{"id":379,"date":"2023-08-01T12:09:39","date_gmt":"2023-08-01T12:09:39","guid":{"rendered":"https:\/\/statorials.org\/tr\/bayes-teoremi\/"},"modified":"2023-08-01T12:09:39","modified_gmt":"2023-08-01T12:09:39","slug":"bayes-teoremi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/bayes-teoremi\/","title":{"rendered":"Bayes teoremi"},"content":{"rendered":"<p>Bu makale Bayes teoreminin ne oldu\u011funu ve olas\u0131l\u0131k ve istatistikte ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131n\u0131 a\u00e7\u0131klamaktad\u0131r. B\u00f6ylece Bayes teoreminin form\u00fcl\u00fcn\u00fcn ne oldu\u011funu, Bayes teoreminin \u00e7\u00f6z\u00fcml\u00fc \u00f6rneklerini ve bu teoremin uygulamalar\u0131n\u0131n neler oldu\u011funu ke\u015ffedeceksiniz.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-el-teorema-de-bayes\"><\/span> Bayes teoremi nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Olas\u0131l\u0131k teorisinde <strong>Bayes teoremi<\/strong> , bir olay hakk\u0131nda \u00f6nceden bilgi bilindi\u011finde o olay\u0131n olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in kullan\u0131lan bir yasad\u0131r.<\/p>\n<p> Daha spesifik olarak Bayes teoremi, A olay\u0131n\u0131n belirli bir B olay\u0131n\u0131n olas\u0131l\u0131\u011f\u0131n\u0131, belirli bir A olay\u0131n\u0131n olas\u0131l\u0131\u011f\u0131 ile matematiksel olarak ili\u015fkilendirir.<\/p>\n<p> \u00d6rne\u011fin, bir ki\u015finin grip oldu\u011funda ba\u015f a\u011fr\u0131s\u0131 ya\u015fama olas\u0131l\u0131\u011f\u0131n\u0131 \u00f6nceden biliyorsan\u0131z, bir ki\u015finin ba\u015f a\u011fr\u0131s\u0131 oldu\u011funda grip olma olas\u0131l\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in Bayes teoremini kullanabilirsiniz.<\/p>\n<p> Bayes teoreminin pek \u00e7ok uygulamas\u0131 vard\u0131r; \u00f6rne\u011fin t\u0131pta, ekonomide veya teknolojide ba\u015fka olaylar taraf\u0131ndan ko\u015fulland\u0131r\u0131lan belirli olaylar\u0131n olas\u0131l\u0131klar\u0131n\u0131 hesaplamak i\u00e7in kullan\u0131l\u0131r. A\u015fa\u011f\u0131da Bayes teoreminin farkl\u0131 uygulamalar\u0131 hakk\u0131nda ayr\u0131nt\u0131l\u0131 bilgi verece\u011fiz.<\/p>\n<p> Bayes teoremi \u0130ngiliz matematik\u00e7i Thomas Bayes (1702-1761) taraf\u0131ndan icat edildi, ancak \u00f6l\u00fcm\u00fcnden sonra 1763&#8217;te yay\u0131nland\u0131. <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Bak\u0131n\u0131z:<\/strong> <a href=\"https:\/\/statorials.org\/tr\/kosullu-kosullu-olasilik\/\">Ko\u015fullu olas\u0131l\u0131k<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-del-teorema-de-bayes\"><\/span> Bayes teoreminin form\u00fcl\u00fc<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Bayes teoremi, olas\u0131l\u0131klar\u0131 s\u0131f\u0131r olmayan bir dizi <a href=\"https:\/\/statorials.org\/tr\/birbirini-dislayan-olaylar\/\">birbirini d\u0131\u015flayan olaylardan<\/a> (A <sub>1<\/sub> , A <sub>2<\/sub> ,\u2026, A <sub>i<\/sub> ,\u2026, A <sub>n<\/sub> ) ve ba\u015fka bir B olay\u0131ndan olu\u015fan bir \u00f6rnek uzay verildi\u011finde, ko\u015fullu durumu matematiksel olarak ili\u015fkilendirebilece\u011fimizi s\u00f6yler. B olay\u0131 verildi\u011finde A <sub>i&#8217;nin<\/sub> olas\u0131l\u0131\u011f\u0131 ve A <sub>i<\/sub> verildi\u011finde B&#8217;nin ko\u015fullu olas\u0131l\u0131\u011f\u0131.<\/p>\n<p> <strong>Bayes kural\u0131<\/strong> olarak da bilinen <strong>Bayes teoreminin form\u00fcl\u00fc<\/strong> \u015f\u00f6yledir: <\/p>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/theoreme-de-bayes.png\" alt=\"Bayes teoreminin form\u00fcl\u00fc, Bayes kural\u0131\" class=\"wp-image-8514\" width=\"370\" height=\"318\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p style=\"margin-bottom:7px\"> Alt\u0131n:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:8px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-62ffcdb184381914ec23155ad31bbfb0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A_i|B)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"65\" style=\"vertical-align: -5px;\"><\/p>\n<p> B olay\u0131 <sub>verildi\u011finde<\/sub> A olay\u0131n\u0131n ko\u015fullu olas\u0131l\u0131\u011f\u0131d\u0131r ve son olas\u0131l\u0131k olarak adland\u0131r\u0131l\u0131r.<\/li>\n<li style=\"margin-bottom:8px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-676b61239ea67554603513360fbea72b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(B|A_i)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"65\" style=\"vertical-align: -5px;\"><\/p>\n<p> A <sub>i<\/sub> olay\u0131 g\u00f6z \u00f6n\u00fcne al\u0131nd\u0131\u011f\u0131nda B olay\u0131n\u0131n ko\u015fullu olas\u0131l\u0131\u011f\u0131d\u0131r.<\/li>\n<li style=\"margin-bottom:8px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-be31252343b496b792bee3e55a99979f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A_i)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"46\" style=\"vertical-align: -5px;\"><\/p>\n<p> a priori olas\u0131l\u0131k olarak adland\u0131r\u0131lan, A <sub>i<\/sub> olay\u0131n\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131d\u0131r.<\/li>\n<\/ul>\n<p> Bayes teoremi form\u00fcl\u00fcn\u00fcn paydas\u0131n\u0131n B olay\u0131n\u0131n <a href=\"https:\/\/statorials.org\/tr\/toplam-olasilik-teoremi\/\">toplam olas\u0131l\u0131\u011f\u0131<\/a> oldu\u011funa dikkat edin. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-del-teorema-de-bayes\"><\/span> Bayes teoreminin \u00f6rne\u011fi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Bayes Teoreminin tan\u0131m\u0131n\u0131 ve form\u00fcl\u00fcn\u00fcn ne oldu\u011funu g\u00f6rd\u00fckten sonra kavram\u0131 daha iyi anlamak i\u00e7in Bayes Teoremi ile bir olas\u0131l\u0131\u011f\u0131n nas\u0131l hesapland\u0131\u011f\u0131na dair \u00e7\u00f6z\u00fcml\u00fc bir \u00f6rnek g\u00f6rece\u011fiz.<\/p>\n<ul>\n<li> Bir elektronik ma\u011fazas\u0131nda X, Y, Z olmak \u00fczere \u00fc\u00e7 marka televizyon sat\u0131lmaktad\u0131r. Sat\u0131\u015flar\u0131n %20&#8217;sinin ar\u0131zal\u0131 marka televizyonlar oldu\u011fu, Y marka televizyonlar\u0131n %3&#8217;\u00fcn\u00fcn ar\u0131zal\u0131, Z marka televizyonlar\u0131n ise %4&#8217;\u00fcn\u00fcn ar\u0131zal\u0131 oldu\u011fu tahmin edilmektedir. Ar\u0131zal\u0131 bir TV verildi\u011finde onun Z Marka TV olma olas\u0131l\u0131\u011f\u0131 nedir?<\/li>\n<\/ul>\n<p> Al\u0131\u015ft\u0131rma bize bir m\u00fc\u015fterinin her marka televizyonu sat\u0131n alma olas\u0131l\u0131\u011f\u0131n\u0131 veriyor:<\/p>\n<ul>\n<li> Olay A <sub>1<\/sub> : Bir m\u00fc\u015fteri X marka televizyon sat\u0131n al\u0131yor \u2192 P(A <sub>1<\/sub> )=0,20<\/li>\n<li> Olay A <sub>2<\/sub> : Bir m\u00fc\u015fteri Y marka televizyon sat\u0131n al\u0131yor \u2192 P(A <sub>2<\/sub> )=0,50<\/li>\n<li> Olay A <sub>3<\/sub> : Bir m\u00fc\u015fteri Z marka televizyon sat\u0131n al\u0131yor \u2192 P(A <sub>3<\/sub> )=0,30<\/li>\n<\/ul>\n<p> Ayr\u0131ca okuma bize her markan\u0131n televizyonunun ar\u0131zal\u0131 olma olas\u0131l\u0131\u011f\u0131n\u0131 da veriyor:<\/p>\n<p class=\"has-text-align-center\"> Olay B: TV ar\u0131zal\u0131<\/p>\n<ul>\n<li> B|A <sub>1<\/sub> : X marka televizyon verildi\u011finde televizyon ar\u0131zal\u0131d\u0131r \u2192 P(B|A <sub>1<\/sub> )=0,05<\/li>\n<li> B|A <sub>2<\/sub> : Y marka televizyon verildi\u011finde televizyon ar\u0131zal\u0131d\u0131r \u2192 P(B|A <sub>2<\/sub> )=0,03<\/li>\n<li> B|A <sub>3<\/sub> : Z marka televizyon verildi\u011finde televizyon ar\u0131zal\u0131d\u0131r \u2192 P(B|A <sub>3<\/sub> )=0,04<\/li>\n<\/ul>\n<p> Yani bizi ilgilendiren t\u00fcm olaylar\u0131n <a href=\"https:\/\/statorials.org\/tr\/agac-diyagrami\/\">olas\u0131l\u0131k a\u011fac\u0131<\/a> \u015fu \u015fekildedir: <\/p>\n<figure class=\"wp-block-image aligncenter size-full\"><img decoding=\"async\" loading=\"lazy\" width=\"370\" height=\"257\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/theoreme-de-probabilite-de-bayes.png\" alt=\"Bayes teoremi a\u011fa\u00e7 diyagram\u0131\" class=\"wp-image-8525\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Dolay\u0131s\u0131yla, ar\u0131zal\u0131 bir televizyonun Z markas\u0131 olma olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in Bayes teoremindeki form\u00fcl\u00fc kullanmal\u0131y\u0131z:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-c15e369635dcf17952b5d832a818d535_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A_i|B)=\\cfrac{P(B|A_i)\\cdot P(A_i)}{\\displaystyle \\sum_{k=1}^n P(B|A_k)\\cdot P(A_k)}\" title=\"Rendered by QuickLaTeX.com\" height=\"77\" width=\"251\" style=\"vertical-align: -49px;\"><\/p>\n<\/p>\n<p> Bu \u00f6rnekte kullan\u0131lan terminolojiyi kullan\u0131rsak Bayes&#8217;in form\u00fcl\u00fc \u015funa benzer:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-7c2b74ac3ed5173c4a40837675d8282d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A_3|B)=\\cfrac{P(B|A_3)\\cdot P(A_3)}{P(B|A_1)\\cdot P(A_1)+P(B|A_2)\\cdot P(A_2)+ P(B|A_3)\\cdot P(A_3)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"525\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Buna g\u00f6re belirli bir ar\u0131zal\u0131 televizyonun Z marka olma ihtimalinin hesaplanmas\u0131 \u015fu \u015fekildedir:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-818d0f3336f855a1315d6a94f01d1876_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}P(A_3|B)&amp;=\\cfrac{P(B|A_3)\\cdot P(A_3)}{P(B|A_1)\\cdot P(A_1)+P(B|A_2)\\cdot P(A_2)+ P(B|A_3)\\cdot P(A_3)}\\\\[2ex]&amp;=\\cfrac{0,04\\cdot 0,30}{0,05\\cdot 0,20+0,03\\cdot 0,50+0,04\\cdot 0,30}\\\\[2ex]&amp;=0,32\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"151\" width=\"525\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Sonu\u00e7 olarak bir televizyonun ar\u0131zal\u0131 olmas\u0131 durumunda Z marka olma ihtimali %32&#8217;dir. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"aplicaciones-del-teorema-de-bayes\"><\/span> Bayes teoreminin uygulamalar\u0131<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Bayes teoreminin a\u015fa\u011f\u0131dakiler dahil bir\u00e7ok uygulamas\u0131 vard\u0131r:<\/p>\n<ol style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>T\u0131bbi Testler<\/strong> : Bayes teoremi t\u0131pta tan\u0131 testlerini ge\u00e7me olas\u0131l\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in s\u0131kl\u0131kla kullan\u0131l\u0131r. \u00d6rne\u011fin, HIV testi s\u00f6z konusu oldu\u011funda teorem, test sonucunun pozitif olmas\u0131 durumunda ki\u015finin ger\u00e7ekten vir\u00fcse sahip olma olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in kullan\u0131labilir.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Finansal Analiz<\/strong> : Finansta, Bayes teoremi, bir dizi ekonomik de\u011fi\u015fken g\u00f6z \u00f6n\u00fcne al\u0131nd\u0131\u011f\u0131nda, hisse senedi de\u011ferindeki art\u0131\u015f veya azal\u0131\u015f gibi belirli ekonomik olaylar\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in kullan\u0131l\u0131r.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Pazar ara\u015ft\u0131rmas\u0131<\/strong> : Bayes teoremi, \u00f6rne\u011fin bir ki\u015finin bu \u00fcr\u00fcn\u00fcn reklam\u0131n\u0131 g\u00f6rd\u00fckten sonra o \u00fcr\u00fcn\u00fc sat\u0131n alma olas\u0131l\u0131\u011f\u0131n\u0131 belirlemeyi m\u00fcmk\u00fcn k\u0131lar.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Hava tahmini<\/strong> : Hava durumu modelleri ayn\u0131 zamanda Bayes teoremini kullanarak g\u00f6zlemlenen verilere dayanan belirli bir hava tahmininin ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131n\u0131 belirler. Bu, iklim tahminlerinin do\u011frulu\u011funu art\u0131r\u0131r.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Bilgisayar G\u00fcvenli\u011fi<\/strong> \u2013 Siber g\u00fcvenlikte, \u015f\u00fcpheli bir etkinli\u011fin ger\u00e7ekten bilgisayar sistemine y\u00f6nelik bir sald\u0131r\u0131 olma olas\u0131l\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in Bayes teoremi uygulanabilir.<\/span> <\/li>\n<\/ol>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-del-teorema-de-bayes\"><\/span> \u00c7\u00f6z\u00fclm\u00fc\u015f Bayes Teoremi Problemleri<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> 1. Egzersiz<\/h3>\n<p> N\u00fcfusun %1&#8217;inin baz\u0131 hastal\u0131klardan muzdarip oldu\u011fu tahmin edilmektedir. Bu hastal\u0131\u011f\u0131 tespit etmek i\u00e7in yap\u0131lan bir test pozitif vakalarda %95, negatif vakalarda ise %90 do\u011frudur. Rastgele se\u00e7ilen bir ki\u015finin testi pozitif \u00e7\u0131karsa, bu ki\u015finin ger\u00e7ekten hastal\u0131\u011fa sahip olma olas\u0131l\u0131\u011f\u0131 nedir? <\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__FFF8E1\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#FFF8E1\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u00c7\u00f6z\u00fcm\u00fc g\u00f6r\u00fcn<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Al\u0131\u015ft\u0131rma ifadesi bize a\u015fa\u011f\u0131daki olas\u0131l\u0131klar\u0131 verir:<\/p>\n<p class=\"has-text-align-center\"> A <sub>1<\/sub> : Ki\u015fide hastal\u0131k var \u2192 P(A <sub>1<\/sub> )=0,01<br \/> A <sub>2<\/sub> : Ki\u015fide hastal\u0131k bulunmuyor \u2192 P(A <sub>2<\/sub> )=0,99<\/p>\n<p class=\"has-text-align-center\"> B: Test pozitif<br \/> B|A <sub>1<\/sub> : Ki\u015fide hastal\u0131k varsa test pozitiftir \u2192 P(B|A <sub>1<\/sub> )=0,95<br \/> B|A <sub>2<\/sub> : Ki\u015fide hastal\u0131k olmad\u0131\u011f\u0131nda test pozitiftir \u2192 P(B|A <sub>2<\/sub> )=1-0.90=0.10<\/p>\n<p class=\"has-text-align-left\"> Daha sonra, rastgele se\u00e7ilen bir ki\u015finin testi pozitif \u00e7\u0131kt\u0131\u011f\u0131nda ger\u00e7ekten hastal\u0131\u011fa sahip olma olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in Bayes kural\u0131 uygulanmal\u0131d\u0131r: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-c15e369635dcf17952b5d832a818d535_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A_i|B)=\\cfrac{P(B|A_i)\\cdot P(A_i)}{\\displaystyle \\sum_{k=1}^n P(B|A_k)\\cdot P(A_k)}\" title=\"Rendered by QuickLaTeX.com\" height=\"77\" width=\"251\" style=\"vertical-align: -49px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-d76df126cb6076aeba65aa7d1c12e344_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A_1|B)=\\cfrac{P(B|A_1)\\cdot P(A_1)}{P(B|A_1)\\cdot P(A_1)+P(B|A_2)\\cdot P(A_2)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"374\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> B\u00f6ylece de\u011ferleri form\u00fclde yerine koyuyoruz ve olas\u0131l\u0131k hesaplamas\u0131n\u0131 ger\u00e7ekle\u015ftiriyoruz:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-135e9ab7de6b44e7392fae0f5e70a125_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}P(A_1|B)&amp;=\\cfrac{P(B|A_1)\\cdot P(A_1)}{P(B|A_1)\\cdot P(A_1)+P(B|A_2)\\cdot P(A_2)}\\\\[2ex]&amp;=\\cfrac{0,95\\cdot 0,01}{0,95\\cdot 0,01+0,10\\cdot 0,99}\\\\[2ex]&amp;=0,0876\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"151\" width=\"374\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> K\u0131sacas\u0131 rastgele se\u00e7ilen bir ki\u015finin testinin pozitif \u00e7\u0131kmas\u0131 ve ger\u00e7ekten hastal\u0131\u011fa sahip olma ihtimali %8,76&#8217;d\u0131r.<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\"> Al\u0131\u015ft\u0131rma 2<\/h3>\n<p> Bir hisse senedinin bir g\u00fcn i\u00e7erisinde y\u00fckselme ihtimali %40, sabit kalma ihtimali %10, d\u00fc\u015fme ihtimali ise %50 olarak tahmin edilmektedir. Ayr\u0131ca, piyasa y\u00fckseldi\u011finde finansal analistin bunu do\u011fru tahmin etme olas\u0131l\u0131\u011f\u0131n\u0131n %90 oldu\u011funu, piyasa sabit kald\u0131\u011f\u0131nda tahminin do\u011fru olma olas\u0131l\u0131\u011f\u0131n\u0131n %75 oldu\u011funu, d\u00fc\u015f\u00fc\u015f durumunda ise tahminin do\u011fru olma olas\u0131l\u0131\u011f\u0131n\u0131n %75 oldu\u011funu biliyoruz. Do\u011fru tahmin olas\u0131l\u0131\u011f\u0131 %75&#8217;tir. %85.%. Bir analist piyasan\u0131n d\u00fc\u015fece\u011fini \u00f6ng\u00f6r\u00fcyorsa, ger\u00e7ekte d\u00fc\u015fme olas\u0131l\u0131\u011f\u0131 ne kadard\u0131r? <\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__FFF8E1\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#FFF8E1\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u00c7\u00f6z\u00fcm\u00fc g\u00f6r\u00fcn<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Bu durumda, al\u0131\u015ft\u0131rma ifadesi bize a\u015fa\u011f\u0131daki olas\u0131l\u0131klar\u0131 sa\u011flar:<\/p>\n<p class=\"has-text-align-center\"> A <sub>1<\/sub> : Piyasa bir g\u00fcnde y\u00fckselir \u2192 P(A <sub>1<\/sub> )=0,40<br \/> A <sub>2<\/sub> : Piyasa bir g\u00fcn boyunca sabit kal\u0131r \u2192 P(A <sub>2<\/sub> )=0,10<br \/> A <sub>3<\/sub> : Piyasa bir g\u00fcnde y\u00fckselir \u2192 P(A <sub>3<\/sub> )=0,50<\/p>\n<p class=\"has-text-align-center\"> B: Analist piyasan\u0131n d\u00fc\u015fece\u011fini \u00f6ng\u00f6r\u00fcyor<br \/> B|A <sub>1<\/sub> : Analist piyasan\u0131n artaca\u011f\u0131n\u0131 do\u011fru bir \u015fekilde tahmin ediyor \u2192 P(B|A <sub>1<\/sub> )=0,90<br \/> B|A <sub>2<\/sub> : Analist piyasan\u0131n istikrarl\u0131 kalaca\u011f\u0131n\u0131 do\u011fru bir \u015fekilde tahmin ediyor \u2192 P(B|A <sub>2<\/sub> )=0,75<br \/> B|A <sub>3<\/sub> : Analist piyasan\u0131n d\u00fc\u015fece\u011fini do\u011fru bir \u015fekilde tahmin ediyor \u2192 P(B|A <sub>3<\/sub> )=0,85<\/p>\n<p class=\"has-text-align-left\"> Bir analistin piyasan\u0131n d\u00fc\u015fece\u011fine dair bir tahminde bulunma ve bunun do\u011fru olma olas\u0131l\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in Bayes Teoremi form\u00fcl\u00fcn\u00fc kullanmam\u0131z gerekir: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-c15e369635dcf17952b5d832a818d535_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A_i|B)=\\cfrac{P(B|A_i)\\cdot P(A_i)}{\\displaystyle \\sum_{k=1}^n P(B|A_k)\\cdot P(A_k)}\" title=\"Rendered by QuickLaTeX.com\" height=\"77\" width=\"251\" style=\"vertical-align: -49px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-7c2b74ac3ed5173c4a40837675d8282d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A_3|B)=\\cfrac{P(B|A_3)\\cdot P(A_3)}{P(B|A_1)\\cdot P(A_1)+P(B|A_2)\\cdot P(A_2)+ P(B|A_3)\\cdot P(A_3)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"525\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Olas\u0131l\u0131k de\u011ferlerini Bayes form\u00fcl\u00fcne koyar\u0131z ve olas\u0131l\u0131\u011f\u0131 hesaplar\u0131z:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-9f98a5a8a91299aa55aab02159dcebec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}P(A_3|B)&amp;=\\cfrac{P(B|A_3)\\cdot P(A_3)}{P(B|A_1)\\cdot P(A_1)+P(B|A_2)\\cdot P(A_2)+ P(B|A_3)\\cdot P(A_3)}\\\\[2ex]&amp;=\\cfrac{0,85\\cdot 0,50}{0,90\\cdot 0,40+0,75\\cdot 0,10+0,85\\cdot 0,50}\\\\[2ex]&amp;=0,4942\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"151\" width=\"525\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dolay\u0131s\u0131yla bir analistin borsan\u0131n d\u00fc\u015fece\u011fini s\u00f6ylerken hakl\u0131 \u00e7\u0131kma olas\u0131l\u0131\u011f\u0131 %49,42&#8217;dir.<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Bu makale Bayes teoreminin ne oldu\u011funu ve olas\u0131l\u0131k ve istatistikte ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131n\u0131 a\u00e7\u0131klamaktad\u0131r. B\u00f6ylece Bayes teoreminin form\u00fcl\u00fcn\u00fcn ne oldu\u011funu, Bayes teoreminin \u00e7\u00f6z\u00fcml\u00fc \u00f6rneklerini ve bu teoremin uygulamalar\u0131n\u0131n neler oldu\u011funu ke\u015ffedeceksiniz. Bayes teoremi nedir? Olas\u0131l\u0131k teorisinde Bayes teoremi , bir olay hakk\u0131nda \u00f6nceden bilgi bilindi\u011finde o olay\u0131n olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in kullan\u0131lan bir yasad\u0131r. Daha spesifik [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[],"class_list":["post-379","post","type-post","status-publish","format-standard","hentry","category-olasilik"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 Bayes teoremi<\/title>\n<meta name=\"description\" content=\"Burada Bayes teoreminin ne s\u00f6yledi\u011fini, ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131n\u0131, Bayes teoreminin form\u00fcl\u00fcn\u00fc ve Bayes teoreminin \u00e7\u00f6z\u00fclm\u00fc\u015f al\u0131\u015ft\u0131rmalar\u0131n\u0131 bulacaks\u0131n\u0131z.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/tr\/bayes-teoremi\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7 Bayes teoremi\" \/>\n<meta property=\"og:description\" content=\"Burada Bayes teoreminin ne s\u00f6yledi\u011fini, ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131n\u0131, Bayes teoreminin form\u00fcl\u00fcn\u00fc ve Bayes teoreminin \u00e7\u00f6z\u00fclm\u00fc\u015f al\u0131\u015ft\u0131rmalar\u0131n\u0131 bulacaks\u0131n\u0131z.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/tr\/bayes-teoremi\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-01T12:09:39+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/theoreme-de-bayes.png\" \/>\n<meta name=\"author\" content=\"Dr.benjamin anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Yazan:\" \/>\n\t<meta name=\"twitter:data1\" content=\"Dr.benjamin anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tahmini okuma s\u00fcresi\" \/>\n\t<meta name=\"twitter:data2\" content=\"7 dakika\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/tr\/bayes-teoremi\/\",\"url\":\"https:\/\/statorials.org\/tr\/bayes-teoremi\/\",\"name\":\"\u25b7 Bayes teoremi\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/tr\/#website\"},\"datePublished\":\"2023-08-01T12:09:39+00:00\",\"dateModified\":\"2023-08-01T12:09:39+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\"},\"description\":\"Burada Bayes teoreminin ne s\u00f6yledi\u011fini, ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131n\u0131, Bayes teoreminin form\u00fcl\u00fcn\u00fc ve Bayes teoreminin \u00e7\u00f6z\u00fclm\u00fc\u015f al\u0131\u015ft\u0131rmalar\u0131n\u0131 bulacaks\u0131n\u0131z.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/tr\/bayes-teoremi\/#breadcrumb\"},\"inLanguage\":\"tr\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/tr\/bayes-teoremi\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/tr\/bayes-teoremi\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Ev\",\"item\":\"https:\/\/statorials.org\/tr\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Bayes teoremi\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/tr\/#website\",\"url\":\"https:\/\/statorials.org\/tr\/\",\"name\":\"Statorials\",\"description\":\"\u0130statistik okuryazarl\u0131\u011f\u0131 rehberiniz!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/tr\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"tr\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\",\"name\":\"Dr.benjamin anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"tr\",\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/statorials.org\/tr\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"https:\/\/statorials.org\/tr\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"caption\":\"Dr.benjamin anderson\"},\"description\":\"Merhaba, ben Benjamin, emekli bir istatistik profes\u00f6r\u00fc ve Statorials \u00f6\u011fretmenine d\u00f6n\u00fc\u015ft\u00fcm. \u0130statistik alan\u0131ndaki kapsaml\u0131 deneyimim ve uzmanl\u0131\u011f\u0131mla, \u00f6\u011frencilerimi Statorials arac\u0131l\u0131\u011f\u0131yla g\u00fc\u00e7lendirmek i\u00e7in bilgilerimi payla\u015fmaya can at\u0131yorum. 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