\u00d6rne\u011fin, yeni meydana gelen bir “B” olay\u0131n\u0131n muhasebele\u015ftirilmesinden sonra “A” olay\u0131n\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131 ilgimizi \u00e7ekebilir. Bu sonsal olas\u0131l\u0131\u011f\u0131 a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanarak hesaplayabiliriz:<\/span><\/p>\n P(A|B)<\/strong> = P(A) * P(B|A) \/ P(B)<\/span><\/p>\n Alt\u0131n:<\/span><\/p>\n P(A|B) = B olay\u0131n\u0131n meydana geldi\u011fi g\u00f6z \u00f6n\u00fcne al\u0131nd\u0131\u011f\u0131nda, A olay\u0131n\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131. \u201c| \u00bb \u201cverilen\u201d anlam\u0131na gelir.<\/span><\/p>\n P(A) = A olay\u0131n\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131.<\/span><\/p>\n P(B) = B olay\u0131n\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131.<\/span><\/p>\n P(B|A) = A olay\u0131n\u0131n meydana geldi\u011fi g\u00f6z \u00f6n\u00fcne al\u0131nd\u0131\u011f\u0131nda, B olay\u0131n\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131.<\/span><\/p>\n Bir orman\u0131n %20’si me\u015fe, %80’i ak\u00e7aa\u011fa\u00e7lardan olu\u015fur. Me\u015fe a\u011fa\u00e7lar\u0131n\u0131n %90’\u0131n\u0131n sa\u011fl\u0131kl\u0131, ak\u00e7aa\u011fa\u00e7lar\u0131n ise yaln\u0131zca %50’sinin sa\u011fl\u0131kl\u0131 oldu\u011funu bildi\u011fimizi varsayal\u0131m.<\/span> Belirli bir a\u011fac\u0131n sa\u011fl\u0131kl\u0131 oldu\u011funu uzaktan s\u00f6yleyebildi\u011finizi varsayal\u0131m. A\u011fac\u0131n me\u015fe olma olas\u0131l\u0131\u011f\u0131 nedir?<\/span><\/p>\n B olay\u0131n\u0131n meydana geldi\u011fi dikkate al\u0131nd\u0131\u011f\u0131nda A olay\u0131n\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131n \u015f\u00f6yle oldu\u011funu hat\u0131rlay\u0131n:<\/span><\/p>\n P(A|B) = P(A) * P(B|A) \/ P(B)<\/span><\/p>\n Bu \u00f6rnekte a\u011fac\u0131n sa\u011fl\u0131kl\u0131 olmas\u0131 durumunda a\u011fac\u0131n me\u015fe olma olas\u0131l\u0131\u011f\u0131:<\/span><\/p>\n P(Me\u015fe|Sa\u011fl\u0131kl\u0131) = P(Me\u015fe) * P(Sa\u011fl\u0131kl\u0131|Me\u015fe) \/ P(Sa\u011fl\u0131kl\u0131)<\/span><\/p>\n P(Me\u015fe) = Belirli bir a\u011fac\u0131n me\u015fe olma olas\u0131l\u0131\u011f\u0131 0,2’dir<\/strong> \u00e7\u00fcnk\u00fc ormandaki t\u00fcm a\u011fa\u00e7lar\u0131n %20’si me\u015fedir.<\/span><\/p>\n P(Sa\u011fl\u0131kl\u0131) = Belirli bir a\u011fac\u0131n sa\u011fl\u0131kl\u0131 olma olas\u0131l\u0131\u011f\u0131 \u015fu \u015fekilde hesaplanabilir: (0,20)*(0,9) + (0,8)*(0,5) = 0,58<\/strong> .<\/span><\/p>\n P(Sa\u011fl\u0131kl\u0131|Me\u015fe) = Bir a\u011fac\u0131n me\u015fe oldu\u011fu dikkate al\u0131nd\u0131\u011f\u0131nda sa\u011fl\u0131kl\u0131 olma olas\u0131l\u0131\u011f\u0131 0,9’dur<\/strong> , \u00e7\u00fcnk\u00fc bize me\u015felerin %90’\u0131n\u0131n sa\u011fl\u0131kl\u0131 oldu\u011fu s\u00f6ylenmi\u015ftir.<\/span><\/p>\n Bu \u00fc\u00e7 say\u0131y\u0131 kullanarak a\u011fac\u0131n sa\u011fl\u0131kl\u0131 olmas\u0131 ko\u015fuluyla me\u015fe olma olas\u0131l\u0131\u011f\u0131n\u0131 bulabiliriz:<\/span><\/p>\n P(Me\u015fe|Sa\u011fl\u0131kl\u0131) = P(Me\u015fe) * P(Sa\u011fl\u0131kl\u0131|Me\u015fe) \/ P(Sa\u011fl\u0131kl\u0131) = (0,2) * (0,9) \/ (0,58) = 0,3103<\/strong> .<\/span><\/p>\n Bu olas\u0131l\u0131\u011f\u0131n sezgisel olarak anla\u015f\u0131lmas\u0131 i\u00e7in a\u015fa\u011f\u0131daki tablonun 100 a\u011fa\u00e7tan olu\u015fan bu orman\u0131 temsil etti\u011fini varsayal\u0131m. A\u011fa\u00e7lar\u0131n tam 20’si me\u015fe, 18’i sa\u011fl\u0131kl\u0131. Di\u011fer 80 a\u011fa\u00e7 ise ak\u00e7aa\u011fa\u00e7 olup 40 tanesi sa\u011fl\u0131kl\u0131d\u0131r.<\/span><\/p>\n (O = Me\u015fe, M = Ak\u00e7aa\u011fa\u00e7, Ye\u015fil = Sa\u011fl\u0131kl\u0131, K\u0131rm\u0131z\u0131 = Sa\u011fl\u0131ks\u0131z)<\/span> <\/p>\n T\u00fcm a\u011fa\u00e7lar\u0131n tam olarak 58’i sa\u011fl\u0131kl\u0131 ve bu sa\u011fl\u0131kl\u0131 a\u011fa\u00e7lar\u0131n 18’i me\u015fedir. Yani sa\u011fl\u0131kl\u0131 bir a\u011fa\u00e7 se\u00e7ti\u011fimizi biliyorsak, bunun me\u015fe olma olas\u0131l\u0131\u011f\u0131 18\/58 = 0,3103’t\u00fcr<\/strong> .<\/span><\/p>\n Arka olas\u0131l\u0131k, finans, t\u0131p, ekonomi ve hava tahmini dahil olmak \u00fczere \u00e7ok \u00e7e\u015fitli alanlarda kullan\u0131lmaktad\u0131r.<\/span><\/p>\n Sonsal olas\u0131l\u0131klar\u0131 kullanman\u0131n amac\u0131, yeni bir bilgi elde etti\u011fimizde bir \u015fey hakk\u0131nda sahip oldu\u011fumuz \u00f6nceki inanc\u0131m\u0131z\u0131 g\u00fcncellemektir.<\/span><\/p>\n \u00d6nceki \u00f6rnekten ormandaki belirli bir a\u011fac\u0131n me\u015fe olma olas\u0131l\u0131\u011f\u0131n\u0131n %20 oldu\u011funu bildi\u011fimizi hat\u0131rlay\u0131n. Buna \u00f6n olas\u0131l\u0131k<\/strong> denir. E\u011fer rastgele bir a\u011fa\u00e7 se\u00e7seydik, onun me\u015fe olma ihtimalinin 0,20 oldu\u011funu biliyorduk.<\/span><\/p>\n Ancak, se\u00e7ti\u011fimiz a\u011fac\u0131n sa\u011fl\u0131kl\u0131 oldu\u011funa dair yeni bilgiyi ald\u0131ktan sonra, bu yeni bilgiyi kullanarak bu a\u011fac\u0131n me\u015fe olma olas\u0131l\u0131\u011f\u0131n\u0131n<\/strong> 0,3103 oldu\u011funu belirleyebildik.<\/span><\/p>\n Ger\u00e7ek d\u00fcnyada insanlar s\u00fcrekli olarak yeni bilgiler ke\u015ffediyorlar. Bu yeni bilgi \u00f6nceki inan\u00e7lar\u0131m\u0131z\u0131 g\u00fcncellememize yard\u0131mc\u0131 olur. \u0130statistiksel a\u00e7\u0131dan bu, meydana gelen olaylar\u0131n arka olas\u0131l\u0131klar\u0131n\u0131 \u00fcretebildi\u011fimiz anlam\u0131na gelir; bu da d\u00fcnyay\u0131 daha do\u011fru bir \u015fekilde anlamam\u0131za yard\u0131mc\u0131 olur ve gelecekteki olaylar hakk\u0131nda daha do\u011fru tahminler yapmam\u0131za olanak tan\u0131r.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":" A posteriori olas\u0131l\u0131k, yeni bilgiler dikkate al\u0131nd\u0131ktan sonra bir olay\u0131n meydana gelme ihtimalinin g\u00fcncellenmi\u015f halidir. \u00d6rne\u011fin, yeni meydana gelen bir “B” olay\u0131n\u0131n muhasebele\u015ftirilmesinden sonra “A” olay\u0131n\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131 ilgimizi \u00e7ekebilir. Bu sonsal olas\u0131l\u0131\u011f\u0131 a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanarak hesaplayabiliriz: P(A|B) = P(A) * P(B|A) \/ P(B) Alt\u0131n: P(A|B) = B olay\u0131n\u0131n meydana geldi\u011fi g\u00f6z \u00f6n\u00fcne al\u0131nd\u0131\u011f\u0131nda, […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-586","post","type-post","status-publish","format-standard","hentry","category-rehber"],"yoast_head":"\n \u00d6rnek: Son olas\u0131l\u0131\u011f\u0131n hesaplanmas\u0131<\/strong><\/span><\/h2>\n
![\"Arka](\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/posterieur_prob0.png\")
<\/p>\n Posterior olas\u0131l\u0131\u011f\u0131 ne zaman kullanmal\u0131s\u0131n\u0131z?<\/strong><\/span><\/h2>\n