 0 R 125 0 R 125 0 R 125 0 R 124 0 R 123 0 R 123 0 R 123 0 R 123 0 R 122 0 R 122 0 R 122 0 R 122 0 R 122 0 R 122 0 R 121 0 R 121 0 R 121 0 R 121 0 R 121 0 R 121 0 R 121 0 R 121 0 R 121 0 R 121 0 R 121 0 R 121 0 R 121 0 R 121 0 R 121 0 R 121 0 R 120 0 R 120 0 R 120 0 R 120 0 R 120 0 R 120 0 R 120 0 R 120 0 R 120 0 R 120 0 R 120 0 R 120 0 R 119 0 R 119 0 R 119 0 R 119 0 R 119 0 R 119 0 R 118 0 R 118 0 R 117 0 R 116 0 R 116 0 R 116 0 R 116 0 R 116 0 R 115 0 R 115 0 R 115 0 R 115 0 R 115 0 R 115 0 R 114 0 R 114 0 R 114 0 R 114 0 R 114 0 R 114 0 R 114 0 R 114 0 R 114 0 R 114 0 R 114 0 R 114 0 R 113 0 R 113 0 R 113 0 R 113 0 R 113 0 R 113 0 R 112 0 R 111 0 R 111 0 R 111 0 R 111 0 R 111 0 R 111 0 R 111 0 R 111 0 R 111 0 R 111 0 R 111 0 R 111 0 R 111 0 R 111 0 R 111 0 R 110 0 R 110 0 R 110 0 R 110 0 R 110 0 R 110 0 R 110 0 R 110 0 R 108 0 R 108 0 R 108 0 R 106 0 R 106 0 R 105 0 R 105 0 R 105 0 R 105 0 R 105 0 R 105 0 R 105 0 R 105 0 R 105 0 R 105 0 R 105 0 R 105 0 R 105 0 R 105 0 R 105 0 R 105 0 R 104 0 R 104 0 R 104 0 R 104 0 R 104 0 R 104 0 R 104 0 R 104 0 R 104 0 R 104 0 R 104 0 R 104 0 R 104 0 R 104 0 R 104 0 R 104 0 R 104 0 R 104 0 R 104 0 R 104 0 R 104 0 R 103 0 R 102 0 R 102 0 R 102 0 R 102 0 R 102 0 R 102 0 R 102 0 R 102 0 R 102 0 R 102 0 R 102 0 R 102 0 R 101 0 R 101 0 R 101 0 R 101 0 R 101 0 R 101 0 R 101 0 R 101 0 R 100 0 R 100 0 R 100 0 R 100 0 R 100 0 R 100 0 R 100 0 R] endobj 19 0 obj -<< - /Type /StructElem - /S /Formula - /P 16 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793] - /Pg 462 0 R ->> +[99 0 R 98 0 R 98 0 R 98 0 R 98 0 R 98 0 R 98 0 R 98 0 R 98 0 R 98 0 R 97 0 R 97 0 R 97 0 R 97 0 R 96 0 R 96 0 R 96 0 R 96 0 R 95 0 R 95 0 R 95 0 R 95 0 R 95 0 R 94 0 R 94 0 R 94 0 R 93 0 R 92 0 R 92 0 R 92 0 R 92 0 R 91 0 R 91 0 R 91 0 R 91 0 R 91 0 R 91 0 R 91 0 R 91 0 R 91 0 R 91 0 R 91 0 R 91 0 R 90 0 R 89 0 R 89 0 R 89 0 R 89 0 R 89 0 R 89 0 R 89 0 R 89 0 R 89 0 R 89 0 R 89 0 R 89 0 R 89 0 R 88 0 R 88 0 R 88 0 R 88 0 R 88 0 R 88 0 R 88 0 R 88 0 R 88 0 R 88 0 R 88 0 R 88 0 R 88 0 R 88 0 R 88 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 87 0 R 85 0 R 82 0 R 82 0 R 83 0 R 83 0 R 83 0 R 83 0 R 83 0 R 83 0 R 83 0 R 83 0 R 83 0 R 83 0 R 83 0 R 83 0 R 83 0 R 83 0 R 83 0 R 83 0 R 83 0 R 83 0 R 83 0 R 83 0 R 83 0 R 83 0 R 83 0 R 80 0 R 80 0 R 81 0 R 80 0 R 80 0 R 79 0 R 79 0 R 79 0 R 77 0 R 75 0 R 72 0 R 71 0 R 70 0 R 68 0 R 67 0 R 66 0 R 64 0 R 63 0 R 62 0 R 60 0 R 59 0 R 58 0 R 56 0 R 55 0 R 54 0 R 51 0 R 49 0 R 48 0 R 45 0 R 45 0 R 47 0 R 45 0 R 45 0 R 45 0 R 45 0 R 46 0 R 46 0 R 46 0 R 46 0 R 46 0 R 46 0 R 46 0 R 46 0 R 45 0 R 42 0 R 41 0 R 40 0 R 37 0 R 36 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 35 0 R 33 0 R 32 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R] endobj 20 0 obj -<< - /Type /StructElem - /S /P - /P 16 0 R - /K [21 0 R] ->> +[28 0 R 27 0 R 25 0 R 25 0 R 25 0 R 26 0 R 26 0 R 26 0 R 26 0 R 26 0 R 26 0 R 26 0 R 25 0 R 25 0 R] endobj 21 0 obj << /Type /StructElem - /S /Strong - /P 20 0 R - /K [740] - /Pg 462 0 R + /S /Document + /P 13 0 R + /K [265 0 R 258 0 R 239 0 R 238 0 R 237 0 R 236 0 R 235 0 R 234 0 R 233 0 R 231 0 R 202 0 R 200 0 R 194 0 R 192 0 R 191 0 R 178 0 R 176 0 R 162 0 R 160 0 R 158 0 R 157 0 R 134 0 R 132 0 R 131 0 R 109 0 R 107 0 R 106 0 R 86 0 R 84 0 R 82 0 R 80 0 R 52 0 R 50 0 R 22 0 R] >> endobj 22 0 obj << /Type /StructElem - /S /P - /P 16 0 R - /K [24 0 R 706 23 0 R] - /Pg 462 0 R + /S /L + /P 21 0 R + /A [<< + /O /List + /ListNumbering /Decimal + >>] + /K [43 0 R 38 0 R 29 0 R 23 0 R] >> endobj 23 0 obj << /Type /StructElem - /S /Formula + /S /LI /P 22 0 R - /K [707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739] - /Pg 462 0 R + /K [28 0 R 24 0 R] >> endobj 24 0 obj << /Type /StructElem - /S /Formula - /P 22 0 R - /K [667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705] - /Pg 462 0 R + /S /LBody + /P 23 0 R + /K [25 0 R] >> endobj 25 0 obj << /Type /StructElem - /S /L - /P 16 0 R - /A [<< - /O /List - /ListNumbering /Circle - >>] - /K [41 0 R 36 0 R 31 0 R 26 0 R] + /S /P + /P 24 0 R + /K [27 0 R 2 3 4 26 0 R 12 13] + /Pg 379 0 R >> endobj 26 0 obj << /Type /StructElem - /S /LI + /S /Formula /P 25 0 R - /K [30 0 R 27 0 R] + /K [5 6 7 8 9 10 11] + /Pg 379 0 R >> endobj 27 0 obj << /Type /StructElem - /S /LBody - /P 26 0 R - /K [29 0 R 644 28 0 R] - /Pg 462 0 R + /S /Strong + /P 25 0 R + /K [1] + /Pg 379 0 R >> endobj 28 0 obj << /Type /StructElem - /S /Formula - /P 27 0 R - /K [645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666] - /Pg 462 0 R + /S /Lbl + /P 23 0 R + /K [0] + /Pg 379 0 R >> endobj 29 0 obj << /Type /StructElem - /S /Formula - /P 27 0 R - /K [637 638 639 640 641 642 643] - /Pg 462 0 R + /S /L + /P 22 0 R + /A [<< + /O /List + /ListNumbering /Circle + >>] + /K [34 0 R 30 0 R] >> endobj 30 0 obj << /Type /StructElem - /S /Lbl - /P 26 0 R - /K [636] - /Pg 462 0 R + /S /LI + /P 29 0 R + /K [33 0 R 31 0 R] >> endobj 31 0 obj << /Type /StructElem - /S /LI - /P 25 0 R - /K [35 0 R 32 0 R] + /S /LBody + /P 30 0 R + /K [32 0 R 168 169 170 171 172] + /Pg 377 0 R >> endobj 32 0 obj << /Type /StructElem - /S /LBody + /S /Strong /P 31 0 R - /K [34 0 R 572 33 0 R] - /Pg 462 0 R + /K [167] + /Pg 377 0 R >> endobj 33 0 obj << /Type /StructElem - /S /Formula - /P 32 0 R - /K [573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635] - /Pg 462 0 R + /S /Lbl + /P 30 0 R + /K [166] + /Pg 377 0 R >> endobj 34 0 obj << /Type /StructElem - /S /Formula - /P 32 0 R - /K [565 566 567 568 569 570 571] - /Pg 462 0 R + /S /LI + /P 29 0 R + /K [37 0 R 35 0 R] >> endobj 35 0 obj << /Type /StructElem - /S /Lbl - /P 31 0 R - /K [564] - /Pg 462 0 R + /S /LBody + /P 34 0 R + /K [36 0 R 158 159 160 161 162 163 164 165] + /Pg 377 0 R >> endobj 36 0 obj << /Type /StructElem - /S /LI - /P 25 0 R - /K [40 0 R 37 0 R] + /S /Strong + /P 35 0 R + /K [157] + /Pg 377 0 R >> endobj 37 0 obj << /Type /StructElem - /S /LBody - /P 36 0 R - /K [39 0 R 541 38 0 R] - /Pg 462 0 R + /S /Lbl + /P 34 0 R + /K [156] + /Pg 377 0 R >> endobj 38 0 obj << /Type /StructElem - /S /Formula - /P 37 0 R - /K [542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563] - /Pg 462 0 R + /S /LI + /P 22 0 R + /K [42 0 R 39 0 R] >> endobj 39 0 obj << /Type /StructElem - /S /Formula - /P 37 0 R - /K [534 535 536 537 538 539 540] - /Pg 462 0 R + /S /LBody + /P 38 0 R + /K [40 0 R] >> endobj 40 0 obj << /Type /StructElem - /S /Lbl - /P 36 0 R - /K [533] - /Pg 462 0 R + /S /P + /P 39 0 R + /K [41 0 R 155] + /Pg 377 0 R >> endobj 41 0 obj << /Type /StructElem - /S /LI - /P 25 0 R - /K [45 0 R 42 0 R] + /S /Strong + /P 40 0 R + /K [154] + /Pg 377 0 R >> endobj 42 0 obj << /Type /StructElem - /S /LBody - /P 41 0 R - /K [44 0 R 469 43 0 R] - /Pg 462 0 R + /S /Lbl + /P 38 0 R + /K [153] + /Pg 377 0 R >> endobj 43 0 obj << /Type /StructElem - /S /Formula - /P 42 0 R - /K [470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532] - /Pg 462 0 R + /S /LI + /P 22 0 R + /K [49 0 R 44 0 R] >> endobj 44 0 obj << /Type /StructElem - /S /Formula - /P 42 0 R - /K [462 463 464 465 466 467 468] - /Pg 462 0 R + /S /LBody + /P 43 0 R + /K [45 0 R] >> endobj 45 0 obj << /Type /StructElem - /S /Lbl - /P 41 0 R - /K [461] - /Pg 462 0 R + /S /P + /P 44 0 R + /K [48 0 R 137 138 47 0 R 140 141 142 143 46 0 R 152] + /Pg 377 0 R >> endobj 46 0 obj << /Type /StructElem - /S /P - /P 16 0 R - /K [50 0 R 432 49 0 R 440 48 0 R 455 47 0 R 460] - /Pg 462 0 R + /S /Formula + /P 45 0 R + /K [144 145 146 147 148 149 150 151] + /Pg 377 0 R >> endobj @@ -438,39 +420,39 @@ endobj << /Type /StructElem /S /Formula - /P 46 0 R - /K [456 457 458 459] - /Pg 462 0 R + /P 45 0 R + /K [139] + /Pg 377 0 R >> endobj 48 0 obj << /Type /StructElem - /S /Formula - /P 46 0 R - /K [441 442 443 444 445 446 447 448 449 450 451 452 453 454] - /Pg 462 0 R + /S /Strong + /P 45 0 R + /K [136] + /Pg 377 0 R >> endobj 49 0 obj << /Type /StructElem - /S /Formula - /P 46 0 R - /K [433 434 435 436 437 438 439] - /Pg 462 0 R + /S /Lbl + /P 43 0 R + /K [135] + /Pg 377 0 R >> endobj 50 0 obj << /Type /StructElem - /S /Strong - /P 46 0 R - /K [431] - /Pg 462 0 R + /S /H1 + /P 21 0 R + /T + /K [51 0 R] >> endobj @@ -478,278 +460,400 @@ endobj << /Type /StructElem /S /P - /P 16 0 R - /K [53 0 R 397 52 0 R] - /Pg 462 0 R + /P 50 0 R + /K [134] + /Pg 377 0 R >> endobj 52 0 obj << /Type /StructElem - /S /Formula - /P 51 0 R - /K [398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430] - /Pg 462 0 R + /S /Table + /P 21 0 R + /A [<< + /O /Layout + /BorderColor [0 0 0] + /BorderThickness 1 + >>] + /K [73 0 R 69 0 R 65 0 R 61 0 R 57 0 R 53 0 R] >> endobj 53 0 obj << /Type /StructElem - /S /Formula - /P 51 0 R - /K [358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396] - /Pg 462 0 R + /S /TR + /P 52 0 R + /K [56 0 R 55 0 R 54 0 R] >> endobj 54 0 obj << /Type /StructElem - /S /L - /P 16 0 R + /S /TD + /P 53 0 R /A [<< - /O /List - /ListNumbering /Circle + /O /Table + /Headers [] + >> << + /O /Layout + /BorderStyle /Solid >>] - /K [70 0 R 65 0 R 60 0 R 55 0 R] + /K [133] + /Pg 377 0 R >> endobj 55 0 obj << /Type /StructElem - /S /LI - /P 54 0 R - /K [59 0 R 56 0 R] + /S /TD + /P 53 0 R + /A [<< + /O /Table + /Headers [] + >> << + /O /Layout + /BorderStyle /Solid + >>] + /K [132] + /Pg 377 0 R >> endobj 56 0 obj << /Type /StructElem - /S /LBody - /P 55 0 R - /K [58 0 R 335 57 0 R] - /Pg 462 0 R + /S /TD + /P 53 0 R + /A [<< + /O /Table + /Headers [] + >> << + /O /Layout + /BorderStyle /Solid + >>] + /K [131] + /Pg 377 0 R >> endobj 57 0 obj << /Type /StructElem - /S /Formula - /P 56 0 R - /K [336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357] - /Pg 462 0 R + /S /TR + /P 52 0 R + /K [60 0 R 59 0 R 58 0 R] >> endobj 58 0 obj << /Type /StructElem - /S /Formula - /P 56 0 R - /K [328 329 330 331 332 333 334] - /Pg 462 0 R + /S /TD + /P 57 0 R + /A [<< + /O /Table + /Headers [] + >> << + /O /Layout + /BorderStyle /Solid + >>] + /K [130] + /Pg 377 0 R >> endobj 59 0 obj << /Type /StructElem - /S /Lbl - /P 55 0 R - /K [327] - /Pg 462 0 R + /S /TD + /P 57 0 R + /A [<< + /O /Table + /Headers [] + >> << + /O /Layout + /BorderStyle /Solid + >>] + /K [129] + /Pg 377 0 R >> endobj 60 0 obj << /Type /StructElem - /S /LI - /P 54 0 R - /K [64 0 R 61 0 R] + /S /TD + /P 57 0 R + /A [<< + /O /Table + /Headers [] + >> << + /O /Layout + /BorderStyle /Solid + >>] + /K [128] + /Pg 377 0 R >> endobj 61 0 obj << /Type /StructElem - /S /LBody - /P 60 0 R - /K [63 0 R 263 62 0 R] - /Pg 462 0 R + /S /TR + /P 52 0 R + /K [64 0 R 63 0 R 62 0 R] >> endobj 62 0 obj << /Type /StructElem - /S /Formula + /S /TD /P 61 0 R - /K [264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326] - /Pg 462 0 R + /A [<< + /O /Table + /Headers [] + >> << + /O /Layout + /BorderStyle /Solid + >>] + /K [127] + /Pg 377 0 R >> endobj 63 0 obj << /Type /StructElem - /S /Formula + /S /TD /P 61 0 R - /K [256 257 258 259 260 261 262] - /Pg 462 0 R + /A [<< + /O /Table + /Headers [] + >> << + /O /Layout + /BorderStyle /Solid + >>] + /K [126] + /Pg 377 0 R >> endobj 64 0 obj << /Type /StructElem - /S /Lbl - /P 60 0 R - /K [255] - /Pg 462 0 R + /S /TD + /P 61 0 R + /A [<< + /O /Table + /Headers [] + >> << + /O /Layout + /BorderStyle /Solid + >>] + /K [125] + /Pg 377 0 R >> endobj 65 0 obj << /Type /StructElem - /S /LI - /P 54 0 R - /K [69 0 R 66 0 R] + /S /TR + /P 52 0 R + /K [68 0 R 67 0 R 66 0 R] >> endobj 66 0 obj << /Type /StructElem - /S /LBody + /S /TD /P 65 0 R - /K [68 0 R 232 67 0 R] - /Pg 462 0 R + /A [<< + /O /Table + /Headers [] + >> << + /O /Layout + /BorderStyle /Solid + >>] + /K [124] + /Pg 377 0 R >> endobj 67 0 obj << /Type /StructElem - /S /Formula - /P 66 0 R - /K [233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254] - /Pg 462 0 R + /S /TD + /P 65 0 R + /A [<< + /O /Table + /Headers [] + >> << + /O /Layout + /BorderStyle /Solid + >>] + /K [123] + /Pg 377 0 R >> endobj 68 0 obj << /Type /StructElem - /S /Formula - /P 66 0 R - /K [225 226 227 228 229 230 231] - /Pg 462 0 R + /S /TD + /P 65 0 R + /A [<< + /O /Table + /Headers [] + >> << + /O /Layout + /BorderStyle /Solid + >>] + /K [122] + /Pg 377 0 R >> endobj 69 0 obj << /Type /StructElem - /S /Lbl - /P 65 0 R - /K [224] - /Pg 462 0 R + /S /TR + /P 52 0 R + /K [72 0 R 71 0 R 70 0 R] >> endobj 70 0 obj << /Type /StructElem - /S /LI - /P 54 0 R - /K [74 0 R 71 0 R] + /S /TD + /P 69 0 R + /A [<< + /O /Table + /Headers [] + >> << + /O /Layout + /BorderStyle /Solid + >>] + /K [121] + /Pg 377 0 R >> endobj 71 0 obj << /Type /StructElem - /S /LBody - /P 70 0 R - /K [73 0 R 160 72 0 R] - /Pg 462 0 R + /S /TD + /P 69 0 R + /A [<< + /O /Table + /Headers [] + >> << + /O /Layout + /BorderStyle /Solid + >>] + /K [120] + /Pg 377 0 R >> endobj 72 0 obj << /Type /StructElem - /S /Formula - /P 71 0 R - /K [161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223] - /Pg 462 0 R + /S /TD + /P 69 0 R + /A [<< + /O /Table + /Headers [] + >> << + /O /Layout + /BorderStyle /Solid + >>] + /K [119] + /Pg 377 0 R >> endobj 73 0 obj << /Type /StructElem - /S /Formula - /P 71 0 R - /K [153 154 155 156 157 158 159] - /Pg 462 0 R + /S /TR + /P 52 0 R + /K [78 0 R 76 0 R 74 0 R] >> endobj 74 0 obj << /Type /StructElem - /S /Lbl - /P 70 0 R - /K [152] - /Pg 462 0 R + /S /TD + /P 73 0 R + /A [<< + /O /Table + /Headers [] + >> << + /O /Layout + /BorderStyle /Solid + >>] + /K [75 0 R] >> endobj 75 0 obj << /Type /StructElem - /S /P - /P 16 0 R - /K [79 0 R 123 78 0 R 131 77 0 R 146 76 0 R 151] - /Pg 462 0 R + /S /Strong + /P 74 0 R + /K [118] + /Pg 377 0 R >> endobj 76 0 obj << /Type /StructElem - /S /Formula - /P 75 0 R - /K [147 148 149 150] - /Pg 462 0 R + /S /TD + /P 73 0 R + /A [<< + /O /Table + /Headers [] + >> << + /O /Layout + /BorderStyle /Solid + >>] + /K [77 0 R] >> endobj 77 0 obj << /Type /StructElem - /S /Formula - /P 75 0 R - /K [132 133 134 135 136 137 138 139 140 141 142 143 144 145] - /Pg 462 0 R + /S /Strong + /P 76 0 R + /K [117] + /Pg 377 0 R >> endobj 78 0 obj << /Type /StructElem - /S /Formula - /P 75 0 R - /K [124 125 126 127 128 129 130] - /Pg 462 0 R + /S /TD + /P 73 0 R + /A [<< + /O /Table + /Headers [] + >> << + /O /Layout + /BorderStyle /Solid + >>] + /K [79 0 R] >> endobj @@ -757,43 +861,39 @@ endobj << /Type /StructElem /S /Strong - /P 75 0 R - /K [122] - /Pg 462 0 R + /P 78 0 R + /K [114 115 116] + /Pg 377 0 R >> endobj 80 0 obj << /Type /StructElem - /S /Formula - /P 16 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121] - /Pg 462 0 R + /S /P + /P 21 0 R + /K [109 110 81 0 R 112 113] + /Pg 377 0 R >> endobj 81 0 obj << /Type /StructElem - /S /P - /P 16 0 R - /K [0 85 0 R 2 84 0 R 17 83 0 R 32 33 82 0 R 77 78] - /Pg 462 0 R + /S /Formula + /P 80 0 R + /K [111] + /Pg 377 0 R >> endobj 82 0 obj << /Type /StructElem - /S /Formula - /P 81 0 R - /K [34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76] - /Pg 462 0 R + /S /P + /P 21 0 R + /K [84 85 83 0 R] + /Pg 377 0 R >> endobj @@ -801,81 +901,82 @@ endobj << /Type /StructElem /S /Formula - /P 81 0 R - /K [18 19 20 21 22 23 24 25 26 27 28 29 30 31] - /Pg 462 0 R + /P 82 0 R + /K [86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108] + /Pg 377 0 R >> endobj 84 0 obj << /Type /StructElem - /S /Formula - /P 81 0 R - /K [3 4 5 6 7 8 9 10 11 12 13 14 15 16] - /Pg 462 0 R + /S /H1 + /P 21 0 R + /T + /K [85 0 R] >> endobj 85 0 obj << /Type /StructElem - /S /Formula - /P 81 0 R - /K [1] - /Pg 462 0 R + /S /P + /P 84 0 R + /K [83] + /Pg 377 0 R >> endobj 86 0 obj << /Type /StructElem - /S /P - /P 16 0 R - /K [89 0 R 87 0 R] + /S /Code + /P 21 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [105 0 R 104 0 R 103 0 R 102 0 R 101 0 R 100 0 R 99 0 R 98 0 R 97 0 R 96 0 R 95 0 R 94 0 R 93 0 R 92 0 R 91 0 R 90 0 R 89 0 R 88 0 R 87 0 R] >> endobj 87 0 obj << /Type /StructElem - /S /Formula + /S /P /P 86 0 R - /K [88 0 R] + /K [72 73 74 75 76 77 78 79 80 81 82] + /Pg 377 0 R >> endobj 88 0 obj << /Type /StructElem - /S /Strong - /P 87 0 R - /K [391 392 393 394 395 396 397 398 399 400 401 402 403 404] - /Pg 460 0 R + /S /P + /P 86 0 R + /K [57 58 59 60 61 62 63 64 65 66 67 68 69 70 71] + /Pg 377 0 R >> endobj 89 0 obj << /Type /StructElem - /S /Strong + /S /P /P 86 0 R - /K [390] - /Pg 460 0 R + /K [44 45 46 47 48 49 50 51 52 53 54 55 56] + /Pg 377 0 R >> endobj 90 0 obj << /Type /StructElem - /S /Span - /P 16 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [385 386 387 388 389] - /Pg 460 0 R + /S /P + /P 86 0 R + /K [43] + /Pg 377 0 R >> endobj @@ -883,18 +984,19 @@ endobj << /Type /StructElem /S /P - /P 16 0 R - /K [92 0 R] + /P 86 0 R + /K [31 32 33 34 35 36 37 38 39 40 41 42] + /Pg 377 0 R >> endobj 92 0 obj << /Type /StructElem - /S /Strong - /P 91 0 R - /K [384] - /Pg 460 0 R + /S /P + /P 86 0 R + /K [27 28 29 30] + /Pg 377 0 R >> endobj @@ -902,40 +1004,39 @@ endobj << /Type /StructElem /S /P - /P 16 0 R - /K [95 0 R 353 354 355 356 357 358 359 360 361 362 363 94 0 R 383] - /Pg 460 0 R + /P 86 0 R + /K [26] + /Pg 377 0 R >> endobj 94 0 obj << /Type /StructElem - /S /Formula - /P 93 0 R - /K [364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382] - /Pg 460 0 R + /S /P + /P 86 0 R + /K [23 24 25] + /Pg 377 0 R >> endobj 95 0 obj << /Type /StructElem - /S /Strong - /P 93 0 R - /K [352] - /Pg 460 0 R + /S /P + /P 86 0 R + /K [18 19 20 21 22] + /Pg 377 0 R >> endobj 96 0 obj << /Type /StructElem - /S /H1 - /P 16 0 R - /T - /K [350 351] - /Pg 460 0 R + /S /P + /P 86 0 R + /K [14 15 16 17] + /Pg 377 0 R >> endobj @@ -943,18 +1044,19 @@ endobj << /Type /StructElem /S /P - /P 16 0 R - /K [98 0 R] + /P 86 0 R + /K [10 11 12 13] + /Pg 377 0 R >> endobj 98 0 obj << /Type /StructElem - /S /Strong - /P 97 0 R - /K [349] - /Pg 460 0 R + /S /P + /P 86 0 R + /K [1 2 3 4 5 6 7 8 9] + /Pg 377 0 R >> endobj @@ -962,47 +1064,39 @@ endobj << /Type /StructElem /S /P - /P 16 0 R - /K [314 100 0 R 348] - /Pg 460 0 R + /P 86 0 R + /K [0] + /Pg 377 0 R >> endobj 100 0 obj << /Type /StructElem - /S /Formula - /P 99 0 R - /K [315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347] - /Pg 460 0 R + /S /P + /P 86 0 R + /K [387 388 389 390 391 392 393] + /Pg 375 0 R >> endobj 101 0 obj << /Type /StructElem - /S /Formula - /P 16 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313] - /Pg 460 0 R + /S /P + /P 86 0 R + /K [379 380 381 382 383 384 385 386] + /Pg 375 0 R >> endobj 102 0 obj << /Type /StructElem - /S /Formula - /P 16 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286] - /Pg 460 0 R + /S /P + /P 86 0 R + /K [367 368 369 370 371 372 373 374 375 376 377 378] + /Pg 375 0 R >> endobj @@ -1010,242 +1104,242 @@ endobj << /Type /StructElem /S /P - /P 16 0 R - /K [245 104 0 R 256 257 258] - /Pg 460 0 R + /P 86 0 R + /K [366] + /Pg 375 0 R >> endobj 104 0 obj << /Type /StructElem - /S /Formula - /P 103 0 R - /K [246 247 248 249 250 251 252 253 254 255] - /Pg 460 0 R + /S /P + /P 86 0 R + /K [345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365] + /Pg 375 0 R >> endobj 105 0 obj << /Type /StructElem - /S /Formula - /P 16 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244] - /Pg 460 0 R + /S /P + /P 86 0 R + /K [329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344] + /Pg 375 0 R >> endobj 106 0 obj << /Type /StructElem - /S /L - /P 16 0 R - /A [<< - /O /List - /ListNumbering /Decimal - >>] - /K [122 0 R 117 0 R 112 0 R 107 0 R] + /S /P + /P 21 0 R + /K [327 328] + /Pg 375 0 R >> endobj 107 0 obj << /Type /StructElem - /S /LI - /P 106 0 R - /K [111 0 R 108 0 R] + /S /H2 + /P 21 0 R + /T + /K [108 0 R] >> endobj 108 0 obj << /Type /StructElem - /S /LBody + /S /P /P 107 0 R - /K [110 0 R 191 109 0 R] - /Pg 460 0 R + /K [324 325 326] + /Pg 375 0 R >> endobj 109 0 obj << /Type /StructElem - /S /Formula - /P 108 0 R - /K [192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208] - /Pg 460 0 R + /S /Code + /P 21 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [130 0 R 129 0 R 128 0 R 127 0 R 126 0 R 125 0 R 124 0 R 123 0 R 122 0 R 121 0 R 120 0 R 119 0 R 118 0 R 117 0 R 116 0 R 115 0 R 114 0 R 113 0 R 112 0 R 111 0 R 110 0 R] >> endobj 110 0 obj << /Type /StructElem - /S /Formula - /P 108 0 R - /K [184 185 186 187 188 189 190] - /Pg 460 0 R + /S /P + /P 109 0 R + /K [316 317 318 319 320 321 322 323] + /Pg 375 0 R >> endobj 111 0 obj << /Type /StructElem - /S /Lbl - /P 107 0 R - /K [183] - /Pg 460 0 R + /S /P + /P 109 0 R + /K [301 302 303 304 305 306 307 308 309 310 311 312 313 314 315] + /Pg 375 0 R >> endobj 112 0 obj << /Type /StructElem - /S /LI - /P 106 0 R - /K [116 0 R 113 0 R] + /S /P + /P 109 0 R + /K [300] + /Pg 375 0 R >> endobj 113 0 obj << /Type /StructElem - /S /LBody - /P 112 0 R - /K [115 0 R 165 114 0 R] - /Pg 460 0 R + /S /P + /P 109 0 R + /K [294 295 296 297 298 299] + /Pg 375 0 R >> endobj 114 0 obj << /Type /StructElem - /S /Formula - /P 113 0 R - /K [166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182] - /Pg 460 0 R + /S /P + /P 109 0 R + /K [282 283 284 285 286 287 288 289 290 291 292 293] + /Pg 375 0 R >> endobj 115 0 obj << /Type /StructElem - /S /Formula - /P 113 0 R - /K [158 159 160 161 162 163 164] - /Pg 460 0 R + /S /P + /P 109 0 R + /K [276 277 278 279 280 281] + /Pg 375 0 R >> endobj 116 0 obj << /Type /StructElem - /S /Lbl - /P 112 0 R - /K [157] - /Pg 460 0 R + /S /P + /P 109 0 R + /K [271 272 273 274 275] + /Pg 375 0 R >> endobj 117 0 obj << /Type /StructElem - /S /LI - /P 106 0 R - /K [121 0 R 118 0 R] + /S /P + /P 109 0 R + /K [270] + /Pg 375 0 R >> endobj 118 0 obj << /Type /StructElem - /S /LBody - /P 117 0 R - /K [120 0 R 139 119 0 R] - /Pg 460 0 R + /S /P + /P 109 0 R + /K [268 269] + /Pg 375 0 R >> endobj 119 0 obj << /Type /StructElem - /S /Formula - /P 118 0 R - /K [140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156] - /Pg 460 0 R + /S /P + /P 109 0 R + /K [262 263 264 265 266 267] + /Pg 375 0 R >> endobj 120 0 obj << /Type /StructElem - /S /Formula - /P 118 0 R - /K [132 133 134 135 136 137 138] - /Pg 460 0 R + /S /P + /P 109 0 R + /K [250 251 252 253 254 255 256 257 258 259 260 261] + /Pg 375 0 R >> endobj 121 0 obj << /Type /StructElem - /S /Lbl - /P 117 0 R - /K [131] - /Pg 460 0 R + /S /P + /P 109 0 R + /K [234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249] + /Pg 375 0 R >> endobj 122 0 obj << /Type /StructElem - /S /LI - /P 106 0 R - /K [126 0 R 123 0 R] + /S /P + /P 109 0 R + /K [228 229 230 231 232 233] + /Pg 375 0 R >> endobj 123 0 obj << /Type /StructElem - /S /LBody - /P 122 0 R - /K [125 0 R 113 124 0 R] - /Pg 460 0 R + /S /P + /P 109 0 R + /K [224 225 226 227] + /Pg 375 0 R >> endobj 124 0 obj << /Type /StructElem - /S /Formula - /P 123 0 R - /K [114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130] - /Pg 460 0 R + /S /P + /P 109 0 R + /K [223] + /Pg 375 0 R >> endobj 125 0 obj << /Type /StructElem - /S /Formula - /P 123 0 R - /K [106 107 108 109 110 111 112] - /Pg 460 0 R + /S /P + /P 109 0 R + /K [211 212 213 214 215 216 217 218 219 220 221 222] + /Pg 375 0 R >> endobj 126 0 obj << /Type /StructElem - /S /Lbl - /P 122 0 R - /K [105] - /Pg 460 0 R + /S /P + /P 109 0 R + /K [199 200 201 202 203 204 205 206 207 208 209 210] + /Pg 375 0 R >> endobj @@ -1253,23 +1347,19 @@ endobj << /Type /StructElem /S /P - /P 16 0 R - /K [100 101 102 103 104] - /Pg 460 0 R + /P 109 0 R + /K [198] + /Pg 375 0 R >> endobj 128 0 obj << /Type /StructElem - /S /Formula - /P 16 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99] - /Pg 460 0 R + /S /P + /P 109 0 R + /K [192 193 194 195 196 197] + /Pg 375 0 R >> endobj @@ -1277,19 +1367,19 @@ endobj << /Type /StructElem /S /P - /P 16 0 R - /K [63 130 0 R 70] - /Pg 460 0 R + /P 109 0 R + /K [186 187 188 189 190 191] + /Pg 375 0 R >> endobj 130 0 obj << /Type /StructElem - /S /Formula - /P 129 0 R - /K [64 65 66 67 68 69] - /Pg 460 0 R + /S /P + /P 109 0 R + /K [170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185] + /Pg 375 0 R >> endobj @@ -1297,362 +1387,259 @@ endobj << /Type /StructElem /S /P - /P 16 0 R - /K [31 133 0 R 40 132 0 R 62] - /Pg 460 0 R + /P 21 0 R + /K [169] + /Pg 375 0 R >> endobj 132 0 obj << /Type /StructElem - /S /Formula - /P 131 0 R - /K [41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61] - /Pg 460 0 R + /S /H2 + /P 21 0 R + /T + /K [133 0 R] >> endobj 133 0 obj << /Type /StructElem - /S /Formula - /P 131 0 R - /K [32 33 34 35 36 37 38 39] - /Pg 460 0 R + /S /P + /P 132 0 R + /K [166 167 168] + /Pg 375 0 R >> endobj 134 0 obj << /Type /StructElem - /S /P - /P 16 0 R - /K [135 0 R] + /S /Code + /P 21 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [156 0 R 155 0 R 154 0 R 153 0 R 152 0 R 151 0 R 150 0 R 149 0 R 148 0 R 147 0 R 146 0 R 145 0 R 144 0 R 143 0 R 142 0 R 141 0 R 140 0 R 139 0 R 138 0 R 137 0 R 136 0 R 135 0 R] >> endobj 135 0 obj << /Type /StructElem - /S /Strong + /S /P /P 134 0 R - /K [27 28 29 30] - /Pg 460 0 R + /K [165] + /Pg 375 0 R >> endobj 136 0 obj << /Type /StructElem - /S /Table - /P 16 0 R - /A [<< - /O /Layout - /BorderColor [0 0 0] - /BorderThickness 1 - >>] - /K [153 0 R 149 0 R 145 0 R 141 0 R 137 0 R] + /S /P + /P 134 0 R + /K [140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164] + /Pg 375 0 R >> endobj 137 0 obj << /Type /StructElem - /S /TR - /P 136 0 R - /K [140 0 R 139 0 R 138 0 R] + /S /P + /P 134 0 R + /K [114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139] + /Pg 375 0 R >> endobj 138 0 obj << /Type /StructElem - /S /TD - /P 137 0 R - /A [<< - /O /Table - /Headers [] - >> << - /O /Layout - /BorderStyle /Solid - >>] - /K [26] - /Pg 460 0 R + /S /P + /P 134 0 R + /K [88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113] + /Pg 375 0 R >> endobj 139 0 obj << /Type /StructElem - /S /TD - /P 137 0 R - /A [<< - /O /Table - /Headers [] - >> << - /O /Layout - /BorderStyle /Solid - >>] - /K [24 25] - /Pg 460 0 R + /S /P + /P 134 0 R + /K [62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87] + /Pg 375 0 R >> endobj 140 0 obj << /Type /StructElem - /S /TD - /P 137 0 R - /A [<< - /O /Table - /Headers [] - >> << - /O /Layout - /BorderStyle /Solid - >>] - /K [22 23] - /Pg 460 0 R + /S /P + /P 134 0 R + /K [57 58 59 60 61] + /Pg 375 0 R >> endobj 141 0 obj << /Type /StructElem - /S /TR - /P 136 0 R - /K [144 0 R 143 0 R 142 0 R] + /S /P + /P 134 0 R + /K [55 56] + /Pg 375 0 R >> endobj 142 0 obj << /Type /StructElem - /S /TD - /P 141 0 R - /A [<< - /O /Table - /Headers [] - >> << - /O /Layout - /BorderStyle /Solid - >>] - /K [21] - /Pg 460 0 R + /S /P + /P 134 0 R + /K [] >> endobj 143 0 obj << /Type /StructElem - /S /TD - /P 141 0 R - /A [<< - /O /Table - /Headers [] - >> << - /O /Layout - /BorderStyle /Solid - >>] - /K [19 20] - /Pg 460 0 R + /S /P + /P 134 0 R + /K [54] + /Pg 375 0 R >> endobj 144 0 obj << /Type /StructElem - /S /TD - /P 141 0 R - /A [<< - /O /Table - /Headers [] - >> << - /O /Layout - /BorderStyle /Solid - >>] - /K [17 18] - /Pg 460 0 R + /S /P + /P 134 0 R + /K [31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53] + /Pg 375 0 R >> endobj 145 0 obj << /Type /StructElem - /S /TR - /P 136 0 R - /K [148 0 R 147 0 R 146 0 R] + /S /P + /P 134 0 R + /K [7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30] + /Pg 375 0 R >> endobj 146 0 obj << /Type /StructElem - /S /TD - /P 145 0 R - /A [<< - /O /Table - /Headers [] - >> << - /O /Layout - /BorderStyle /Solid - >>] - /K [16] - /Pg 460 0 R + /S /P + /P 134 0 R + /K [2 3 4 5 6] + /Pg 375 0 R >> endobj 147 0 obj << /Type /StructElem - /S /TD - /P 145 0 R - /A [<< - /O /Table - /Headers [] - >> << - /O /Layout - /BorderStyle /Solid - >>] - /K [14 15] - /Pg 460 0 R + /S /P + /P 134 0 R + /K [0 1] + /Pg 375 0 R >> endobj 148 0 obj << /Type /StructElem - /S /TD - /P 145 0 R - /A [<< - /O /Table - /Headers [] - >> << - /O /Layout - /BorderStyle /Solid - >>] - /K [12 13] - /Pg 460 0 R + /S /P + /P 134 0 R + /K [] >> endobj 149 0 obj << /Type /StructElem - /S /TR - /P 136 0 R - /K [152 0 R 151 0 R 150 0 R] + /S /P + /P 134 0 R + /K [202] + /Pg 373 0 R >> endobj 150 0 obj << /Type /StructElem - /S /TD - /P 149 0 R - /A [<< - /O /Table - /Headers [] - >> << - /O /Layout - /BorderStyle /Solid - >>] - /K [11] - /Pg 460 0 R + /S /P + /P 134 0 R + /K [179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201] + /Pg 373 0 R >> endobj 151 0 obj << /Type /StructElem - /S /TD - /P 149 0 R - /A [<< - /O /Table - /Headers [] - >> << - /O /Layout - /BorderStyle /Solid - >>] - /K [9 10] - /Pg 460 0 R + /S /P + /P 134 0 R + /K [155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178] + /Pg 373 0 R >> endobj 152 0 obj << /Type /StructElem - /S /TD - /P 149 0 R - /A [<< - /O /Table - /Headers [] - >> << - /O /Layout - /BorderStyle /Solid - >>] - /K [7 8] - /Pg 460 0 R + /S /P + /P 134 0 R + /K [150 151 152 153 154] + /Pg 373 0 R >> endobj 153 0 obj << /Type /StructElem - /S /TR - /P 136 0 R - /K [156 0 R 155 0 R 154 0 R] + /S /P + /P 134 0 R + /K [148 149] + /Pg 373 0 R >> endobj 154 0 obj << /Type /StructElem - /S /TD - /P 153 0 R - /A [<< - /O /Table - /Headers [] - >> << - /O /Layout - /BorderStyle /Solid - >>] - /K [4 5 6] - /Pg 460 0 R + /S /P + /P 134 0 R + /K [] >> endobj 155 0 obj << /Type /StructElem - /S /TD - /P 153 0 R - /A [<< - /O /Table - /Headers [] - >> << - /O /Layout - /BorderStyle /Solid - >>] - /K [2 3] - /Pg 460 0 R + /S /P + /P 134 0 R + /K [128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147] + /Pg 373 0 R >> endobj 156 0 obj << /Type /StructElem - /S /TD - /P 153 0 R - /A [<< - /O /Table - /Headers [] - >> << - /O /Layout - /BorderStyle /Solid - >>] - /K [0 1] - /Pg 460 0 R + /S /P + /P 134 0 R + /K [126 127] + /Pg 373 0 R >> endobj @@ -1660,213 +1647,198 @@ endobj << /Type /StructElem /S /P - /P 16 0 R - /K [158 0 R] + /P 21 0 R + /K [123 124 125] + /Pg 373 0 R >> endobj 158 0 obj << /Type /StructElem - /S /Strong - /P 157 0 R - /K [432 433] - /Pg 458 0 R + /S /H2 + /P 21 0 R + /T + /K [159 0 R] >> endobj 159 0 obj << /Type /StructElem - /S /Span - /P 16 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [426 427 428 429 430 431] - /Pg 458 0 R + /S /P + /P 158 0 R + /K [122] + /Pg 373 0 R >> endobj 160 0 obj << /Type /StructElem - /S /P - /P 16 0 R - /K [419 161 0 R 425] - /Pg 458 0 R + /S /H1 + /P 21 0 R + /T + /K [161 0 R] >> endobj 161 0 obj << /Type /StructElem - /S /Formula + /S /P /P 160 0 R - /K [420 421 422 423 424] - /Pg 458 0 R + /K [121] + /Pg 373 0 R >> endobj 162 0 obj << /Type /StructElem - /S /P - /P 16 0 R - /K [163 0 R] + /S /L + /P 21 0 R + /A [<< + /O /List + /ListNumbering /Decimal + >>] + /K [173 0 R 170 0 R 166 0 R 163 0 R] >> endobj 163 0 obj << /Type /StructElem - /S /Strong + /S /LI /P 162 0 R - /K [416 417 418] - /Pg 458 0 R + /K [165 0 R 164 0 R] >> endobj 164 0 obj << /Type /StructElem - /S /P - /P 16 0 R - /K [166 0 R 387 388 389 390 391 392 165 0 R 414 415] - /Pg 458 0 R + /S /LBody + /P 163 0 R + /K [120] + /Pg 373 0 R >> endobj 165 0 obj << /Type /StructElem - /S /Formula - /P 164 0 R - /K [393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413] - /Pg 458 0 R + /S /Lbl + /P 163 0 R + /K [119] + /Pg 373 0 R >> endobj 166 0 obj << /Type /StructElem - /S /Strong - /P 164 0 R - /K [386] - /Pg 458 0 R + /S /LI + /P 162 0 R + /K [169 0 R 167 0 R] >> endobj 167 0 obj << /Type /StructElem - /S /H1 - /P 16 0 R - /T - /K [384 385] - /Pg 458 0 R + /S /LBody + /P 166 0 R + /K [101 102 168 0 R 117 118] + /Pg 373 0 R >> endobj 168 0 obj << /Type /StructElem - /S /P - /P 16 0 R - /K [358 171 0 R 360 170 0 R 376 169 0 R 382 383] - /Pg 458 0 R + /S /Formula + /P 167 0 R + /K [103 104 105 106 107 108 109 110 111 112 113 114 115 116] + /Pg 373 0 R >> endobj 169 0 obj << /Type /StructElem - /S /Formula - /P 168 0 R - /K [377 378 379 380 381] - /Pg 458 0 R + /S /Lbl + /P 166 0 R + /K [100] + /Pg 373 0 R >> endobj 170 0 obj << /Type /StructElem - /S /Formula - /P 168 0 R - /K [361 362 363 364 365 366 367 368 369 370 371 372 373 374 375] - /Pg 458 0 R + /S /LI + /P 162 0 R + /K [172 0 R 171 0 R] >> endobj 171 0 obj << /Type /StructElem - /S /Strong - /P 168 0 R - /K [359] - /Pg 458 0 R + /S /LBody + /P 170 0 R + /K [99] + /Pg 373 0 R >> endobj 172 0 obj << /Type /StructElem - /S /P - /P 16 0 R - /K [173 0 R] + /S /Lbl + /P 170 0 R + /K [98] + /Pg 373 0 R >> endobj 173 0 obj << /Type /StructElem - /S /Strong - /P 172 0 R - /K [356 357] - /Pg 458 0 R + /S /LI + /P 162 0 R + /K [175 0 R 174 0 R] >> endobj 174 0 obj << /Type /StructElem - /S /Formula - /P 16 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355] - /Pg 458 0 R + /S /LBody + /P 173 0 R + /K [94 95 96 97] + /Pg 373 0 R >> endobj 175 0 obj << /Type /StructElem - /S /Formula - /P 16 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207] - /Pg 458 0 R + /S /Lbl + /P 173 0 R + /K [93] + /Pg 373 0 R >> endobj 176 0 obj << /Type /StructElem - /S /Formula - /P 16 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180] - /Pg 458 0 R + /S /H1 + /P 21 0 R + /T + /K [177 0 R] >> endobj @@ -1874,407 +1846,418 @@ endobj << /Type /StructElem /S /P - /P 16 0 R - /K [152 153 154] - /Pg 458 0 R + /P 176 0 R + /K [92] + /Pg 373 0 R >> endobj 178 0 obj << /Type /StructElem - /S /P - /P 16 0 R - /K [181 0 R 179 0 R] + /S /L + /P 21 0 R + /A [<< + /O /List + /ListNumbering /Decimal + >>] + /K [188 0 R 185 0 R 182 0 R 179 0 R] >> endobj 179 0 obj << /Type /StructElem - /S /Formula + /S /LI /P 178 0 R - /K [180 0 R] + /K [181 0 R 180 0 R] >> endobj 180 0 obj << /Type /StructElem - /S /Strong + /S /LBody /P 179 0 R - /K [142 143 144 145 146 147 148 149 150 151] - /Pg 458 0 R + /K [87 88 89 90 91] + /Pg 373 0 R >> endobj 181 0 obj << /Type /StructElem - /S /Strong - /P 178 0 R - /K [136 137 138 139 140 141] - /Pg 458 0 R + /S /Lbl + /P 179 0 R + /K [86] + /Pg 373 0 R >> endobj 182 0 obj << /Type /StructElem - /S /Formula - /P 16 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135] - /Pg 458 0 R + /S /LI + /P 178 0 R + /K [184 0 R 183 0 R] >> endobj 183 0 obj << /Type /StructElem - /S /Formula - /P 16 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100] - /Pg 458 0 R + /S /LBody + /P 182 0 R + /K [84 85] + /Pg 373 0 R >> endobj 184 0 obj << /Type /StructElem - /S /Formula - /P 16 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24] - /Pg 458 0 R + /S /Lbl + /P 182 0 R + /K [83] + /Pg 373 0 R >> endobj 185 0 obj << /Type /StructElem - /S /P - /P 16 0 R - /K [0] - /Pg 458 0 R + /S /LI + /P 178 0 R + /K [187 0 R 186 0 R] >> endobj 186 0 obj << /Type /StructElem - /S /P - /P 16 0 R - /K [189 0 R 187 0 R] + /S /LBody + /P 185 0 R + /K [81 82] + /Pg 373 0 R >> endobj 187 0 obj << /Type /StructElem - /S /Formula - /P 186 0 R - /K [188 0 R] + /S /Lbl + /P 185 0 R + /K [80] + /Pg 373 0 R >> endobj 188 0 obj << /Type /StructElem - /S /Strong - /P 187 0 R - /K [593 594 595 596 597 598 599] - /Pg 456 0 R + /S /LI + /P 178 0 R + /K [190 0 R 189 0 R] >> endobj 189 0 obj << /Type /StructElem - /S /Strong - /P 186 0 R - /K [589 590 591 592] - /Pg 456 0 R + /S /LBody + /P 188 0 R + /K [79] + /Pg 373 0 R >> endobj 190 0 obj << /Type /StructElem - /S /P - /P 16 0 R - /K [194 0 R 525 193 0 R 536 537 192 0 R 562 563 191 0 R 588] - /Pg 456 0 R + /S /Lbl + /P 188 0 R + /K [78] + /Pg 373 0 R >> endobj 191 0 obj << /Type /StructElem - /S /Formula - /P 190 0 R - /K [564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587] - /Pg 456 0 R + /S /P + /P 21 0 R + /K [77] + /Pg 373 0 R >> endobj 192 0 obj << /Type /StructElem - /S /Formula - /P 190 0 R - /K [538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561] - /Pg 456 0 R + /S /H1 + /P 21 0 R + /T + /K [193 0 R] >> endobj 193 0 obj << /Type /StructElem - /S /Formula - /P 190 0 R - /K [526 527 528 529 530 531 532 533 534 535] - /Pg 456 0 R + /S /P + /P 192 0 R + /K [76] + /Pg 373 0 R >> endobj 194 0 obj << /Type /StructElem - /S /Strong - /P 190 0 R - /K [524] - /Pg 456 0 R + /S /P + /P 21 0 R + /K [1 2 3 4 5 6 7 8 9 10 11 12 13 14 199 0 R 34 35 36 37 38 39 40 41 198 0 R 45 46 47 197 0 R 51 52 53 196 0 R 57 58 59 60 195 0 R 75] + /Pg 373 0 R >> endobj 195 0 obj << /Type /StructElem - /S /H1 - /P 16 0 R - /T - /K [522 523] - /Pg 456 0 R + /S /Formula + /P 194 0 R + /K [61 62 63 64 65 66 67 68 69 70 71 72 73 74] + /Pg 373 0 R >> endobj 196 0 obj << /Type /StructElem - /S /L - /P 16 0 R - /A [<< - /O /List - /ListNumbering /Decimal - >>] - /K [235 0 R 223 0 R 197 0 R] + /S /Formula + /P 194 0 R + /K [54 55 56] + /Pg 373 0 R >> endobj 197 0 obj << /Type /StructElem - /S /LI - /P 196 0 R - /K [222 0 R 198 0 R] + /S /Formula + /P 194 0 R + /K [48 49 50] + /Pg 373 0 R >> endobj 198 0 obj << /Type /StructElem - /S /LBody - /P 197 0 R - /K [206 0 R 199 0 R] + /S /Formula + /P 194 0 R + /K [42 43 44] + /Pg 373 0 R >> endobj 199 0 obj << /Type /StructElem - /S /P - /P 198 0 R - /K [508 205 0 R 510 204 0 R 512 203 0 R 514 515 202 0 R 517 201 0 R 519 200 0 R 521] - /Pg 456 0 R + /S /Formula + /P 194 0 R + /K [15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33] + /Pg 373 0 R >> endobj 200 0 obj << /Type /StructElem - /S /Formula - /P 199 0 R - /K [520] - /Pg 456 0 R + /S /H1 + /P 21 0 R + /T + /K [201 0 R] >> endobj 201 0 obj << /Type /StructElem - /S /Formula - /P 199 0 R - /K [518] - /Pg 456 0 R + /S /P + /P 200 0 R + /K [0] + /Pg 373 0 R >> endobj 202 0 obj << /Type /StructElem - /S /Formula - /P 199 0 R - /K [516] - /Pg 456 0 R + /S /TOC + /P 21 0 R + /K [228 0 R 225 0 R 222 0 R 219 0 R 209 0 R 206 0 R 203 0 R] >> endobj 203 0 obj << /Type /StructElem - /S /Formula - /P 199 0 R - /K [513] - /Pg 456 0 R + /S /TOCI + /P 202 0 R + /K [204 0 R] >> endobj 204 0 obj << /Type /StructElem - /S /Formula - /P 199 0 R - /K [511] - /Pg 456 0 R + /S /Reference + /P 203 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [205 0 R] >> endobj 205 0 obj << /Type /StructElem - /S /Formula - /P 199 0 R - /K [509] - /Pg 456 0 R + /S /Link + /P 204 0 R + /K [27 28 29 << + /Type /OBJR + /Pg 371 0 R + /Obj 370 0 R + >>] + /Pg 371 0 R >> endobj 206 0 obj << /Type /StructElem - /S /P - /P 198 0 R - /K [221 0 R 219 0 R 218 0 R 216 0 R 215 0 R 482 214 0 R 484 213 0 R 486 212 0 R 488 211 0 R 492 210 0 R 500 209 0 R 502 503 208 0 R 505 207 0 R 507] - /Pg 456 0 R + /S /TOCI + /P 202 0 R + /K [207 0 R] >> endobj 207 0 obj << /Type /StructElem - /S /Formula + /S /Reference /P 206 0 R - /K [506] - /Pg 456 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [208 0 R] >> endobj 208 0 obj << /Type /StructElem - /S /Formula - /P 206 0 R - /K [504] - /Pg 456 0 R + /S /Link + /P 207 0 R + /K [24 25 26 << + /Type /OBJR + /Pg 371 0 R + /Obj 369 0 R + >>] + /Pg 371 0 R >> endobj 209 0 obj << /Type /StructElem - /S /Formula - /P 206 0 R - /K [501] - /Pg 456 0 R + /S /TOC + /P 202 0 R + /K [216 0 R 213 0 R 210 0 R] >> endobj 210 0 obj << /Type /StructElem - /S /Formula - /P 206 0 R - /K [493 494 495 496 497 498 499] - /Pg 456 0 R + /S /TOCI + /P 209 0 R + /K [211 0 R] >> endobj 211 0 obj << /Type /StructElem - /S /Formula - /P 206 0 R - /K [489 490 491] - /Pg 456 0 R + /S /Reference + /P 210 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [212 0 R] >> endobj 212 0 obj << /Type /StructElem - /S /Formula - /P 206 0 R - /K [487] - /Pg 456 0 R + /S /Link + /P 211 0 R + /K [20 21 22 23 << + /Type /OBJR + /Pg 371 0 R + /Obj 368 0 R + >>] + /Pg 371 0 R >> endobj 213 0 obj << /Type /StructElem - /S /Formula - /P 206 0 R - /K [485] - /Pg 456 0 R + /S /TOCI + /P 209 0 R + /K [214 0 R] >> endobj 214 0 obj << /Type /StructElem - /S /Formula - /P 206 0 R - /K [483] - /Pg 456 0 R + /S /Reference + /P 213 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [215 0 R] >> endobj 215 0 obj << /Type /StructElem - /S /Strong - /P 206 0 R - /K [481] - /Pg 456 0 R + /S /Link + /P 214 0 R + /K [16 17 18 19 << + /Type /OBJR + /Pg 371 0 R + /Obj 367 0 R + >>] + /Pg 371 0 R >> endobj 216 0 obj << /Type /StructElem - /S /Formula - /P 206 0 R + /S /TOCI + /P 209 0 R /K [217 0 R] >> endobj @@ -2282,28 +2265,35 @@ endobj 217 0 obj << /Type /StructElem - /S /Strong + /S /Reference /P 216 0 R - /K [480] - /Pg 456 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [218 0 R] >> endobj 218 0 obj << /Type /StructElem - /S /Strong - /P 206 0 R - /K [479] - /Pg 456 0 R + /S /Link + /P 217 0 R + /K [13 14 15 << + /Type /OBJR + /Pg 371 0 R + /Obj 366 0 R + >>] + /Pg 371 0 R >> endobj 219 0 obj << /Type /StructElem - /S /Formula - /P 206 0 R + /S /TOCI + /P 202 0 R /K [220 0 R] >> endobj @@ -2311,87 +2301,107 @@ endobj 220 0 obj << /Type /StructElem - /S /Strong + /S /Reference /P 219 0 R - /K [476 477 478] - /Pg 456 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [221 0 R] >> endobj 221 0 obj << /Type /StructElem - /S /Strong - /P 206 0 R - /K [475] - /Pg 456 0 R + /S /Link + /P 220 0 R + /K [10 11 12 << + /Type /OBJR + /Pg 371 0 R + /Obj 365 0 R + >>] + /Pg 371 0 R >> endobj 222 0 obj << /Type /StructElem - /S /Lbl - /P 197 0 R - /K [474] - /Pg 456 0 R + /S /TOCI + /P 202 0 R + /K [223 0 R] >> endobj 223 0 obj << /Type /StructElem - /S /LI - /P 196 0 R - /K [234 0 R 224 0 R] + /S /Reference + /P 222 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [224 0 R] >> endobj 224 0 obj << /Type /StructElem - /S /LBody + /S /Link /P 223 0 R - /K [233 0 R 231 0 R 230 0 R 228 0 R 227 0 R 469 226 0 R 471 225 0 R 473] - /Pg 456 0 R + /K [7 8 9 << + /Type /OBJR + /Pg 371 0 R + /Obj 364 0 R + >>] + /Pg 371 0 R >> endobj 225 0 obj << /Type /StructElem - /S /Formula - /P 224 0 R - /K [472] - /Pg 456 0 R + /S /TOCI + /P 202 0 R + /K [226 0 R] >> endobj 226 0 obj << /Type /StructElem - /S /Formula - /P 224 0 R - /K [470] - /Pg 456 0 R + /S /Reference + /P 225 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [227 0 R] >> endobj 227 0 obj << /Type /StructElem - /S /Strong - /P 224 0 R - /K [468] - /Pg 456 0 R + /S /Link + /P 226 0 R + /K [4 5 6 << + /Type /OBJR + /Pg 371 0 R + /Obj 363 0 R + >>] + /Pg 371 0 R >> endobj 228 0 obj << /Type /StructElem - /S /Formula - /P 224 0 R + /S /TOCI + /P 202 0 R /K [229 0 R] >> endobj @@ -2399,28 +2409,36 @@ endobj 229 0 obj << /Type /StructElem - /S /Strong + /S /Reference /P 228 0 R - /K [467] - /Pg 456 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [230 0 R] >> endobj 230 0 obj << /Type /StructElem - /S /Strong - /P 224 0 R - /K [466] - /Pg 456 0 R + /S /Link + /P 229 0 R + /K [1 2 3 << + /Type /OBJR + /Pg 371 0 R + /Obj 362 0 R + >>] + /Pg 371 0 R >> endobj 231 0 obj << /Type /StructElem - /S /Formula - /P 224 0 R + /S /H1 + /P 21 0 R + /T /K [232 0 R] >> endobj @@ -2428,3303 +2446,1584 @@ endobj 232 0 obj << /Type /StructElem - /S /Strong + /S /P /P 231 0 R - /K [463 464 465] - /Pg 456 0 R + /K [0] + /Pg 371 0 R >> endobj 233 0 obj << /Type /StructElem - /S /Strong - /P 224 0 R - /K [462] - /Pg 456 0 R + /S /P + /P 21 0 R + /K [76 77 78 79 80] + /Pg 360 0 R >> endobj 234 0 obj << /Type /StructElem - /S /Lbl - /P 223 0 R - /K [461] - /Pg 456 0 R + /S /P + /P 21 0 R + /K [34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 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R 241 0 R 240 0 R] >> endobj 240 0 obj << /Type /StructElem - /S /Formula - /P 236 0 R - /K [241 0 R] + /S /Div + /P 239 0 R + /K [] >> endobj 241 0 obj << /Type /StructElem - /S /Strong - /P 240 0 R - /K [454] - /Pg 456 0 R + /S /Div + /P 239 0 R + /K [] >> endobj 242 0 obj << /Type /StructElem - /S /Strong - /P 236 0 R - /K [453] - /Pg 456 0 R + /S /Div + /P 239 0 R + /K [243 0 R] >> endobj 243 0 obj << /Type /StructElem - /S /Formula - /P 236 0 R - /K [244 0 R] + /S /Span + /P 242 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [10] + /Pg 358 0 R >> endobj 244 0 obj << /Type /StructElem - /S /Strong - /P 243 0 R - /K [450 451 452] - /Pg 456 0 R + /S /Div + /P 239 0 R + /K [245 0 R] >> endobj 245 0 obj << /Type /StructElem - /S /Strong - /P 236 0 R - /K [449] - /Pg 456 0 R + /S /Span + /P 244 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [9] + /Pg 358 0 R >> endobj 246 0 obj << /Type /StructElem - /S /Lbl - /P 235 0 R - /K [448] - /Pg 456 0 R + /S /Div + /P 239 0 R + /K [] >> endobj 247 0 obj << /Type /StructElem - /S /P - /P 16 0 R - /K [257 0 R 421 256 0 R 423 255 0 R 427 254 0 R 429 253 0 R 431 252 0 R 435 251 0 R 437 250 0 R 439 249 0 R 441 248 0 R 447] - /Pg 456 0 R + /S /Div + /P 239 0 R + /K [] >> endobj 248 0 obj << /Type /StructElem - /S /Formula - /P 247 0 R - /K [442 443 444 445 446] - /Pg 456 0 R + /S /Div + /P 239 0 R + /K [249 0 R] >> endobj 249 0 obj << /Type /StructElem - /S /Formula - /P 247 0 R - /K [440] - /Pg 456 0 R + /S /Span + /P 248 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [8] + /Pg 358 0 R >> endobj 250 0 obj << /Type /StructElem - /S /Formula - /P 247 0 R - /K [438] - /Pg 456 0 R + /S /Div + /P 239 0 R + /K [251 0 R] >> endobj 251 0 obj << /Type /StructElem - /S /Formula - /P 247 0 R - /K [436] - /Pg 456 0 R + /S /Span + /P 250 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [5 6 7] + /Pg 358 0 R >> endobj 252 0 obj << /Type /StructElem - /S /Formula - /P 247 0 R - /K [432 433 434] - /Pg 456 0 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/Formula - /P 260 0 R - /K [399 400 401] - /Pg 456 0 R + /S /Span + /P 21 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [0] + /Pg 358 0 R >> endobj 266 0 obj << - /Type /StructElem - /S /Formula - /P 260 0 R - /K [393 394 395 396 397] - /Pg 456 0 R + /Type /PageLabel >> endobj 267 0 obj << - /Type /StructElem - /S /Formula - /P 260 0 R - /K [391] - /Pg 456 0 R + /Type /PageLabel + /S /r + /St 2 >> endobj 268 0 obj << - /Type /StructElem - /S /Formula - /P 260 0 R - /K [387 388 389] - /Pg 456 0 R + /Type /PageLabel + /S /D + /St 3 >> endobj 269 0 obj << - /Type /StructElem - /S /Strong - /P 260 0 R - /K [385] - /Pg 456 0 R + /Type /PageLabel + /S /D + /St 4 >> endobj 270 0 obj << - /Type /StructElem - /S /H1 - /P 16 0 R - /T - /K [383 384] - /Pg 456 0 R + /Type /PageLabel + /S /D + /St 5 >> endobj 271 0 obj << - /Type /StructElem - /S /P - /P 16 0 R - /K [347 274 0 R 370 273 0 R 380 272 0 R 382] - /Pg 456 0 R + /Type /PageLabel + /S /D + /St 6 >> endobj 272 0 obj << - /Type 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page(paper: "a4", margin: (x: 2cm, y: 2cm)) -#set heading(numbering: "1.") - -#let answer(body) = block( - fill: luma(240), - stroke: (left: 2pt + blue), - inset: 10pt, - radius: 2pt, - width: 100%, - body +#import "labtemplate.typ": * +#show: nudtlabpaper.with( + author: "程景愉", + id: "202302723005", + title: "贝叶斯网络编程实验", + training_type: "普通本科生", + grade: "2023级", + major: "网络工程", + department: "计算机学院", + advisor: "祝恩", + jobtitle: "教授", + lab: "306-707", + date: "2025.12.31", + header_str: "贝叶斯网络编程实验报告", + simple_cover: true, ) -#align(center)[ - #text(size: 18pt, weight: "bold")[第13-14章 概率与贝叶斯网络 习题解答] - - #v(1em) - // *生成时间:* #datetime.today().display() +#set page(header: [ + #set par(spacing: 6pt) + #align(center)[#text(size: 11pt)[人工智能实验报告]] + #v(-0.3em) + #line(length: 100%, stroke: (thickness: 1pt)) +],) + +#show heading: it => if it.level == 1 [ + #v(1em) + #set text(font: hei, size: 16pt) + #it.body + #v(0.5em) +] else [ + #v(0.8em) + #set text(font: "New Computer Modern", weight: "bold", style: "italic") + #it.body + #v(0.5em) ] -= 题目 1 -*题意:* 已知 $P(a) = 0.3$, $P(b | a) = 0.2$, $P(c | a) = 0.5$。比较 $P(a and b)$ 与 $P(a and c)$。 +#set heading(numbering: none) -#answer[ - 根据乘法公式 $P(x and y) = P(x)P(y|x)$: - $ P(a and b) &= P(a) dot P(b | a) = 0.3 times 0.2 = 0.06 \ - P(a and c) &= P(a) dot P(c | a) = 0.3 times 0.5 = 0.15 $ - 因为 $0.06 < 0.15$,所以 *$P(a and b) < P(a and c)$*。 - - *答案:B* + +#outline(title: "目录",depth: 2, indent: 1em) + +#set enum(indent: 0.5em,body-indent: 0.5em,) +#pagebreak() + += 实验介绍 +#para[ + 本次实验旨在实现并比较两种贝叶斯网络近似推理算法:拒绝采样(Rejection Sampling)和似然加权(Likelihood Weighting)。 + 实验使用的贝叶斯网络模型包含四个布尔变量:Cloudy (C), Sprinkler (S), Rain (R), WetGrass (W)。 + 网络结构为 $C \to S, C \to R, S \to W, R \to W$。 + 实验目标是根据给定的条件概率表(CPTs),在已知证据 $S=T$ 和 $W=T$ 的情况下,估计 $R=T$ 的后验概率 $P(R=T | S=T, W=T)$。 ] -= 题目 2 -*题意:* $P(a or b)=0.7$, $P(a)=0.4$, $P(b)=0.5$,求 $P(a and b)$。 += 实验内容 +#para[ + 实验主要包含以下内容: +] ++ 根据题目描述的贝叶斯网络结构和条件概率表,构建数据结构表示该网络。 ++ 实现拒绝采样算法:从先验分布中采样,拒绝与证据不一致的样本,利用保留样本中查询变量的频率作为后验概率的估计。 ++ 实现似然加权算法:固定证据变量的值,对非证据变量进行采样,并根据证据变量的条件概率计算样本权重,利用加权频率估计后验概率。 ++ 比较两种算法在不同采样数量(N=100, 1000, ...)下的估计结果与真实值的偏差,分析算法收敛性。 -#answer[ - 根据概率加法公式(容斥原理): - $ P(a or b) = P(a) + P(b) - P(a and b) $ - 代入已知数值: - $ 0.7 = 0.4 + 0.5 - P(a and b) \ - P(a and b) = 0.9 - 0.7 = 0.2 $ - - *答案:0.2* += 实验情况 ++ 使用 Python 语言实现算法。 ++ 代码需清晰易读,包含必要的注释。 ++ 计算并输出 $P(R=T | S=T, W=T)$ 的精确值以便对比。 ++ 撰写实验报告,展示核心代码和实验结果。 + += 实验步骤与实现 + +== 网络定义与概率表 +首先定义网络的条件概率表(CPTs)。 +```python +# CPTs +P_C = {True: 0.5, False: 0.5} + +# P(S | C) +P_S_given_C = { + True: {True: 0.10, False: 0.90}, # C=T + False: {True: 0.50, False: 0.50} # C=F +} + +# P(R | C) +P_R_given_C = { + True: {True: 0.80, False: 0.20}, # C=T + False: {True: 0.20, False: 0.80} # C=F +} + +# P(W | S, R) +P_W_given_SR = { + (True, True): {True: 0.99, False: 0.01}, + (True, False): {True: 0.90, False: 0.10}, + (False, True): {True: 0.90, False: 0.10}, + (False, False): {True: 0.00, False: 1.00} +} +``` + +== 拒绝采样 (Rejection Sampling) +拒绝采样通过生成先验分布的样本,并丢弃那些与证据不符的样本来工作。 +```python +def rejection_sampling(query_var, query_val, evidence, num_samples): + consistent_count = 0 + query_match_count = 0 + + for _ in range(num_samples): + sample = get_prior_sample() # 从联合分布采样 + + # 检查样本是否与证据一致 + is_consistent = True + for var, val in evidence.items(): + if sample[var] != val: + is_consistent = False + break + + if is_consistent: + consistent_count += 1 + if sample[query_var] == query_val: + query_match_count += 1 + + if consistent_count == 0: return 0.0 + return query_match_count / consistent_count +``` + +== 似然加权 (Likelihood Weighting) +似然加权强制证据变量取观测值,并将样本权重设为证据变量在其父节点给定情况下的似然概率乘积。 +```python +def likelihood_weighting(query_var, query_val, evidence, num_samples): + weighted_counts = {True: 0.0, False: 0.0} + + for _ in range(num_samples): + weight = 1.0 + sample = {} + + # 以 C, S, R, W 的拓扑顺序采样/赋值 + # 若变量在证据中,则赋值为证据值并更新权重 + # 若变量不在证据中,则根据父节点采样 + # (代码细节略,参见附件源程序) + # ... + + # 累加权重 + weighted_counts[sample[query_var]] += weight + + total_weight = sum(weighted_counts.values()) + if total_weight == 0: return 0.0 + return weighted_counts[query_val] / total_weight +``` + += 实验结果 +#para[ + 首先通过精确计算(枚举联合概率分布)得到理论真实值: + $P(R=T | S=T, W=T) approx 0.320388$ ] -= 题目 3 -*数据:* 全联合概率分布表如下(Cavity, Toothache, Catch): +#para[ + 下表展示了在不同采样数量 $N$ 下,两种算法的估计结果: +] #table( - columns: (auto, auto, auto, auto, auto), - inset: 8pt, + columns: (auto, auto, auto), + inset: 10pt, align: center, - [], [T, Catch], [T, $not$ Catch], [$not$ T, Catch], [$not$ T, $not$ Catch], - [Cavity], [0.108], [0.012], [0.072], [0.008], - [$not$ Cavity], [0.016], [0.064], [0.144], [0.576] + [*样本数量 N*], [*拒绝采样结果*], [*似然加权结果*], + [100], [0.480000], [0.377902], + [1000], [0.353741], [0.311148], + [10000], [0.320734], [0.317552], + [100000], [0.318791], [0.321722], + [1000000], [0.319916], [0.319471], ) -#answer[ - *1. 计算 $P("Toothache" or not "Cavity")$* - - 利用补集思想:$P(A) = 1 - P(not A)$。 - 事件的补集是 $not "Toothache" and "Cavity"$。 - 对应表格中的项为:(Cavity, $not$ T, Catch) 和 (Cavity, $not$ T, $not$ Catch)。 - $ P(not T and "Cav") = 0.072 + 0.008 = 0.080 $ - $ P(T or not "Cav") = 1 - 0.080 = 0.92 $ += 实验总结 - *2. 计算 $P(not "toothache" or "catch")$* - - 补集是 $"toothache" and not "catch"$。 - 对应表格列为 (T, $not$ Catch),即第 2 列。 - $ P(T and not "Catch") = 0.012 ("Cav") + 0.064 (not "Cav") = 0.076 $ - $ P(not T or "Catch") = 1 - 0.076 = 0.924 $ ++ *收敛性*:从实验结果可以看出,随着采样数量 $N$ 的增加,拒绝采样和似然加权算法的结果都逐渐收敛于真实值 $0.320388$。 - *3. 计算 $P("Toothache" or not "Cavity" | not "catch")$ 和 $P(not "catch" | "Toothache" or not "Cavity")$* - - 令 $A = "Toothache" or not "Cavity"$, $B = not "catch"$。 - - - *计算 $P(B)$*: Sum of all $not$ Catch columns (Col 2, Col 4). - $P(B) = (0.012 + 0.064) + (0.008 + 0.576) = 0.076 + 0.584 = 0.66$ - - *计算 $P(A and B)$*: 在 $not$ Catch 列中满足 $T or not "Cav"$ 的项。 - - (Cav, T, $not$ C): 0.012 (满足 T) - - ($not$ Cav, T, $not$ C): 0.064 (满足 T) - - ($not$ Cav, $not$ T, $not$ C): 0.576 (满足 $not$ Cav) - - (Cav, $not$ T, $not$ C): 0.008 (不满足,既无T也无$not$Cav) - Sum $= 0.012 + 0.064 + 0.576 = 0.652$ - - 结果 1: $P(A | B) = 0.652 / 0.66 approx 0.9879$ - 结果 2: $P(B | A) = P(A and B) / P(A) = 0.652 / 0.92 approx 0.7087$ (其中 P(A) 来自第1小问) ++ *算法比较*: + - *拒绝采样*:实现简单,直接利用先验分布采样。但在证据概率较低时(本例中证据发生的概率约为 0.278,尚可),会拒绝大量样本,导致计算资源浪费。在样本量较小(如 N=100)时波动较大。 + - *似然加权*:利用了证据信息,所有生成的样本都是有效的(权重不为0),因此在相同采样数量下,通常能提供比拒绝采样更稳定的估计,尤其是当证据发生概率很低时优势更明显。 - *4. 判断 Cavity 与 Toothache 是否独立* - - $ P("Cav") &= 0.108+0.012+0.072+0.008 = 0.2 \ - P("Toothache") &= 0.108+0.012+0.016+0.064 = 0.2 \ - P("Cav" and "T") &= 0.108 + 0.012 = 0.12 $ - 检验:$P("Cav") times P("T") = 0.2 times 0.2 = 0.04$。 - 因为 $0.12 != 0.04$,所以两者 *不独立*。 -] - -= 题目 4 -*题意:* 设 $X, Y$ 条件独立于 $Z$(即 $X perp Y | Z$),$Y, W$ 条件独立于 $Z$(即 $Y perp W | Z$)。问 $X, W$ 是否条件独立于 $Z$? - -#answer[ - *结论:不能。* 条件独立性不具备传递性。 - - *反例证明:* - 假设 $Z$ 是一个公平的硬币投掷(0 或 1)。 - 令 $X = Z$($X$ 完全依赖于 $Z$)。 - 令 $W = Z$($W$ 完全依赖于 $Z$)。 - 令 $Y$ 是一个与 $X, W, Z$ 都完全独立的随机变量(例如掷骰子)。 - - 1. *检查 $X, Y$ 关于 $Z$ 的独立性*:给定 $Z$, $X$ 变为常数。常数与任何变量独立,故成立。 - 2. *检查 $Y, W$ 关于 $Z$ 的独立性*:同理,给定 $Z$,$W$ 变为常数,故成立。 - 3. *检查 $X, W$ 关于 $Z$ 的独立性*: - 给定 $Z$,$X$ 和 $W$ 的值完全确定且相同(例如若 $Z=1$,则 $X=1, W=1$)。虽然在 $Z$ 固定的情况下它们的方差为0(技术上可视作独立),但如果我们考虑一种因果结构: - 令 $X$ 和 $W$ 为同一变量的两个副本。显然它们是强相关的。 - - 更直观的例子:$X$ 和 $W$ 互为因果或由共同隐变量控制,而它们都与 $Y$ 独立。仅仅知道它们分别与 $Y$ 独立,无法切断 $X$ 和 $W$ 之间的联系。 -] - -= 题目 5 -*题意:* 罕见病检测。$P(D)=0.001$。 -检测A:$P(+|D)=0.95, P(+|not D)=0.05$。 -检测B:$P(+|D)=0.90, P(+|not D)=0.10$。 - -#answer[ - *a. 单次检测 A 为阳性,求 $P(D|A+)$* - - 使用贝叶斯公式: - $ P(D|A+) = (P(A+|D)P(D)) / P(A+) $ - $ P(A+) &= P(A+|D)P(D) + P(A+|not D)P(not D) \ - &= 0.95 times 0.001 + 0.05 times 0.999 \ - &= 0.00095 + 0.04995 = 0.0509 $ - $ P(D|A+) &= 0.00095 / 0.0509 approx 0.0187 (1.87%) $ - - *b. 两次检测 A 和 B 均为阳性,求 $P(D|A+, B+)$* - - 由于检测独立(Naive Bayes 假设): - $ P(A+, B+ | D) = 0.95 times 0.90 = 0.855 $ - $ P(A+, B+ | not D) = 0.05 times 0.10 = 0.005 $ - - $ P(D | A+, B+) &= (P(A+, B+ | D)P(D)) / (P(A+, B+ | D)P(D) + P(A+, B+ | not D)P(not D)) \ - &= (0.855 times 0.001) / (0.855 times 0.001 + 0.005 times 0.999) \ - &= 0.000855 / (0.000855 + 0.004995) \ - &= 0.000855 / 0.00585 approx 0.1462 (14.62%) $ - - *c. 解释* - - 联合检测通过引入第二次独立测试,极大地降低了*假阳性率*(从 0.05 降至 $0.05 times 0.10 = 0.005$)。虽然真阳性率也略有下降,但分母中占主导地位的假阳性项(由 $P(not D)$ 权重放大)被大幅削减,从而显著提升了后验概率。 -] - -= 题目 6 -*场景:* 骑车(B) 取决于 天气(W) 和 熬夜(S)。 -$P(W="Sun")=0.7, P(S="Yes")=0.4$。 -CPT 已知。 - -#answer[ - *a. 贝叶斯网络与 CPT* - - 结构:$W -> B <- S$ (V-structure) - - #cetz.canvas({ - import cetz.draw: * - - let r = 0.8 - // Nodes - circle((0, 0), radius: r, name: "B") - content("B", "B (骑车)") - - circle((-2, 3), radius: r, name: "W") - content("W", "W (天气)") - - circle((2, 3), radius: r, name: "S") - content("S", "S (熬夜)") - - // Edges - line("W", "B", mark: (end: ">")) - line("S", "B", mark: (end: ">")) - }) - - *条件概率表 (CPT) for B:* - #table( - columns: 3, - align: center, - [W (天气)], [S (熬夜)], [P(B=是 | W, S)], - [晴 (Sun)], [否 (No)], [0.9], - [晴 (Sun)], [是 (Yes)], [0.6], - [雨 (Rain)], [否 (No)], [0.2], - [雨 (Rain)], [是 (Yes)], [0.1] - ) - - *b. 推理:已知骑车(B=Yes),求天气概率* - - 我们需要计算 $P(W | B="Yes")$。根据贝叶斯法则:$P(W|B) = P(B|W)P(W) / P(B)$。 - - 首先计算边缘概率 $P(B="Yes")$。 - $ P(B=y) = sum_(w, s) P(B=y|w,s)P(w)P(s) $ - 因 W 和 S 独立,联合概率直接相乘。 - - 1. $W="Sun", S="No"$: $0.9 times 0.7 times 0.6 = 0.378$ - 2. $W="Sun", S="Yes"$: $0.6 times 0.7 times 0.4 = 0.168$ - 3. $W="Rain", S="No"$: $0.2 times 0.3 times 0.6 = 0.036$ - 4. $W="Rain", S="Yes"$: $0.1 times 0.3 times 0.4 = 0.012$ - - $ P(B="Yes") = 0.378 + 0.168 + 0.036 + 0.012 = 0.594 $ - - 计算 $P(W="Sun" | B="Yes")$: - 分子为 W=Sun 的所有情况之和(项1 + 项2): - $ P(B=y, W="Sun") = 0.378 + 0.168 = 0.546 $ - $ P(W="Sun" | B="Yes") = 0.546 / 0.594 approx 0.919 $ - - 同理,$P(W="Rain" | B="Yes") = (0.036 + 0.012) / 0.594 approx 0.081$。 - - *结论:这天最可能是晴天。* -] - -= 题目 7 -*智能健康助手:* 变量 S(吸烟), G(基因), L(肺癌), C(咳嗽), X(胸片)。 -关系:$S->L, G->L, S->C, L->C, L->X$。 - -#answer[ - *问题 1:贝叶斯网络图* - - #align(center)[ - #cetz.canvas({ - import cetz.draw: * - // Manually positioning nodes for clarity - let r = 0.5 - circle((0, 0), radius: r, name: "L") - content("L", "L") - - circle((-2, 2), radius: r, name: "S") - content("S", "S") - - circle((2, 2), radius: r, name: "G") - content("G", "G") - - circle((-1, -2), radius: r, name: "C") - content("C", "C") - - circle((1, -2), radius: r, name: "X") - content("X", "X") - - line("S", "L", mark: (end: ">")) - line("G", "L", mark: (end: ">")) - line("L", "X", mark: (end: ">")) - line("L", "C", mark: (end: ">")) - - // S -> C 直接边 - line("S", "C", mark: (end: ">")) - }) - ] - - *问题 2:概率推理 $P(L="Yes" | C="No", X="Yes")$* - - 令 $alpha$ 为归一化常数。我们需要计算 $P(L=y, C=n, X=y)$ 和 $P(L=n, C=n, X=y)$。 - 公式分解:$P(S,G,L,C,X) = P(S)P(G)P(L|S,G)P(C|L,S)P(X|L)$。 - 求和消除 S, G: - $ P(L, C, X) = P(X|L) sum_S sum_G P(C|L,S) P(L|S,G) P(S) P(G) $ - - *Case 1: L = Yes* (且 $C=n, X=y$) - 因子 $P(X=y|L=y) = 0.9$。 - 内部求和 $Sigma_(L=y)$: - - $S=y, G=h$: $P(C=n|L=y,S=y)P(L=y|S=y,G=h)P(S=y)P(G=h) = 0.2 times 0.6 times 0.3 times 0.2 = 0.0072$ - - $S=y, G=l$: $0.2 times 0.3 times 0.3 times 0.8 = 0.0144$ - - $S=n, G=h$: $P(C=n|L=y,S=n)P(L=y|S=n,G=h)P(S=n)P(G=h) = 0.4 times 0.4 times 0.7 times 0.2 = 0.0224$ - - $S=n, G=l$: $0.4 times 0.1 times 0.7 times 0.8 = 0.0224$ - - $Sigma_(L=y) = 0.0072 + 0.0144 + 0.0224 + 0.0224 = 0.0664$ - $P(L=y, C=n, X=y) = 0.9 times 0.0664 = 0.05976$ - - *Case 2: L = No* (且 $C=n, X=y$) - 因子 $P(X=y|L=n) = 0.1$。 - 内部求和 $Sigma_(L=n)$: - - $S=y, G=h$: $P(C=n|L=n,S=y)P(L=n|S=y,G=h)P(S=y)P(G=h) = 0.7 times 0.4 times 0.3 times 0.2 = 0.0168$ - - $S=y, G=l$: $0.7 times 0.7 times 0.3 times 0.8 = 0.1176$ - - $S=n, G=h$: $P(C=n|L=n,S=n)P(L=n|S=n,G=h)P(S=n)P(G=h) = 0.9 times 0.6 times 0.7 times 0.2 = 0.0756$ - - $S=n, G=l$: $0.9 times 0.9 times 0.7 times 0.8 = 0.4536$ - - $Sigma_(L=n) = 0.0168 + 0.1176 + 0.0756 + 0.4536 = 0.6636$ - $P(L=n, C=n, X=y) = 0.1 times 0.6636 = 0.06636$ - - *最终归一化:* - $ P(L="Yes" | ...) &= 0.05976 / (0.05976 + 0.06636) \ - &= 0.05976 / 0.12612 approx 0.4738 $ - - *答案:47.38%* -] ++ *结论*:两种算法均能有效进行近似推理。对于本实验中的简单网络和非极端概率证据,两者在 $N=10000$ 以上时均能给出较好的估计结果。 diff --git a/bayesian/task.txt b/bayesian/task.txt new file mode 100644 index 0000000..8618974 --- /dev/null +++ b/bayesian/task.txt @@ -0,0 +1,34 @@ +作业二:实现贝叶斯网络近似推理算法 +(一)问题描述 +实现两种基本的近似推理算法——拒绝采样和似然加权,并在一个简单的 +贝叶斯网络(PPT 示例)上进行应用和比较。 +网络结构图: + C -> S + C -> R + S -> W + R -> W +变量解释: + C(Cloudy): 是否多云 (Boolean) + S(Sprinkler): 洒水器是否开启 (Boolean) + R(Rain): 是否下雨 (Boolean) + W(WetGrass): 草坪是否湿润 (Boolean) +条件概率表 (CPTs): + P(C=T) = 0.5 + P(S | C): + P(S=T | C=T) = 0.10 + P(S=T | C=F) = 0.50 + P(R | C): + P(R=T | C=T) = 0.80 + P(R=T | C=F) = 0.20 + P(W | S, R): + P(W=T | S=T, R=T) = 0.99 + P(W=T | S=T, R=F) = 0.90 + P(W=T | S=F, R=T) = 0.90 + P(W=T | S=F, R=F) = 0.00 + +(二) 任务要求 +实现拒绝采样算法和似然加权算法,算法需要能够估计条件概率 P(X | e), +其中 X 是查询变量,e 是证据。使用你实现的两种算法估计 P(R | S=T, +W=T)。 + +要求撰写实验报告,提供源程序。 diff --git a/bayesian/实验题(贝叶斯网络).pdf b/bayesian/实验题(贝叶斯网络).pdf new file mode 100644 index 0000000..c6a15a6 Binary files /dev/null and b/bayesian/实验题(贝叶斯网络).pdf differ