Bir arkada\u015f\u0131n\u0131z size \u201ctestim pozitif \u00e7\u0131kt\u0131, o hastal\u0131\u011fa yakalanm\u0131\u015f olabilirim\u201d dedi\u011finde, \u00e7o\u011fumuzun ilk tepkisi paniklemek olur. Ama ger\u00e7ek \u015fu ki, testin do\u011fruluk oran\u0131 ne kadar y\u00fcksek olursa olsun, \u201cpozitif \u00e7\u0131kt\u0131\u201d c\u00fcmlesi tek ba\u015f\u0131na neredeyse hi\u00e7bir \u015fey ifade etmez. Ger\u00e7ek olas\u0131l\u0131\u011f\u0131 hesaplamak i\u00e7in ba\u015fka bir \u015feye ihtiyac\u0131n\u0131z var: Bayes teoremi.<\/p>\n\n\n\n
Diyelim ki bir hastal\u0131k n\u00fcfusun yaln\u0131zca y\u00fczde 1\u2019ini etkiliyor. Test, ger\u00e7ekten hasta olan ki\u015filerde y\u00fczde 95 do\u011fru sonu\u00e7 veriyor. Ama sa\u011fl\u0131kl\u0131 ki\u015filerin de y\u00fczde 5\u2019inde yanl\u0131\u015fl\u0131kla \u201cpozitif\u201d \u00e7\u0131k\u0131yor. Siz teste girdiniz ve sonu\u00e7 pozitif \u00e7\u0131kt\u0131. Akl\u0131n\u0131za gelen ilk soru: \u201cGer\u00e7ekten hasta olma ihtimalim y\u00fczde 95 mi?\u201d<\/p>\n\n\n\n
Cevap, \u00e7o\u011fu insan\u0131n tahmin etti\u011finden \u00e7ok daha d\u00fc\u015f\u00fck. \u00c7\u00fcnk\u00fc n\u00fcfusun b\u00fcy\u00fck \u00e7o\u011funlu\u011fu zaten sa\u011fl\u0131kl\u0131 oldu\u011fu i\u00e7in, \u201cyanl\u0131\u015f pozitif\u201d \u00e7\u0131kan sa\u011fl\u0131kl\u0131 insan say\u0131s\u0131, ger\u00e7ekten hasta olup do\u011fru pozitif \u00e7\u0131kan insan say\u0131s\u0131ndan \u00e7ok daha kalabal\u0131k olabiliyor. \u0130\u015fte Bayes teoremi tam da bu noktada devreye giriyor: Elinizdeki \u00f6nsel bilgiyi (n\u00fcfusun ne kadar\u0131n\u0131n hasta oldu\u011funu) ve yeni kan\u0131t\u0131 (test sonucunu) birle\u015ftirerek ger\u00e7ek olas\u0131l\u0131\u011f\u0131 hesapl\u0131yor.<\/p>\n\n\n\n
Matematiksel g\u00f6sterimi karma\u015f\u0131k g\u00f6r\u00fcnse de, mant\u0131\u011f\u0131 asl\u0131nda \u00e7ok insani: Elinizde bir ba\u015flang\u0131\u00e7 inanc\u0131 var (\u00f6nsel olas\u0131l\u0131k), yeni bir kan\u0131t geliyor, ve siz bu kan\u0131t \u0131\u015f\u0131\u011f\u0131nda inanc\u0131n\u0131z\u0131 g\u00fcncelliyorsunuz (sonsal olas\u0131l\u0131k). Yani Bayes teoremi, asl\u0131nda \u201cak\u0131ll\u0131ca d\u00fc\u015f\u00fcnmenin\u201d matemati\u011fe d\u00f6k\u00fclm\u00fc\u015f hali.<\/p>\n\n\n\n
Bu yakla\u015f\u0131m, kumarbaz\u0131n yan\u0131lg\u0131s\u0131n\u0131 ele ald\u0131\u011f\u0131m\u0131z yaz\u0131m\u0131zda<\/a> bahsetti\u011fimiz sezgisel hatalar\u0131n tam tersi bir disiplin sunuyor. Kumarbaz\u0131n yan\u0131lg\u0131s\u0131nda insanlar ge\u00e7mi\u015f sonu\u00e7lar\u0131n gelecekteki ba\u011f\u0131ms\u0131z olas\u0131l\u0131klar\u0131 etkileyece\u011fini san\u0131yordu \u2014 hatal\u0131yd\u0131. Bayes teoreminde ise ge\u00e7mi\u015f bilgi (\u00f6nsel), gelecekteki tahminimizi etkilemesi gereken<\/em>, matematiksel olarak me\u015fru bir unsur. Fark, hangi bilginin ger\u00e7ekten ilgili oldu\u011funu ay\u0131rt edebilmekte yat\u0131yor.<\/p>\n\n\n\n \u0130nsan beyni, \u201ctest pozitif \u00e7\u0131kt\u0131, demek ki hasta olma ihtimalim testin do\u011fruluk oran\u0131 kadar y\u00fcksek\u201d diye d\u00fc\u015f\u00fcnme e\u011filiminde. Bu, istatistikte s\u0131k kar\u015f\u0131la\u015f\u0131lan bir tuzak ve asl\u0131nda korelasyon ile nedenselli\u011fi kar\u0131\u015ft\u0131rmam\u0131z gerekti\u011fini anlatt\u0131\u011f\u0131m\u0131z yaz\u0131m\u0131zdaki<\/a> mant\u0131\u011fa benzer bir dikkatsizlik: G\u00f6r\u00fcnen ile ger\u00e7ek olan aras\u0131ndaki fark\u0131 atlamak. Bayes teoremi, bu atlamay\u0131 engelleyen bir kontrol mekanizmas\u0131 gibi \u00e7al\u0131\u015f\u0131yor.<\/p>\n\n\n\n Bayes teoreminin kullan\u0131m alan\u0131 hastane laboratuvarlar\u0131yla s\u0131n\u0131rl\u0131 de\u011fil. Spam filtreleri, adli t\u0131p delillerinin de\u011ferlendirilmesi, hatta \u0130kinci D\u00fcnya Sava\u015f\u0131\u2019nda Enigma \u015fifresinin \u00e7\u00f6z\u00fclmesi gibi tarihi olaylarda bile Bayes\u00e7i d\u00fc\u015f\u00fcnce kilit rol oynad\u0131. Spor analiti\u011finde de ayn\u0131 mant\u0131k i\u015fliyor: Bir tak\u0131m\u0131n sezon ba\u015f\u0131ndaki g\u00fc\u00e7 tahmini (\u00f6nsel), her ma\u00e7tan gelen yeni sonu\u00e7larla (kan\u0131t) g\u00fcncellenerek daha isabetli hale geliyor \u2014 t\u0131pk\u0131 xG modellerinde<\/a> bir tak\u0131m\u0131n gol beklentisinin, ma\u00e7 i\u00e7indeki her yeni \u015fansla g\u00fcncellenmesi gibi.<\/p>\n\n\n\n Bir dahaki sefere \u00e7arp\u0131c\u0131 bir istatistik ya da test sonucuyla kar\u015f\u0131la\u015ft\u0131\u011f\u0131n\u0131zda kendinize \u015funu sorun: \u201cBu sonucun arkas\u0131ndaki \u00f6nsel olas\u0131l\u0131k nedir? Olay\u0131n kendisi ne kadar nadir?\u201d \u00c7o\u011fu zaman g\u00f6zden ka\u00e7\u0131rd\u0131\u011f\u0131m\u0131z \u015fey, kan\u0131t\u0131n kendisi de\u011fil, o kan\u0131t\u0131n ortaya \u00e7\u0131kt\u0131\u011f\u0131 ba\u011flamdaki temel oran (base rate). Bu, yan\u0131lt\u0131c\u0131 grafikleri tan\u0131may\u0131 \u00f6\u011frendi\u011fimiz yaz\u0131m\u0131zdaki<\/a> gibi, say\u0131lara k\u00f6r\u00fc k\u00f6r\u00fcne de\u011fil, ele\u015ftirel bir g\u00f6zle bakmay\u0131 gerektiriyor.<\/p>\n\n\n\n Sonu\u00e7 olarak Bayes teoremi, bize kesin cevaplar vermez; ama elimizdeki bilgiyle en ak\u0131lc\u0131 tahmini yapmam\u0131z\u0131 sa\u011flar. Ve modern veri biliminden t\u0131bbi te\u015fhise kadar pek \u00e7ok alanda, \u201cne kadar eminiz?\u201d sorusunun en d\u00fcr\u00fcst cevab\u0131n\u0131 bu teorem veriyor.<\/p>\n\n\n\n Teoremin tarih\u00e7esi, form\u00fcl\u00fc ve daha ayr\u0131nt\u0131l\u0131 a\u00e7\u0131klamas\u0131 i\u00e7in <\/em>Bayes teoremi \u00fczerine Vikipedi maddesine<\/em><\/a> g\u00f6z atabilirsiniz.<\/em><\/p>\n","protected":false},"excerpt":{"rendered":" Bir arkada\u015f\u0131n\u0131z size \u201ctestim pozitif \u00e7\u0131kt\u0131, o hastal\u0131\u011fa yakalanm\u0131\u015f olabilirim\u201d dedi\u011finde, \u00e7o\u011fumuzun ilk tepkisi paniklemek olur. Ama ger\u00e7ek \u015fu ki, testin do\u011fruluk oran\u0131 ne kadar y\u00fcksek olursa olsun, \u201cpozitif \u00e7\u0131kt\u0131\u201d c\u00fcmlesi tek ba\u015f\u0131na neredeyse hi\u00e7bir \u015fey ifade etmez. Ger\u00e7ek olas\u0131l\u0131\u011f\u0131 hesaplamak i\u00e7in ba\u015fka bir \u015feye ihtiyac\u0131n\u0131z var: Bayes teoremi. \u00d6nce Basit Bir Senaryo Diyelim ki … Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"class_list":["post-41","post","type-post","status-publish","format-standard","hentry","category-istatistik-olasilik"],"_links":{"self":[{"href":"https:\/\/hocabul.net\/index.php?rest_route=\/wp\/v2\/posts\/41","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/hocabul.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/hocabul.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/hocabul.net\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/hocabul.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=41"}],"version-history":[{"count":1,"href":"https:\/\/hocabul.net\/index.php?rest_route=\/wp\/v2\/posts\/41\/revisions"}],"predecessor-version":[{"id":42,"href":"https:\/\/hocabul.net\/index.php?rest_route=\/wp\/v2\/posts\/41\/revisions\/42"}],"wp:attachment":[{"href":"https:\/\/hocabul.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=41"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hocabul.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=41"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hocabul.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=41"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Neden Sezgimiz Bizi Yan\u0131lt\u0131yor?<\/a><\/h2>\n\n\n\n
Sadece T\u0131pta De\u011fil, Her Yerde<\/a><\/h2>\n\n\n\n
Peki Bu Bilgiyi Nas\u0131l Kullanmal\u0131?<\/h2>\n\n\n\n