Bayes teoremi, kula\u011fa karma\u015f\u0131k gelen ama asl\u0131nda son derece sezgisel bir fikri anlat\u0131r: yeni bir kan\u0131t geldi\u011finde, bir \u015feye olan inanc\u0131m\u0131z\u0131 ne kadar g\u00fcncellememiz gerekti\u011fi. Hava karar\u0131nca \u015femsiye almak ya da bir doktorun test sonucuna g\u00f6re te\u015fhisini de\u011fi\u015ftirmesi hep bu mant\u0131\u011f\u0131n g\u00fcnl\u00fck halidir. Bu yaz\u0131da Bayes\u00e7i d\u00fc\u015f\u00fcnmeyi formule bo\u011fulmadan ele al\u0131yoruz.<\/p>
Bayes\u2019in \u00f6z\u00fc \u015fudur: bir \u015feye ba\u015flang\u0131\u00e7ta verdi\u011finiz olas\u0131l\u0131k (\u00f6nsel) ile yeni kan\u0131t\u0131 birle\u015ftirip g\u00fcncellenmi\u015f bir olas\u0131l\u0131\u011fa (sonsal) ula\u015f\u0131rs\u0131n\u0131z. Yani inan\u00e7lar\u0131m\u0131z ta\u015fa kaz\u0131nm\u0131\u015f de\u011fildir; kan\u0131t geldik\u00e7e \u00f6l\u00e7\u00fcl\u00fc bi\u00e7imde de\u011fi\u015fmelidir. \u201cTamamen emindim ama yeni bilgiyle fikrimi de\u011fi\u015ftirdim\u201d demek, asl\u0131nda Bayes\u00e7i davranmakt\u0131r.<\/p>
Diyelim ki nadir bir hastal\u0131k her 1000 ki\u015fiden yaln\u0131zca 1\u2019inde var. Testin do\u011fruluk oran\u0131 da y\u00fczde 99 olsun. Testiniz pozitif \u00e7\u0131kt\u0131; ger\u00e7ekten hasta m\u0131s\u0131n\u0131z? Sezgi \u201cy\u00fczde 99\u201d der, ama do\u011fru yan\u0131t \u015fa\u015f\u0131rt\u0131c\u0131 derecede d\u00fc\u015f\u00fckt\u00fcr. \u00c7\u00fcnk\u00fc hastal\u0131k o kadar nadirdir ki, sa\u011fl\u0131kl\u0131 ama \u201cyanl\u0131\u015f pozitif\u201d \u00e7\u0131kan ki\u015fi say\u0131s\u0131, ger\u00e7ek hastalar\u0131 say\u0131ca g\u00f6lgede b\u0131rak\u0131r. Bu \u201ctaban oran\u0131\u201d (base rate) etkisini g\u00f6rmezden gelmek, en s\u0131k yap\u0131lan olas\u0131l\u0131k hatalar\u0131ndan biridir.<\/p>
Bayes\u00e7i d\u00fc\u015f\u00fcnmenin \u00fc\u00e7 par\u00e7as\u0131 vard\u0131r: \u00f6nsel (kan\u0131ttan \u00f6nceki inanc\u0131n\u0131z), olabilirlik (kan\u0131t\u0131n bu durumda ne kadar beklenir oldu\u011fu) ve sonsal (g\u00fcncellenmi\u015f inanc\u0131n\u0131z). \u00d6nsel olas\u0131l\u0131k ne kadar d\u00fc\u015f\u00fckse, sonucu de\u011fi\u015ftirmek i\u00e7in o kadar g\u00fc\u00e7l\u00fc kan\u0131t gerekir. \u201cOla\u011fan\u00fcst\u00fc iddialar, ola\u011fan\u00fcst\u00fc kan\u0131t gerektirir\u201d s\u00f6z\u00fc tam da budur.<\/p>
Bir haberi okurken, bir te\u015fhis duyarken ya da bir s\u00f6ylentiyle kar\u015f\u0131la\u015f\u0131rken \u015funu sorun: bunu duymadan \u00f6nce ne kadar olas\u0131 g\u00f6r\u00fcyordum, ve bu yeni kan\u0131t inanc\u0131m\u0131 ne kadar de\u011fi\u015ftirmeli? Bu disiplin, hem a\u015f\u0131r\u0131 tepkiden hem de yeni kan\u0131t\u0131 yok saymaktan korur. Olas\u0131l\u0131\u011f\u0131 yanl\u0131\u015f okuman\u0131n bir ba\u015fka klasik bi\u00e7imi i\u00e7in kumarbaz\u0131n yan\u0131lg\u0131s\u0131 yaz\u0131m\u0131za<\/a> da bakabilirsiniz. Form\u00fcl\u00fcn matematiksel a\u00e7\u0131klamas\u0131 i\u00e7in Bayes teoreminin tan\u0131m\u0131<\/a> iyi bir kaynakt\u0131r. \u0130\u015fin hocas\u0131, inanc\u0131n\u0131 kan\u0131ta g\u00f6re g\u00fcncelleyebilen, ama her r\u00fczgarda da savrulmayand\u0131r.<\/p>","protected":false},"excerpt":{"rendered":" Bayes teoremi, kula\u011fa karma\u015f\u0131k gelen ama asl\u0131nda son derece sezgisel bir fikri anlat\u0131r: yeni bir kan\u0131t geldi\u011finde, bir \u015feye olan inanc\u0131m\u0131z\u0131 ne kadar g\u00fcncellememiz gerekti\u011fi. Hava karar\u0131nca \u015femsiye almak ya da bir doktorun test sonucuna g\u00f6re te\u015fhisini de\u011fi\u015ftirmesi hep bu mant\u0131\u011f\u0131n g\u00fcnl\u00fck halidir. Bu yaz\u0131da Bayes\u00e7i d\u00fc\u015f\u00fcnmeyi formule bo\u011fulmadan ele al\u0131yoruz. Temel sezgi Bayes\u2019in \u00f6z\u00fc … 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-37","post","type-post","status-publish","format-standard","hentry","category-istatistik-olasilik"],"_links":{"self":[{"href":"https:\/\/hocabul.net\/index.php?rest_route=\/wp\/v2\/posts\/37","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=37"}],"version-history":[{"count":1,"href":"https:\/\/hocabul.net\/index.php?rest_route=\/wp\/v2\/posts\/37\/revisions"}],"predecessor-version":[{"id":48,"href":"https:\/\/hocabul.net\/index.php?rest_route=\/wp\/v2\/posts\/37\/revisions\/48"}],"wp:attachment":[{"href":"https:\/\/hocabul.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=37"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hocabul.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=37"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hocabul.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=37"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}