{"id":5463,"date":"2025-08-06T14:32:50","date_gmt":"2025-08-06T11:32:50","guid":{"rendered":"https:\/\/datakapital.com\/blog\/?p=5463"},"modified":"2025-08-06T14:35:38","modified_gmt":"2025-08-06T11:35:38","slug":"istatistik-modelleme","status":"publish","type":"post","link":"https:\/\/datakapital.com\/blog\/istatistik-modelleme\/","title":{"rendered":"\u0130statistik Modelleme"},"content":{"rendered":"<p>G\u00fcn\u00fcm\u00fczde veri, her sekt\u00f6rde karar alma s\u00fcre\u00e7lerinin merkezinde yer al\u0131yor. Ancak verinin kendisi yaln\u0131zca bir ba\u015flang\u0131\u00e7t\u0131r. As\u0131l \u00f6nemli olan, bu verilerden anlam \u00e7\u0131karabilmek, gelece\u011fe dair \u00e7\u0131kar\u0131mlarda bulunabilmek ve belirsizlikleri y\u00f6netebilmektir. \u0130\u015fte bu noktada <strong>istatistik modelleme<\/strong>, g\u00fc\u00e7l\u00fc bir ara\u00e7 olarak kar\u015f\u0131m\u0131za \u00e7\u0131kar.<\/p>\n<p>\u0130statistiksel modelleme, veriyle bilinmeyeni anlamland\u0131rman\u0131n pusulas\u0131d\u0131r. Da\u011f\u0131l\u0131mlar, varyanslar, beklenen de\u011ferler ve olas\u0131l\u0131k teorisi gibi kavramlar arac\u0131l\u0131\u011f\u0131yla, sadece &#8220;ne oldu?&#8221; sorusuna de\u011fil, &#8220;neden oldu?&#8221; ve &#8220;bundan sonra ne olabilir?&#8221; sorular\u0131na da yan\u0131t verir. Bu nedenle istatistiksel modelleme, veri biliminin matematiksel omurgas\u0131d\u0131r.<\/p>\n<p>Bu yaz\u0131da, istatistiksel modellemenin temel yap\u0131 ta\u015flar\u0131n\u0131 ele alaca\u011f\u0131z. Makine \u00f6\u011frenmesiyle olan ili\u015fkisini a\u00e7\u0131klayacak; beklenen de\u011fer, varyans, olas\u0131l\u0131k da\u011f\u0131l\u0131mlar\u0131 gibi kavramlar\u0131 \u00f6rneklerle somutla\u015ft\u0131raca\u011f\u0131z. Ayr\u0131ca Bernoulli\u2019den Dirichlet\u2019e kadar farkl\u0131 da\u011f\u0131l\u0131mlar\u0131n hangi senaryolarda nas\u0131l kullan\u0131ld\u0131\u011f\u0131n\u0131 g\u00f6stererek, bu kavramlar\u0131n hem teorik hem pratik boyutlar\u0131n\u0131 inceleyece\u011fiz.<\/p>\n<p><strong>\u0130statistiksel modelleme<\/strong>, verilerle olas\u0131l\u0131ksal ili\u015fkiler kurarak hem bilinmeyen yap\u0131lar\u0131 ke\u015ffetmek hem de gelece\u011fe dair tahminlerde bulunmak i\u00e7in kullan\u0131lan g\u00fc\u00e7l\u00fc bir y\u00f6ntemdir. Bu modeller, hedef de\u011fi\u015fkenin bilinip bilinmemesine g\u00f6re <strong>denetimli (supervised)<\/strong> ya da <strong>denetimsiz (unsupervised)<\/strong> olarak ikiye ayr\u0131l\u0131r.<\/p>\n<h3><strong>Y\u00f6ntemler:<\/strong><\/h3>\n<ol>\n<li><strong>Bayesian Modeling (Bayesyen Modelleme):<\/strong> \u00d6nceden bilinen bilgileri (prior) ve g\u00f6zlemlenen verileri birle\u015ftirerek parametreler hakk\u0131nda g\u00fcncellenmi\u015f olas\u0131l\u0131k (posterior) elde etmeyi ama\u00e7layan olas\u0131l\u0131ksal modelleme yakla\u015f\u0131m\u0131d\u0131r.<\/li>\n<li><strong>Decision Trees (Karar A\u011fa\u00e7lar\u0131):<\/strong> Veriyi dallara ay\u0131rarak karar kurallar\u0131 olu\u015fturan ve sonu\u00e7lara ula\u015fan, g\u00f6rsel olarak da yorumlanabilir denetimli \u00f6\u011frenme algoritmas\u0131d\u0131r.<\/li>\n<li><strong>Random Forest (Rastgele Orman):<\/strong> Birden fazla karar a\u011fac\u0131n\u0131n (decision tree) toplulu\u011fuyla \u00e7al\u0131\u015fan, varyans\u0131 d\u00fc\u015f\u00fcr\u00fcp a\u015f\u0131r\u0131 \u00f6\u011frenmeyi azaltan g\u00fc\u00e7l\u00fc bir topluluk \u00f6\u011frenmesi (ensemble) y\u00f6ntemidir.<\/li>\n<li><strong>Gradient Boosting(A\u015famal\u0131 Art\u0131rma):<\/strong> Zay\u0131f \u00f6\u011frenicilerin (genellikle karar a\u011fa\u00e7lar\u0131n\u0131n) art arda e\u011fitilerek hata pay\u0131n\u0131n ad\u0131m ad\u0131m azalt\u0131ld\u0131\u011f\u0131, y\u00fcksek do\u011frulu\u011fa sahip bir tahminleme y\u00f6ntemidir.<\/li>\n<li><strong>K-means Clustering(K-ortalama k\u00fcmeleme):<\/strong> Belirli say\u0131da k\u00fcme merkezine (k) en yak\u0131n verileri gruplayan ve her veri noktas\u0131n\u0131 en yak\u0131n merkeze atayan denetimsiz bir k\u00fcmeleme algoritmas\u0131d\u0131r.<\/li>\n<li><strong>Lineer Regresyon:<\/strong> Ba\u011f\u0131ml\u0131 ve ba\u011f\u0131ms\u0131z de\u011fi\u015fkenler aras\u0131ndaki do\u011frusal ili\u015fkiyi modelleyen ve s\u00fcrekli de\u011fi\u015fkenleri tahmin etmek i\u00e7in kullan\u0131lan temel regresyon tekni\u011fidir.<\/li>\n<li><strong>Lojistik Regresyon:<\/strong> Olas\u0131l\u0131k temelli s\u0131n\u0131fland\u0131rma yapmak i\u00e7in kullan\u0131lan, \u00f6zellikle ikili(binary) s\u0131n\u0131fland\u0131rma problemlerinde yayg\u0131n olarak tercih edilen regresyon t\u00fcr\u00fcd\u00fcr.<\/li>\n<li><strong>Principal Component Analysis(Temel Bile\u015fenler Analizi):<\/strong> \u00c7ok boyutlu verideki temel yap\u0131y\u0131 ortaya \u00e7\u0131karmak ve boyut indirgeme yapmak i\u00e7in kullan\u0131lan istatistiksel bir d\u00f6n\u00fc\u015f\u00fcm tekni\u011fidir.<\/li>\n<li><strong>DBSCAN(Yo\u011funluk Tabanl\u0131 K\u00fcmeleme):<\/strong> Yo\u011funluk tabanl\u0131, k\u00fcme say\u0131s\u0131n\u0131 \u00f6nceden belirlemeye gerek duymayan, g\u00fcr\u00fclt\u00fcye ve \u015fekil \u00e7e\u015fitlili\u011fine duyarl\u0131 bir denetimsiz \u00f6\u011frenme algoritmas\u0131d\u0131r.<\/li>\n<\/ol>\n<p><strong>\u00a0<\/strong><\/p>\n<h2><strong>Makine \u00d6\u011frenmesi Algoritma T\u00fcrleri<\/strong><\/h2>\n<p><a href=\"https:\/\/datakapital.com\/blog\/makine-ogrenimi-machine-learning-nedir\/\">Makine \u00f6\u011frenmesi<\/a>, verinin yap\u0131s\u0131na ve probleme yakla\u015f\u0131m bi\u00e7imine g\u00f6re d\u00f6rt ana kategoriye ayr\u0131l\u0131r: <strong>denetimli \u00f6\u011frenme<\/strong>, <strong>denetimsiz \u00f6\u011frenme<\/strong>, <strong>yar\u0131 denetimli \u00f6\u011frenme<\/strong> ve <strong>peki\u015ftirmeli \u00f6\u011frenme<\/strong>.<\/p>\n<p><strong>Denetimli \u00f6\u011frenme<\/strong>, hem giri\u015f (X) hem de do\u011fru \u00e7\u0131k\u0131\u015f (Y) verisinin bulundu\u011fu durumlarda kullan\u0131l\u0131r. Model, bu veriler \u00fczerinden \u00f6\u011frenerek yeni gelen veriler i\u00e7in do\u011fru tahminler yapmay\u0131 ama\u00e7lar. \u00d6rne\u011fin, ge\u00e7mi\u015f konut sat\u0131\u015f verilerine bakarak yeni bir evin fiyat\u0131n\u0131 tahmin etmek bu kapsama girer.<\/p>\n<p><strong>Denetimsiz \u00f6\u011frenme<\/strong>, yaln\u0131zca giri\u015f verisiyle \u00e7al\u0131\u015f\u0131r; yani etiketli veri (Y) yoktur. Bu durumda model, verinin i\u00e7 yap\u0131s\u0131n\u0131 analiz ederek k\u00fcmeleri, benzerlikleri veya kal\u0131plar\u0131 ke\u015ffetmeye \u00e7al\u0131\u015f\u0131r. M\u00fc\u015fteri segmentasyonu ve boyut indirgeme teknikleri bu t\u00fcrdendir.<\/p>\n<p><strong>Yar\u0131 denetimli \u00f6\u011frenme<\/strong>, verilerin bir k\u0131sm\u0131 etiketliyken b\u00fcy\u00fck bir k\u0131sm\u0131 etiketsiz oldu\u011funda kullan\u0131l\u0131r. Bu model, etiketsiz veriyi de e\u011fitime dahil ederek daha g\u00fc\u00e7l\u00fc sonu\u00e7lar elde etmeye \u00e7al\u0131\u015f\u0131r. Etiketlemenin maliyetli oldu\u011fu senaryolarda olduk\u00e7a pratiktir.<\/p>\n<p><strong>Peki\u015ftirmeli \u00f6\u011frenme<\/strong> ise bir ajan\u0131n \u00e7evresiyle etkile\u015fim kurarak \u00f6d\u00fcl toplad\u0131\u011f\u0131 ve zamanla en iyi stratejiyi \u00f6\u011frenmeye \u00e7al\u0131\u015ft\u0131\u011f\u0131 bir yakla\u015f\u0131md\u0131r. Oyun oynayan yapay zeka sistemleri veya otonom ara\u00e7 kontrol sistemleri bu kategoriye \u00f6rnek verilebilir.<\/p>\n<p><strong>\u0130ndikat\u00f6r Fonksiyon:\u00a0\u00a0 <\/strong><\/p>\n<p>Bir k\u00fcme <strong><em>A<\/em><\/strong> i\u00e7in indikat\u00f6r fonksiyon <strong><em>I<sub>A<\/sub>(x)<\/em><\/strong>, eleman <strong><em>x<\/em><\/strong>&#8216;in bu k\u00fcmede olup olmad\u0131\u011f\u0131n\u0131 kontrol eder ve \u015f\u00f6yle tan\u0131mlan\u0131r:<\/p>\n<p><img decoding=\"async\" class=\"alignnone size-full wp-image-5464\" src=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Indikator-Fonksiyonu.jpg\" alt=\"Makine \u00d6\u011frenmesi Fonskiyon \u0130ndikat\u00f6r\" width=\"253\" height=\"76\" title=\"\" srcset=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Indikator-Fonksiyonu.jpg 253w, https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Indikator-Fonksiyonu-150x45.jpg 150w\" sizes=\"(max-width: 253px) 100vw, 253px\" \/><\/p>\n<p><strong>Beklenen De\u011fer(Expected Value)<\/strong><\/p>\n<p>Beklenen de\u011fer (di\u011fer ad\u0131yla beklenti ya da ortalama), bir rassal de\u011fi\u015fken <strong><em>X<\/em><\/strong>\u2019in <strong><em>E(X)<\/em><\/strong> ile g\u00f6sterilen ortalama de\u011feridir.<\/p>\n<p>Bu, <strong><em>X<\/em><\/strong>\u2019in alabilece\u011fi t\u00fcm de\u011ferlerin, bu de\u011ferlerin olas\u0131l\u0131klar\u0131 ile a\u011f\u0131rl\u0131kland\u0131r\u0131lm\u0131\u015f ortalamas\u0131d\u0131r.<\/p>\n<p>E\u011fer <strong><em>X<\/em><\/strong> ayr\u0131k bir de\u011fi\u015fkense:<\/p>\n<p><img decoding=\"async\" class=\"alignnone size-full wp-image-5465\" src=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Beklenen-Deger.jpg\" alt=\"Beklenen De\u011fer De\u011fi\u015fkeni\" width=\"266\" height=\"63\" title=\"\" srcset=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Beklenen-Deger.jpg 266w, https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Beklenen-Deger-150x36.jpg 150w\" sizes=\"(max-width: 266px) 100vw, 266px\" \/><\/p>\n<p>veya:<\/p>\n<p><img decoding=\"async\" class=\"alignnone size-full wp-image-5466\" src=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Beklenen-deger-formulu.jpg\" alt=\"Yapay zeka beklenen de\u011fer\" width=\"261\" height=\"60\" title=\"\" srcset=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Beklenen-deger-formulu.jpg 261w, https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Beklenen-deger-formulu-150x34.jpg 150w\" sizes=\"(max-width: 261px) 100vw, 261px\" \/><\/p>\n<p>E\u011fer <strong><em>X<\/em><\/strong> s\u00fcrekli bir de\u011fi\u015fkense ve olas\u0131l\u0131k yo\u011funluk fonksiyonu (PDF) <strong><em>f(x)<\/em><\/strong> ile tan\u0131mlanm\u0131\u015fsa, toplam yerine integral al\u0131n\u0131r:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-5467\" src=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Surekli-beklenen-deger.jpg\" alt=\"Beklenen de\u011fer integral\" width=\"314\" height=\"77\" title=\"\" srcset=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Surekli-beklenen-deger.jpg 314w, https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Surekli-beklenen-deger-300x74.jpg 300w, https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Surekli-beklenen-deger-150x37.jpg 150w\" sizes=\"(max-width: 314px) 100vw, 314px\" \/><\/p>\n<p><strong>Varyans<\/strong><\/p>\n<p>Bir rassal de\u011fi\u015fkenin varyans\u0131, de\u011ferlerinin ne kadar yay\u0131ld\u0131\u011f\u0131n\u0131 \u00f6l\u00e7er.<\/p>\n<p>E\u011fer <strong><em>X<\/em><\/strong> ortalamas\u0131 <strong><em>E(X) = \u03bc<\/em><\/strong> olan bir rassal de\u011fi\u015fkense, varyans<strong><em> E[(X &#8211; \u03bc)<sup>2<\/sup>]<\/em><\/strong> olarak tan\u0131mlan\u0131r.<\/p>\n<p>Ba\u015fka bir deyi\u015fle, <strong><em>X<\/em><\/strong>\u2019in ortalamas\u0131ndan sapmas\u0131n\u0131n karesinin beklenen de\u011feridir.<\/p>\n<p>E\u011fer <strong><em>X<\/em><\/strong> ayr\u0131k bir de\u011fi\u015fkense, varyans \u015fu \u015fekilde hesaplan\u0131r:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-5468\" src=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Ayrik-degisken-hesaplama.jpg\" alt=\"\u0130statistik modelleme ayr\u0131k de\u011fi\u015fken\" width=\"506\" height=\"83\" title=\"\" srcset=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Ayrik-degisken-hesaplama.jpg 506w, https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Ayrik-degisken-hesaplama-300x49.jpg 300w, https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Ayrik-degisken-hesaplama-150x25.jpg 150w, https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Ayrik-degisken-hesaplama-450x74.jpg 450w\" sizes=\"(max-width: 506px) 100vw, 506px\" \/><\/p>\n<p>ve e\u011fer <strong><em>X<\/em><\/strong> s\u00fcrekli ise:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-5469\" src=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Istatistik-Modelleme-Surekli-Ayrik-Degisken.jpg\" alt=\"S\u00fcrekli ayr\u0131k de\u011fi\u015fken \" width=\"496\" height=\"80\" title=\"\" srcset=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Istatistik-Modelleme-Surekli-Ayrik-Degisken.jpg 496w, https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Istatistik-Modelleme-Surekli-Ayrik-Degisken-300x48.jpg 300w, https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Istatistik-Modelleme-Surekli-Ayrik-Degisken-150x24.jpg 150w, https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Istatistik-Modelleme-Surekli-Ayrik-Degisken-450x73.jpg 450w\" sizes=\"(max-width: 496px) 100vw, 496px\" \/><\/p>\n<p><strong>Argmax<\/strong><\/p>\n<p>E\u011fer elimizde bir fonksiyon <strong><em>f(x)<\/em><\/strong> varsa:<\/p>\n<p><strong><em>argmax<sub>x<\/sub> f(x)<\/em><\/strong><\/p>\n<p>anlam\u0131:<\/p>\n<p><strong><em>f(x)<\/em><\/strong> fonksiyonunun <strong>maksimum de\u011ferini ald\u0131\u011f\u0131<\/strong> <strong><em>x<\/em><\/strong> de\u011feri (veya de\u011ferlerini) bul.<\/p>\n<p><strong>Likelihood (Olabilirlik) <\/strong><\/p>\n<p>Verilen bir model parametresi alt\u0131nda g\u00f6zlemlenen verinin meydana gelme olas\u0131l\u0131\u011f\u0131d\u0131r.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-5470 size-full\" src=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Olabilirlik.jpg\" alt=\"Likelihood, olabilirlik\" width=\"259\" height=\"74\" title=\"\" srcset=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Olabilirlik.jpg 259w, https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Olabilirlik-150x43.jpg 150w\" sizes=\"(max-width: 259px) 100vw, 259px\" \/><\/p>\n<p><strong>Log-Likelihood(Log-Olabilirlik)<\/strong><\/p>\n<p>Olas\u0131l\u0131klar\u0131n \u00e7arp\u0131m\u0131 yerine toplam\u0131 al\u0131narak hesaplama kolayla\u015ft\u0131r\u0131l\u0131r.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-5471\" src=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Log-olabilirlik.jpg\" alt=\"Log likelihood\" width=\"417\" height=\"69\" title=\"\" srcset=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Log-olabilirlik.jpg 417w, https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Log-olabilirlik-300x50.jpg 300w, https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Log-olabilirlik-150x25.jpg 150w\" sizes=\"(max-width: 417px) 100vw, 417px\" \/><\/p>\n<p><strong>Maximum Likelihood Estimation (En Y\u00fcksek Olabilirlik Tahmini) <\/strong><\/p>\n<p>G\u00f6zlemlenen veri i\u00e7in likelihood fonksiyonunu maksimize eden parametre\u00a0 <strong><em>\u03b8<\/em><\/strong>&#8216;y\u0131 bulma y\u00f6ntemidir.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-5472\" src=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/En-yuksek-olabilirlik.jpg\" alt=\"Most likelihood\" width=\"376\" height=\"78\" title=\"\" srcset=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/En-yuksek-olabilirlik.jpg 376w, https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/En-yuksek-olabilirlik-300x62.jpg 300w, https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/En-yuksek-olabilirlik-150x31.jpg 150w\" sizes=\"(max-width: 376px) 100vw, 376px\" \/><\/p>\n<p><strong>Bayesian Likelihood (Posterior, G\u00fcncellenmi\u015f Olabilirlik)\u00a0 <\/strong><\/p>\n<p>Bayes Teoremi kullan\u0131larak parametre hakk\u0131nda \u00f6n bilgiyle birlikte g\u00fcncellenmi\u015f olas\u0131l\u0131k elde edilir:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-5473\" src=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Bayesian-Olabilirlik.jpg\" alt=\"Bayesian Likelihood\" width=\"312\" height=\"94\" title=\"\" srcset=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Bayesian-Olabilirlik.jpg 312w, https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Bayesian-Olabilirlik-300x90.jpg 300w, https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Bayesian-Olabilirlik-150x45.jpg 150w\" sizes=\"(max-width: 312px) 100vw, 312px\" \/><\/p>\n<p><strong>K\u00fcm\u00fclatif Da\u011f\u0131l\u0131m Fonksiyonu (CDF)<\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-5474\" src=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Kumulatif-Dagilim-Fonksiyonu.jpg\" alt=\"CDF fonksiyonu istatistik modelleme\" width=\"275\" height=\"78\" title=\"\" srcset=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Kumulatif-Dagilim-Fonksiyonu.jpg 275w, https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Kumulatif-Dagilim-Fonksiyonu-150x43.jpg 150w\" sizes=\"(max-width: 275px) 100vw, 275px\" \/><\/p>\n<p>Burada <strong><em>X<\/em><\/strong> rassal bir de\u011fi\u015fkendir.<\/p>\n<p>E\u011fer <strong><em>X<\/em><\/strong> ayr\u0131k ise, CDF \u015fu \u015fekilde hesaplan\u0131r:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-5475\" src=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Ayrik-kumulatif-Dagilim-Fonksiyonu.jpg\" alt=\"istatistik modelleme ayr\u0131k da\u011f\u0131l\u0131m fonksiyonu\" width=\"316\" height=\"88\" title=\"\" srcset=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Ayrik-kumulatif-Dagilim-Fonksiyonu.jpg 316w, https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Ayrik-kumulatif-Dagilim-Fonksiyonu-300x84.jpg 300w, https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Ayrik-kumulatif-Dagilim-Fonksiyonu-150x42.jpg 150w\" sizes=\"(max-width: 316px) 100vw, 316px\" \/><\/p>\n<p>Burada <strong><em>f(t) = P(X = t)<\/em><\/strong>, yani olas\u0131l\u0131k k\u00fctle fonksiyonudur (PMF).<\/p>\n<p>E\u011fer <strong><em>X<\/em><\/strong> s\u00fcrekli bir de\u011fi\u015fkense:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-5476\" src=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Olasilik-Yogunluk-Fonksiyonu.jpg\" alt=\"\u0130statistik modelleme yo\u011funluk fonksiyonu\" width=\"296\" height=\"74\" title=\"\" srcset=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Olasilik-Yogunluk-Fonksiyonu.jpg 296w, https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Olasilik-Yogunluk-Fonksiyonu-150x38.jpg 150w\" sizes=\"(max-width: 296px) 100vw, 296px\" \/><\/p>\n<p>Burada\u00a0 <strong><em>f(t)<\/em><\/strong>, olas\u0131l\u0131k yo\u011funluk fonksiyonudur(PDF).<\/p>\n<p><strong>Kantil (Quantile) Fonksiyonu<\/strong><\/p>\n<p>K\u00fcm\u00fclatif da\u011f\u0131l\u0131m fonksiyonu (CDF), bir rassal de\u011fi\u015fken i\u00e7in bir de\u011fer al\u0131r ve buna kar\u015f\u0131l\u0131k gelen bir olas\u0131l\u0131k d\u00f6nd\u00fcr\u00fcr.<\/p>\n<p>Bunun yerine, 0 ile 1 aras\u0131nda bir say\u0131 (\u00f6rne\u011fin <strong><em>p<\/em><\/strong>) ile ba\u015flay\u0131p,<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-5477\" src=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Kantil-Fonksiyonu.jpg\" alt=\"Quantile Fonksiyonu\" width=\"243\" height=\"81\" title=\"\" srcset=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Kantil-Fonksiyonu.jpg 243w, https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Kantil-Fonksiyonu-150x50.jpg 150w\" sizes=\"(max-width: 243px) 100vw, 243px\" \/><\/p>\n<p>e\u015fitli\u011fini sa\u011flayan <strong><em>x<\/em><\/strong> de\u011ferini bulmak istedi\u011fimizi d\u00fc\u015f\u00fcnelim.<\/p>\n<p>Bu e\u015fitli\u011fi sa\u011flayan <strong><em>x<\/em><\/strong> de\u011feri, <strong><em>p<\/em><\/strong> kantili (ya da da\u011f\u0131l\u0131m\u0131n %100 <strong><em>p<\/em><\/strong> y\u00fczdelik dilimi) olarak adland\u0131r\u0131l\u0131r.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Bayesian Modeling: <\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>Bayesyen modelleme, \u00f6n bilgi (prior) ile g\u00f6zlemlenen verileri (data\/likelihood) birle\u015ftirerek g\u00fcncellenmi\u015f bilgi (posterior) elde etmeye dayan\u0131r.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Bayes Teoremi<\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-5478\" src=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/bayes-Teoremi.jpg\" alt=\"Bayes ve istatistiksel modelleme\" width=\"601\" height=\"121\" title=\"\" srcset=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/bayes-Teoremi.jpg 601w, https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/bayes-Teoremi-300x60.jpg 300w, https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/bayes-Teoremi-150x30.jpg 150w, https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/bayes-Teoremi-450x91.jpg 450w\" sizes=\"(max-width: 601px) 100vw, 601px\" \/><\/p>\n<p><strong>Modelleme a\u015famalar\u0131:<\/strong><\/p>\n<ol>\n<li>Prior belirleme<\/li>\n<li>Likelihood<\/li>\n<li>Posterior hesaplama<\/li>\n<\/ol>\n<p><strong>Da\u011f\u0131l\u0131m T\u00fcrleri:<\/strong><\/p>\n<ol>\n<li><strong> Bernoulli(Geometrik) Da\u011f\u0131l\u0131m\u0131 <\/strong><\/li>\n<\/ol>\n<p>Bernoulli da\u011f\u0131l\u0131m\u0131, yaln\u0131zca iki olas\u0131 sonucu olan deneyleri modellemek i\u00e7in kullan\u0131l\u0131r. Bu sonu\u00e7lar genellikle \u201cba\u015far\u0131\u201d ve \u201cba\u015far\u0131s\u0131zl\u0131k\u201d (veya 1 ve 0) olarak temsil edilir.<\/p>\n<p>Binary s\u0131n\u0131fland\u0131rma problemleri, ba\u015far\u0131-olas\u0131l\u0131k modelleri, kullan\u0131c\u0131 davran\u0131\u015f tahmini gibi durumlarda kullan\u0131l\u0131r. Bir madeni para at\u0131ld\u0131\u011f\u0131nda yaz\u0131 gelmesini \u201cba\u015far\u0131 (1)\u201d ve tura gelmesini \u201cba\u015far\u0131s\u0131zl\u0131k (0)\u201d olarak kodlayal\u0131m. E\u011fer para adilse, ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131 <strong><em>p <\/em><\/strong>= 0.5\u2019tir. Bu deney <strong>Bernoulli da\u011f\u0131l\u0131m\u0131<\/strong> ile modellenebilir \u00e7\u00fcnk\u00fc:<\/p>\n<ul>\n<li>Deney yaln\u0131zca bir kez yap\u0131l\u0131r.<\/li>\n<li>Sonu\u00e7lar ikilidir (yaz\u0131 ya da tura).<\/li>\n<li>Her bir at\u0131\u015f birbirinden ba\u011f\u0131ms\u0131zd\u0131r.<\/li>\n<\/ul>\n<p>Parametre: <strong><em>p<\/em><\/strong> <strong><em>\u2208 <\/em><\/strong><strong><em>[0,1]<\/em><\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-5479\" src=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Beornolli-Dagilimi.jpg\" alt=\"Bernoulli Da\u011f\u0131l\u0131m\u0131 istatistik modelleme\" width=\"265\" height=\"290\" title=\"\" srcset=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Beornolli-Dagilimi.jpg 265w, https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Beornolli-Dagilimi-150x164.jpg 150w\" sizes=\"(max-width: 265px) 100vw, 265px\" \/><\/p>\n<ol start=\"2\">\n<li><strong> Binomial Da\u011f\u0131l\u0131m\u0131<\/strong><\/li>\n<\/ol>\n<p>Binom da\u011f\u0131l\u0131m\u0131, ayn\u0131 Bernoulli deneyinin birden fazla kez (n kez) tekrarlanmas\u0131yla olu\u015fan toplam ba\u015far\u0131 say\u0131s\u0131n\u0131 modellemek i\u00e7in kullan\u0131l\u0131r. Ba\u015far\u0131 say\u0131s\u0131n\u0131n hesapland\u0131\u011f\u0131 durumlar, A\/B testleri, kalite kontrol uygulamalar\u0131 gibi alanlarda kullan\u0131l\u0131r. \u00d6rne\u011fin bir \u00fcr\u00fcn\u00fcn kalite kontrol testinde, her biri ba\u011f\u0131ms\u0131z 10 test yap\u0131l\u0131r ve her testte \u00fcr\u00fcn\u00fcn hatas\u0131z \u00e7\u0131kma olas\u0131l\u0131\u011f\u0131 olarak bilinir. Bu durumda, 10 testte ka\u00e7 tanesinin hatas\u0131z \u00e7\u0131kaca\u011f\u0131n\u0131 modellemek i\u00e7in <strong>binom da\u011f\u0131l\u0131m\u0131<\/strong> kullan\u0131l\u0131r. Binom da\u011f\u0131l\u0131m\u0131, Bernoulli da\u011f\u0131l\u0131m\u0131n\u0131n \u00e7oklu tekrar\u0131 olarak d\u00fc\u015f\u00fcn\u00fclebilir.<\/p>\n<p>Parametre: <strong><em>n<\/em><\/strong>(deneme say\u0131s\u0131),\u00a0 <strong><em>p<\/em><\/strong>(ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131)<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-5480\" src=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Binom-Dagilimi.jpg\" alt=\"\u0130statistik Modelleme Binom Da\u011f\u0131l\u0131m\u0131\" width=\"300\" height=\"249\" title=\"\" srcset=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Binom-Dagilimi.jpg 300w, https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Binom-Dagilimi-150x125.jpg 150w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<ol start=\"3\">\n<li><strong> Normal (Gaussian) Da\u011f\u0131l\u0131m <\/strong><\/li>\n<\/ol>\n<p>Normal da\u011f\u0131l\u0131m, s\u00fcrekli veri noktalar\u0131n\u0131n bir ortalama etraf\u0131nda simetrik olarak da\u011f\u0131lmas\u0131yla olu\u015fan da\u011f\u0131l\u0131md\u0131r. \u00c7an e\u011frisi(bell curve) olarak da bilinir. Do\u011fal olaylar\u0131n \u00e7o\u011fu (boy uzunlu\u011fu, s\u0131nav puan\u0131, \u00fcretim hatalar\u0131 vb.) normal da\u011f\u0131l\u0131ma yak\u0131nd\u0131r. Ayr\u0131ca bir\u00e7ok istatistiksel testin ve regresyon modelinin temel varsay\u0131m\u0131d\u0131r. Mesela bir \u00fcniversitede 1000 \u00f6\u011frencinin s\u0131navdan ald\u0131\u011f\u0131 notlar ortalama 70, standart sapma 10 olsun. Bu durumda, not da\u011f\u0131l\u0131m\u0131 yakla\u015f\u0131k olarak normal da\u011f\u0131l\u0131ma uyar. \u00d6\u011frencilerin b\u00fcy\u00fck bir k\u0131sm\u0131 60-80 aral\u0131\u011f\u0131nda not al\u0131rken, u\u00e7 de\u011ferler daha az g\u00f6r\u00fcl\u00fcr. Ayr\u0131ca normal da\u011f\u0131l\u0131m\u0131n \u00f6nemli bir \u00f6zelli\u011fi de Merkezi Limit Teoremi sayesinde, yeterince b\u00fcy\u00fck \u00f6rneklemlerden elde edilen ortalamalar\u0131n normal da\u011f\u0131l\u0131ma yak\u0131nsamas\u0131d\u0131r.<\/p>\n<p>Parametre: <strong><em>\u03bc<\/em><\/strong>(ortalama), <strong><em>\u03c3<sup>2<\/sup><\/em><\/strong>(varyans)<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-5481\" src=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Normal-dagilim-Gaussian.jpg\" alt=\"\u0130statistik modelleme normal da\u011f\u0131l\u0131m\" width=\"350\" height=\"265\" title=\"\" srcset=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Normal-dagilim-Gaussian.jpg 350w, https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Normal-dagilim-Gaussian-300x227.jpg 300w, https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Normal-dagilim-Gaussian-150x114.jpg 150w\" sizes=\"(max-width: 350px) 100vw, 350px\" \/><\/p>\n<ol start=\"4\">\n<li><strong> Poisson Da\u011f\u0131l\u0131m\u0131 <\/strong><\/li>\n<\/ol>\n<p>Poisson da\u011f\u0131l\u0131m\u0131, belirli bir zaman aral\u0131\u011f\u0131nda veya sabit bir alanda meydana gelen olaylar\u0131n say\u0131s\u0131n\u0131 modellemek i\u00e7in kullan\u0131l\u0131r. Bu olaylar nadir ve ba\u011f\u0131ms\u0131z olarak ger\u00e7ekle\u015fir. Say\u0131labilir olaylar\u0131n modellenmesinde yayg\u0131n olarak kullan\u0131l\u0131r. \u00d6rne\u011fin bir banka \u015fubesine bir saatte ortalama 5 m\u00fc\u015fteri gelmektedir. Bu durumda, bir saatte tam olarak 3 m\u00fc\u015fteri gelme olas\u0131l\u0131\u011f\u0131 <a href=\"https:\/\/tr.wikipedia.org\/wiki\/Poisson_da%C4%9F%C4%B1l%C4%B1m%C4%B1\" target=\"_blank\" rel=\"noopener\"><strong>Poisson da\u011f\u0131l\u0131m\u0131<\/strong><\/a> ile hesaplanabilir. Poisson da\u011f\u0131l\u0131m\u0131, olaylar\u0131n nadir ama d\u00fczenli aral\u0131klarla ger\u00e7ekle\u015fti\u011fi durumlar i\u00e7in idealdir.<\/p>\n<p>Parametre: <strong><em>\u03bb&gt;0<\/em><\/strong> (Belirli bir aral\u0131ktaki beklenen ortalama olay say\u0131s\u0131)<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-5482\" src=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Poisson-dagilimi.jpg\" alt=\"Poisson da\u011f\u0131l\u0131m\u0131 istatistik modelleme\" width=\"359\" height=\"420\" title=\"\" srcset=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Poisson-dagilimi.jpg 359w, https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Poisson-dagilimi-256x300.jpg 256w, https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Poisson-dagilimi-150x175.jpg 150w\" sizes=\"(max-width: 359px) 100vw, 359px\" \/><\/p>\n<ol start=\"5\">\n<li><strong> Exponential(\u00dcstel) Da\u011f\u0131l\u0131m<\/strong><\/li>\n<\/ol>\n<p>\u00dcstel da\u011f\u0131l\u0131m, iki olay aras\u0131ndaki s\u00fcreyi modellemek i\u00e7in kullan\u0131l\u0131r. Bir olay\u0131n meydana gelmesini bekleme s\u00fcresinin olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131 ifade eder. Ar\u0131zalanma s\u00fcreleri, m\u00fc\u015fteri geli\u015f aral\u0131klar\u0131, servis s\u00fcreleri gibi olaylar aras\u0131nda ge\u00e7en zaman\u0131n modellenmesinde kullan\u0131l\u0131r. \u00d6rne\u011fin bir ATM\u2019ye ortalama olarak her 10 dakikada bir m\u00fc\u015fteri geliyorsa, bir sonraki m\u00fc\u015fterinin geli\u015f s\u00fcresi <strong>\u00fcstel da\u011f\u0131l\u0131m<\/strong> ile modellenebilir. Ayr\u0131ca \u00fcstel da\u011f\u0131l\u0131m Poisson s\u00fcrecinde olaylar aras\u0131 zaman aral\u0131klar\u0131n\u0131n da\u011f\u0131l\u0131m\u0131d\u0131r.<\/p>\n<p>Parametre: <strong><em>\u03bb<\/em><\/strong>(Olay\u0131n birim zamanda ger\u00e7ekle\u015fme oran\u0131(rate))<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-5483\" src=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Ussel-dagilim.png\" alt=\"Exponential da\u011f\u0131l\u0131m\" width=\"357\" height=\"334\" title=\"\" srcset=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Ussel-dagilim.png 357w, https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Ussel-dagilim-300x281.png 300w, https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Ussel-dagilim-150x140.png 150w\" sizes=\"(max-width: 357px) 100vw, 357px\" \/><\/p>\n<ol start=\"6\">\n<li><strong> Gamma Da\u011f\u0131l\u0131m\u0131<\/strong><\/li>\n<\/ol>\n<p>Gamma da\u011f\u0131l\u0131m\u0131, pozitif s\u00fcrekli de\u011ferli verileri modellemek i\u00e7in kullan\u0131lan esnek bir da\u011f\u0131l\u0131md\u0131r. \u00dcstel da\u011f\u0131l\u0131m\u0131n genelle\u015ftirilmi\u015f halidir ve olaylar aras\u0131 toplam s\u00fcrenin modellemesinde kullan\u0131l\u0131r. Varyans modelleme, bekleme s\u00fcresi birikimi, Poisson da\u011f\u0131l\u0131mlar\u0131nda prior olarak kullan\u0131m\u0131 gibi alanlarda kullan\u0131l\u0131r. Bir \u00e7a\u011fr\u0131 merkezinde, arka arkaya 3 \u00e7a\u011fr\u0131n\u0131n gelmesi i\u00e7in ge\u00e7en toplam s\u00fcreyi modellemek istiyorsak ve her \u00e7a\u011fr\u0131 geli\u015fi ba\u011f\u0131ms\u0131z \u015fekilde \u00fcstel da\u011f\u0131l\u0131ma uyuyorsa, bu toplam s\u00fcre <strong>Gamma da\u011f\u0131l\u0131m\u0131<\/strong> ile modellenebilir. Ayr\u0131ca <strong><em>\u03b1 <\/em><\/strong>= 1 durumunda Gamma da\u011f\u0131l\u0131m\u0131, \u00fcstel da\u011f\u0131l\u0131ma e\u015fit olur.<\/p>\n<p>Parametre: <strong><em>\u03b1<\/em><\/strong> (\u015fekil), <strong><em>\u03b2<\/em><\/strong> (\u00f6l\u00e7ek)<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-5484\" src=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Gamma-dagilimi.jpg\" alt=\"Gamma da\u011f\u0131l\u0131m\u0131 istatistik modelleme\" width=\"400\" height=\"291\" title=\"\" srcset=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Gamma-dagilimi.jpg 400w, https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Gamma-dagilimi-300x218.jpg 300w, https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Gamma-dagilimi-150x109.jpg 150w\" sizes=\"(max-width: 400px) 100vw, 400px\" \/><\/p>\n<ol start=\"7\">\n<li><strong> Beta Da\u011f\u0131l\u0131m\u0131 <\/strong><\/li>\n<\/ol>\n<p>Beta da\u011f\u0131l\u0131m\u0131, 0 ile 1 aras\u0131nda yer alan s\u00fcrekli de\u011ferli olas\u0131l\u0131klar\u0131n modellenmesinde kullan\u0131l\u0131r. \u00d6zellikle ba\u015far\u0131 oranlar\u0131n\u0131 modellemek i\u00e7in uygundur. Bernoulli ve Binom da\u011f\u0131l\u0131mlar\u0131 i\u00e7in \u00f6nc\u00fcl(prior) da\u011f\u0131l\u0131m olarak Bayesyen istatistikte yayg\u0131n \u015fekilde kullan\u0131l\u0131r. Ayr\u0131ca oran verileri(\u00f6rne\u011fin ba\u015far\u0131 y\u00fczdesi) i\u00e7in de uygundur. \u00d6rne\u011fin bir e-ticaret sitesinde yeni bir \u00fcr\u00fcn sayfas\u0131 i\u00e7in t\u0131klama oran\u0131 \u00f6l\u00e7\u00fclmek isteniyor diyelim. \u0130lk etapta \u00e7ok az veri oldu\u011funda, \u00f6nc\u00fcl bilgi olarak Beta(1,1) (yani e\u015fit da\u011f\u0131l\u0131ml\u0131 ve belirsiz) kullan\u0131labilir. Daha fazla veri geldik\u00e7e da\u011f\u0131l\u0131m g\u00fcncellenir. Ayr\u0131ca <strong><em>\u03b1<\/em><\/strong>=<strong><em>\u03b2<\/em><\/strong>=1 oldu\u011funda Beta da\u011f\u0131l\u0131m\u0131 Uniform(0,1) da\u011f\u0131l\u0131m\u0131na e\u015fit olur.<\/p>\n<p>Parametre: <strong><em>\u03b1, \u03b2\u00a0\u00a0\u00a0 <\/em><\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-5485\" src=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Beta-dagilimi.jpg\" alt=\"Beta da\u011f\u0131l\u0131m\u0131 istatistik modelleme\" width=\"379\" height=\"277\" title=\"\" srcset=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Beta-dagilimi.jpg 379w, https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Beta-dagilimi-300x219.jpg 300w, https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Beta-dagilimi-150x110.jpg 150w\" sizes=\"(max-width: 379px) 100vw, 379px\" \/><\/p>\n<ol start=\"8\">\n<li><strong> Dirichlet Da\u011f\u0131l\u0131m\u0131 <\/strong><\/li>\n<\/ol>\n<p>Dirichlet da\u011f\u0131l\u0131m\u0131, Beta da\u011f\u0131l\u0131m\u0131n\u0131n \u00e7ok de\u011fi\u015fkenli (multinom) genelle\u015ftirilmi\u015f halidir. 0 ile 1 aras\u0131nda kalan, toplam\u0131 1 olan birden fazla oran\u0131n ortak da\u011f\u0131l\u0131m\u0131n\u0131 tan\u0131mlar. Bayesyen modellemede, \u00f6zellikle \u00e7ok s\u0131n\u0131fl\u0131 (kategorik) da\u011f\u0131l\u0131mlar\u0131n \u00f6nc\u00fcl (prior) bilgisi olarak kullan\u0131l\u0131r. Konu modelleme, kar\u0131\u015f\u0131m modelleri ve s\u0131n\u0131fland\u0131rma gibi \u00e7ok kategorili problemlerde s\u0131k\u00e7a tercih edilir. \u00d6rne\u011fin bir haber sitesinde ziyaret\u00e7ilerin ilgilendi\u011fi kategoriler \u00fczerine yap\u0131lan analizlerde, kullan\u0131c\u0131lar\u0131n bu kategorilere olan e\u011filimlerini modellemek i\u00e7in Dirichlet da\u011f\u0131l\u0131m\u0131 kullan\u0131labilir. Her kategoriye ili\u015fkin oranlar toplamda 1 olacak \u015fekilde ifade edilir. Ayr\u0131ca<strong><em> K<\/em> <\/strong>= 2 oldu\u011funda Dirichlet da\u011f\u0131l\u0131m\u0131 Beta da\u011f\u0131l\u0131m\u0131na indirgenir.<\/p>\n<p>Parametre: <strong><em>\u03b1<sub>1<\/sub>,\u03b1<sub>2<\/sub>,&#8230;, \u03b1<sub>K<\/sub> <\/em><\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-5486\" src=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Drichlet-dagilimi.jpg\" alt=\"Drichlet da\u011f\u0131l\u0131m\u0131, istatistik modelleme \" width=\"377\" height=\"263\" title=\"\" srcset=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Drichlet-dagilimi.jpg 377w, https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Drichlet-dagilimi-300x209.jpg 300w, https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Drichlet-dagilimi-150x105.jpg 150w\" sizes=\"(max-width: 377px) 100vw, 377px\" \/><\/p>\n<ol start=\"9\">\n<li><strong> Uniform Da\u011f\u0131l\u0131m<\/strong><\/li>\n<\/ol>\n<p>Uniform da\u011f\u0131l\u0131m, belirli bir aral\u0131kta t\u00fcm de\u011ferlerin e\u015fit olas\u0131l\u0131kla ger\u00e7ekle\u015fti\u011fi da\u011f\u0131l\u0131md\u0131r. S\u00fcrekli ve ayr\u0131k versiyonlar\u0131 vard\u0131r. Sim\u00fclasyonlar, rastgele say\u0131 \u00fcretimi, belirsizli\u011fin modellendi\u011fi durumlar ve Bayesyen analizlerde \u00f6nc\u00fcl da\u011f\u0131l\u0131m olarak kullan\u0131l\u0131r. \u00d6rne\u011fin bir oyunda kullan\u0131c\u0131n\u0131n rastgele bir \u00f6d\u00fcl kazanmas\u0131 i\u00e7in sistem 1 ile 100 aras\u0131nda e\u015fit olas\u0131l\u0131kla bir say\u0131 se\u00e7ti\u011fini d\u00fc\u015f\u00fcnelim. Bu se\u00e7im <strong>Uniform(<em>a<\/em>=1, <em>b<\/em>=100)<\/strong> da\u011f\u0131l\u0131m\u0131 ile modellenebilir. Ayr\u0131ca Uniform(0,1) da\u011f\u0131l\u0131m\u0131 bir\u00e7ok ba\u015fka da\u011f\u0131l\u0131m\u0131n t\u00fcretilmesinde temel olarak kullan\u0131l\u0131r.<\/p>\n<p>Parametre: <strong><em>a \u2192<\/em><\/strong> minimum de\u011fer, <strong><em>b \u2192<\/em><\/strong> maksimum de\u011fer<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-5487\" src=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Uniform-Dagilimi.jpg\" alt=\"Uniform Da\u011f\u0131l\u0131m\u0131, istatistik da\u011f\u0131l\u0131m\" width=\"394\" height=\"347\" title=\"\" srcset=\"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Uniform-Dagilimi.jpg 394w, https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Uniform-Dagilimi-300x264.jpg 300w, https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Uniform-Dagilimi-150x132.jpg 150w\" sizes=\"(max-width: 394px) 100vw, 394px\" \/><\/p>\n<p><strong>Merkezi Limit Teoremi(Central Limit Theorem):\u00a0\u00a0\u00a0 <\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong><em>X\u2081, X\u2082, &#8230;, X\u2099<\/em><\/strong> ba\u011f\u0131ms\u0131z ve ayn\u0131 da\u011f\u0131l\u0131ma sahip, ortalamas\u0131 \u03bc ve varyans\u0131 \u03c3\u00b2 olan rassal de\u011fi\u015fkenler olsun. <strong>Merkezi Limit Teoremi<\/strong>&#8216;ne g\u00f6re, n artt\u0131k\u00e7a (yani \u00f6rneklem b\u00fcy\u00fcd\u00fck\u00e7e), bu de\u011fi\u015fkenlerin \u00f6rneklem ortalamas\u0131, yakla\u015f\u0131k olarak ortalamas\u0131 \u03bc ve varyans\u0131 \u03c3\u00b2\/n olan bir <strong>normal da\u011f\u0131l\u0131ma<\/strong> yak\u0131nsar.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Merkezi Limit Teoremi<\/strong>, istatistikte en \u00f6nemli kavramlardan biridir. Temel olarak \u015funu s\u00f6yler: E\u011fer ayn\u0131 da\u011f\u0131l\u0131ma sahip, ba\u011f\u0131ms\u0131z rastgele de\u011fi\u015fkenlerden olu\u015fan yeterince b\u00fcy\u00fck bir \u00f6rneklem al\u0131rsan\u0131z, bu \u00f6rneklemlerin ortalamalar\u0131 neredeyse her zaman normal da\u011f\u0131l\u0131ma yakla\u015f\u0131r, orijinal da\u011f\u0131l\u0131m ne olursa olsun! \u00d6rne\u011fin, bir kafede sipari\u015f verilen kahve haz\u0131rlama s\u00fcresi \u00e7ok d\u00fczensiz da\u011f\u0131lm\u0131\u015f olabilir. Ancak bu s\u00fcrelerden rastgele 50 tanesinin ortalamas\u0131n\u0131 al\u0131rsan\u0131z, bu ortalama de\u011ferler <strong>normal da\u011f\u0131l\u0131ma<\/strong> olduk\u00e7a yak\u0131nsar. Bu \u00f6zellik, bir\u00e7ok istatistiksel testin ve g\u00fcven aral\u0131\u011f\u0131n\u0131n temel dayana\u011f\u0131d\u0131r.<\/p>\n<p>&nbsp;<\/p>\n<p>Bu yaz\u0131da, istatistiksel modellemenin temel kavramlar\u0131n\u0131 hem teorik hem pratik y\u00f6nleriyle ele ald\u0131k. Beklenen de\u011fer, varyans, olas\u0131l\u0131k da\u011f\u0131l\u0131mlar\u0131 ve merkezi limit teoremi gibi kavramlar sayesinde verilerden nas\u0131l anlam \u00e7\u0131karabilece\u011fimizi g\u00f6rd\u00fck. Ayr\u0131ca farkl\u0131 da\u011f\u0131l\u0131mlar\u0131n hangi durumlarda kullan\u0131ld\u0131\u011f\u0131n\u0131 \u00f6\u011frenerek, istatistiksel d\u00fc\u015f\u00fcnme bi\u00e7iminin temellerini peki\u015ftirdik.<\/p>\n<p>Veri bilimi, sadece algoritmalar\u0131 \u00e7al\u0131\u015ft\u0131rmak de\u011fil; ayn\u0131 zamanda verinin do\u011fas\u0131n\u0131 anlayarak do\u011fru modelleri kurmakt\u0131r. \u0130statistiksel da\u011f\u0131l\u0131mlar bu yolculukta bize olduk\u00e7a y\u00f6n verir. Do\u011fru da\u011f\u0131l\u0131m\u0131 se\u00e7mek, modelin do\u011frulu\u011funu art\u0131r\u0131rken yorumlanabilirli\u011fini de g\u00fc\u00e7lendirir. \u0130statistiksel modelleme konusundaki bu temel bilgiler, veriyle \u00e7al\u0131\u015fan herkes i\u00e7in vazge\u00e7ilmezdir.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>G\u00fcn\u00fcm\u00fczde veri, her sekt\u00f6rde karar alma s\u00fcre\u00e7lerinin merkezinde yer al\u0131yor. Ancak verinin kendisi yaln\u0131zca bir ba\u015flang\u0131\u00e7t\u0131r. As\u0131l \u00f6nemli olan, bu verilerden anlam \u00e7\u0131karabilmek, gelece\u011fe dair \u00e7\u0131kar\u0131mlarda bulunabilmek ve belirsizlikleri y\u00f6netebilmektir. \u0130\u015fte bu noktada istatistik modelleme, g\u00fc\u00e7l\u00fc bir ara\u00e7 olarak kar\u015f\u0131m\u0131za \u00e7\u0131kar. \u0130statistiksel modelleme, veriyle bilinmeyeni anlamland\u0131rman\u0131n pusulas\u0131d\u0131r. Da\u011f\u0131l\u0131mlar, varyanslar, beklenen de\u011ferler ve olas\u0131l\u0131k teorisi gibi<\/p>\n","protected":false},"author":18,"featured_media":5486,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[39,38,41],"tags":[402,537],"class_list":{"0":"post-5463","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-analiz-teknikleri","8":"category-python-ile-veri-isleme","9":"category-veri-turleri-ve-kavramlar","10":"tag-istatistik","11":"tag-makine-ogrenmesi"},"better_featured_image":{"id":5486,"alt_text":"","caption":"","description":"","media_type":"image","media_details":{"width":377,"height":263,"file":"2025\/08\/Drichlet-dagilimi.jpg","filesize":29783,"sizes":{"medium":{"file":"Drichlet-dagilimi-300x209.jpg","width":300,"height":209,"mime-type":"image\/jpeg","filesize":11520,"source_url":"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Drichlet-dagilimi-300x209.jpg"},"thumbnail":{"file":"Drichlet-dagilimi-150x150.jpg","width":150,"height":150,"mime-type":"image\/jpeg","filesize":6866,"source_url":"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Drichlet-dagilimi-150x150.jpg"},"bunyad-small":{"file":"Drichlet-dagilimi-150x105.jpg","width":150,"height":105,"mime-type":"image\/jpeg","filesize":4014,"source_url":"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Drichlet-dagilimi-150x105.jpg"}},"image_meta":{"aperture":"0","credit":"","camera":"","caption":"","created_timestamp":"0","copyright":"","focal_length":"0","iso":"0","shutter_speed":"0","title":"","orientation":"0","keywords":[]}},"post":5463,"source_url":"https:\/\/datakapital.com\/blog\/wp-content\/uploads\/2025\/08\/Drichlet-dagilimi.jpg"},"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/datakapital.com\/blog\/wp-json\/wp\/v2\/posts\/5463","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/datakapital.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/datakapital.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/datakapital.com\/blog\/wp-json\/wp\/v2\/users\/18"}],"replies":[{"embeddable":true,"href":"https:\/\/datakapital.com\/blog\/wp-json\/wp\/v2\/comments?post=5463"}],"version-history":[{"count":2,"href":"https:\/\/datakapital.com\/blog\/wp-json\/wp\/v2\/posts\/5463\/revisions"}],"predecessor-version":[{"id":5489,"href":"https:\/\/datakapital.com\/blog\/wp-json\/wp\/v2\/posts\/5463\/revisions\/5489"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/datakapital.com\/blog\/wp-json\/wp\/v2\/media\/5486"}],"wp:attachment":[{"href":"https:\/\/datakapital.com\/blog\/wp-json\/wp\/v2\/media?parent=5463"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/datakapital.com\/blog\/wp-json\/wp\/v2\/categories?post=5463"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/datakapital.com\/blog\/wp-json\/wp\/v2\/tags?post=5463"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}