22:
1018:
With more than one conditioning variable, the table would still have one row for each potential value of the variable whose conditional probabilities are to be given, and there would be one column for each possible combination of values of the conditioning variables.
1022:
Moreover, the number of columns in the table could be substantially expanded to display the probabilities of the variable of interest conditional on specific values of only some, rather than all, of the other variables.
137:
of a single variable with respect to the others (i.e., the probability of each possible value of one variable if we know the values taken on by the other variables). For example, assume there are three random variables
751:
311:
541:
651:
821:
189:
435:
598:
568:
462:
391:
364:
236:
39:
482:
333:
209:
86:
58:
65:
105:
1061:
72:
839:
43:
662:
54:
241:
127:
32:
487:
603:
134:
79:
780:
141:
921:
656:
396:
964:=1. Combining these pieces of information gives us this table of conditional probabilities for
774:
948:=0, which is 4/9 ÷ 6/9 = 4/6. Likewise, in the same column we find that the probability that
573:
956:=0 is 2/9 ÷ 6/9 = 2/6. In the same way, we can also find the conditional probabilities for
546:
440:
369:
342:
214:
828:
130:
467:
316:
194:
1055:
904:
Each of the four central cells shows the probability of a particular combination of
21:
119:
920:
equals any of the values it can have – that is, the column sum 6/9 is the
600:
the CPT for any one of them has the number of cells equal to the product
15:
659:
form. As an example with only two variables, the values of
940:=0, we compute the fraction of the probabilities in the
746:{\displaystyle P(x_{1}=a_{k}\mid x_{2}=b_{j})=T_{kj},}
912:
values. The first column sum is the probability that
783:
665:
606:
576:
549:
490:
470:
443:
399:
372:
345:
319:
244:
217:
197:
144:
211:states. Then, the conditional probability table of
46:. Unsourced material may be challenged and removed.
815:
745:
645:
592:
562:
535:
476:
456:
429:
385:
358:
327:
305:
230:
203:
183:
655:A conditional probability table can be put into
393:and for each possible combination of values of
335:means “given the values of” – for each of the
306:{\displaystyle P(x_{1}=a_{k}\mid x_{2},x_{3})}
126:is defined for a set of discrete and mutually
1042:Machine learning: a probabilistic perspective
8:
928:=0. If we want to find the probability that
238:provides the conditional probability values
798:
788:
782:
731:
715:
702:
689:
676:
664:
634:
621:
611:
605:
581:
575:
554:
548:
536:{\displaystyle x_{1},x_{2},\ldots ,x_{M}}
527:
508:
495:
489:
469:
448:
442:
418:
413:
404:
398:
377:
371:
350:
344:
320:
318:
294:
281:
268:
255:
243:
222:
216:
196:
175:
162:
149:
143:
106:Learn how and when to remove this message
970:
844:
1032:
646:{\displaystyle K_{1}K_{2}\cdots K_{M}.}
7:
44:adding citations to reliable sources
124:conditional probability table (CPT)
14:
816:{\displaystyle \sum _{k}T_{kj}=1}
777:since the columns sum to 1; i.e.
184:{\displaystyle x_{1},x_{2},x_{3}}
827:. For example, suppose that two
20:
55:"Conditional probability table"
31:needs additional citations for
944:=0 column that have the value
840:joint probability distribution
721:
669:
430:{\displaystyle x_{2},\,x_{3}.}
321:
300:
248:
1:
960:equalling 0 or 1 given that
1078:
773:matrix. This matrix is a
570:states for each variable
313:– where the vertical bar
135:conditional probabilities
1062:Conditional probability
464:cells. In general, for
817:
747:
647:
594:
593:{\displaystyle x_{i},}
564:
537:
478:
458:
431:
387:
360:
329:
307:
232:
205:
185:
842:given in this table:
818:
748:
648:
595:
565:
563:{\displaystyle K_{i}}
538:
479:
459:
457:{\displaystyle K^{3}}
432:
388:
386:{\displaystyle x_{1}}
361:
359:{\displaystyle a_{k}}
330:
308:
233:
231:{\displaystyle x_{1}}
206:
186:
922:marginal probability
781:
663:
604:
574:
547:
488:
468:
441:
397:
370:
343:
317:
242:
215:
195:
142:
40:improve this article
1040:Murphy, KP (2012).
813:
793:
743:
643:
590:
560:
533:
474:
454:
427:
383:
356:
325:
303:
228:
201:
181:
1016:
1015:
902:
901:
784:
775:stochastic matrix
765:values, create a
477:{\displaystyle M}
328:{\displaystyle |}
204:{\displaystyle K}
116:
115:
108:
90:
1069:
1046:
1045:
1044:. The MIT Press.
1037:
971:
845:
829:binary variables
822:
820:
819:
814:
806:
805:
792:
752:
750:
749:
744:
739:
738:
720:
719:
707:
706:
694:
693:
681:
680:
652:
650:
649:
644:
639:
638:
626:
625:
616:
615:
599:
597:
596:
591:
586:
585:
569:
567:
566:
561:
559:
558:
542:
540:
539:
534:
532:
531:
513:
512:
500:
499:
483:
481:
480:
475:
463:
461:
460:
455:
453:
452:
436:
434:
433:
428:
423:
422:
409:
408:
392:
390:
389:
384:
382:
381:
366:of the variable
365:
363:
362:
357:
355:
354:
339:possible values
334:
332:
331:
326:
324:
312:
310:
309:
304:
299:
298:
286:
285:
273:
272:
260:
259:
237:
235:
234:
229:
227:
226:
210:
208:
207:
202:
190:
188:
187:
182:
180:
179:
167:
166:
154:
153:
131:random variables
111:
104:
100:
97:
91:
89:
48:
24:
16:
1077:
1076:
1072:
1071:
1070:
1068:
1067:
1066:
1052:
1051:
1050:
1049:
1039:
1038:
1034:
1029:
995:P(y=1 given x)
984:P(y=0 given x)
794:
779:
778:
727:
711:
698:
685:
672:
661:
660:
630:
617:
607:
602:
601:
577:
572:
571:
550:
545:
544:
523:
504:
491:
486:
485:
466:
465:
444:
439:
438:
437:This table has
414:
400:
395:
394:
373:
368:
367:
346:
341:
340:
315:
314:
290:
277:
264:
251:
240:
239:
218:
213:
212:
193:
192:
191:where each has
171:
158:
145:
140:
139:
112:
101:
95:
92:
49:
47:
37:
25:
12:
11:
5:
1075:
1073:
1065:
1064:
1054:
1053:
1048:
1047:
1031:
1030:
1028:
1025:
1014:
1013:
1010:
1007:
1003:
1002:
999:
996:
992:
991:
988:
985:
981:
980:
977:
974:
952:=1 given that
900:
899:
896:
893:
890:
886:
885:
882:
879:
876:
872:
871:
868:
865:
862:
858:
857:
854:
851:
848:
812:
809:
804:
801:
797:
791:
787:
742:
737:
734:
730:
726:
723:
718:
714:
710:
705:
701:
697:
692:
688:
684:
679:
675:
671:
668:
642:
637:
633:
629:
624:
620:
614:
610:
589:
584:
580:
557:
553:
530:
526:
522:
519:
516:
511:
507:
503:
498:
494:
473:
451:
447:
426:
421:
417:
412:
407:
403:
380:
376:
353:
349:
323:
302:
297:
293:
289:
284:
280:
276:
271:
267:
263:
258:
254:
250:
247:
225:
221:
200:
178:
174:
170:
165:
161:
157:
152:
148:
114:
113:
28:
26:
19:
13:
10:
9:
6:
4:
3:
2:
1074:
1063:
1060:
1059:
1057:
1043:
1036:
1033:
1026:
1024:
1020:
1011:
1008:
1005:
1004:
1000:
997:
994:
993:
989:
986:
983:
982:
978:
975:
973:
972:
969:
967:
963:
959:
955:
951:
947:
943:
939:
935:
931:
927:
923:
919:
915:
911:
907:
897:
894:
891:
888:
887:
883:
880:
877:
874:
873:
869:
866:
863:
860:
859:
855:
852:
849:
847:
846:
843:
841:
837:
833:
830:
826:
810:
807:
802:
799:
795:
789:
785:
776:
772:
768:
764:
761:ranging over
760:
756:
740:
735:
732:
728:
724:
716:
712:
708:
703:
699:
695:
690:
686:
682:
677:
673:
666:
658:
653:
640:
635:
631:
627:
622:
618:
612:
608:
587:
582:
578:
555:
551:
528:
524:
520:
517:
514:
509:
505:
501:
496:
492:
471:
449:
445:
424:
419:
415:
410:
405:
401:
378:
374:
351:
347:
338:
295:
291:
287:
282:
278:
274:
269:
265:
261:
256:
252:
245:
223:
219:
198:
176:
172:
168:
163:
159:
155:
150:
146:
136:
132:
129:
125:
121:
110:
107:
99:
96:December 2013
88:
85:
81:
78:
74:
71:
67:
64:
60:
57: –
56:
52:
51:Find sources:
45:
41:
35:
34:
29:This article
27:
23:
18:
17:
1041:
1035:
1021:
1017:
965:
961:
957:
953:
949:
945:
941:
937:
933:
929:
925:
917:
913:
909:
905:
903:
835:
831:
824:
770:
766:
762:
758:
754:
654:
336:
123:
117:
102:
93:
83:
76:
69:
62:
50:
38:Please help
33:verification
30:
133:to display
1027:References
484:variables
120:statistics
66:newspapers
838:have the
786:∑
696:∣
628:⋯
518:…
275:∣
128:dependent
1056:Category
823:for all
916:=0 and
80:scholar
657:matrix
122:, the
82:
75:
68:
61:
53:
936:that
934:given
924:that
889:P(x)
856:P(y)
753:with
543:with
87:JSTOR
73:books
1006:Sum
1001:2/3
990:1/3
979:x=1
908:and
884:4/9
875:y=1
870:5/9
861:y=0
834:and
757:and
59:news
998:2/6
987:4/6
976:x=0
932:=0
895:3/9
892:6/9
881:2/9
878:2/9
867:1/9
864:4/9
853:x=1
850:x=0
118:In
42:by
1058::
1012:1
968::
898:1
1009:1
966:y
962:x
958:y
954:x
950:y
946:y
942:x
938:x
930:y
926:x
918:y
914:x
910:y
906:x
836:y
832:x
825:j
811:1
808:=
803:j
800:k
796:T
790:k
771:K
769:×
767:K
763:K
759:j
755:k
741:,
736:j
733:k
729:T
725:=
722:)
717:j
713:b
709:=
704:2
700:x
691:k
687:a
683:=
678:1
674:x
670:(
667:P
641:.
636:M
632:K
623:2
619:K
613:1
609:K
588:,
583:i
579:x
556:i
552:K
529:M
525:x
521:,
515:,
510:2
506:x
502:,
497:1
493:x
472:M
450:3
446:K
425:.
420:3
416:x
411:,
406:2
402:x
379:1
375:x
352:k
348:a
337:K
322:|
301:)
296:3
292:x
288:,
283:2
279:x
270:k
266:a
262:=
257:1
253:x
249:(
246:P
224:1
220:x
199:K
177:3
173:x
169:,
164:2
160:x
156:,
151:1
147:x
109:)
103:(
98:)
94:(
84:·
77:·
70:·
63:·
36:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
