{"id":29423,"date":"2025-09-13T01:00:28","date_gmt":"2025-09-12T22:00:28","guid":{"rendered":"https:\/\/fatihsoysal.com\/blog\/probabilistik-akil-yurutme-bir-baslangic-rehberi\/"},"modified":"2025-09-13T01:00:28","modified_gmt":"2025-09-12T22:00:28","slug":"probabilistik-akil-yurutme-bir-baslangic-rehberi","status":"publish","type":"post","link":"https:\/\/fatihsoysal.com\/blog\/probabilistik-akil-yurutme-bir-baslangic-rehberi\/","title":{"rendered":"Probabilistik Ak\u0131l Y\u00fcr\u00fctme: Bir Ba\u015flang\u0131\u00e7 Rehberi"},"content":{"rendered":"

Probabilistik Ak\u0131l Y\u00fcr\u00fctme: Bir Ba\u015flang\u0131\u00e7 Rehberi<\/p>\n

Ya\u015fam\u0131m\u0131zda her g\u00fcn y\u00fczlerce karar al\u0131r\u0131z. Hava durumuna g\u00f6re \u015femsiye al\u0131p almamak, bir yat\u0131r\u0131ma para yat\u0131rmak veya hangi yolu kullanarak i\u015fe gitmek gibi basit kararlar bile asl\u0131nda olas\u0131l\u0131k hesaplamalar\u0131na dayan\u0131r. Probabilistik ak\u0131l y\u00fcr\u00fctme, belirsizli\u011fin oldu\u011fu durumlarda karar vermeyi m\u00fcmk\u00fcn k\u0131lan g\u00fc\u00e7l\u00fc bir ara\u00e7t\u0131r. Bu makale, bu alana giri\u015f yapman\u0131z\u0131 ve olas\u0131l\u0131klar\u0131n gizemli d\u00fcnyas\u0131n\u0131 ke\u015ffetmenizi sa\u011flayacak kapsaml\u0131 bir rehber niteli\u011findedir.<\/p>\n

Probabilistik Ak\u0131l Y\u00fcr\u00fctme Nedir? Nas\u0131l Anla\u015f\u0131l\u0131r?<\/h2>\n

Probabilistik ak\u0131l y\u00fcr\u00fctme, belirsiz ve eksik bilgi alt\u0131nda karar verme s\u00fcrecini ifade eder. Bu s\u00fcre\u00e7, olaylar\u0131n ger\u00e7ekle\u015fme olas\u0131l\u0131klar\u0131n\u0131 de\u011ferlendirerek, en olas\u0131 senaryolar\u0131 belirlemeyi ve buna g\u00f6re hareket etmeyi i\u00e7erir. Basit\u00e7e, bir olay\u0131n ger\u00e7ekle\u015fme ihtimalini say\u0131sal olarak ifade etme ve bu say\u0131sal ifadeleri kullanarak ak\u0131l y\u00fcr\u00fctme yapmakt\u0131r. Bu, kesin sonu\u00e7lar yerine olas\u0131l\u0131klar\u0131 kullanarak mant\u0131ksal sonu\u00e7lar \u00e7\u0131karmay\u0131 gerektirir. \u00d6rne\u011fin, hastal\u0131k belirtileri g\u00f6steren bir hastada belirli bir hastal\u0131\u011f\u0131n olma olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamak veya bir makine \u00f6\u011frenmesi modelinin do\u011frulu\u011funu tahmin etmek probabilistik ak\u0131l y\u00fcr\u00fctmenin uygulama alanlar\u0131ndan sadece ikisidir. Bu alan, Bayes teoremi, olas\u0131l\u0131k da\u011f\u0131l\u0131mlar\u0131 ve istatistiksel \u00e7\u0131kar\u0131m gibi \u00f6nemli kavramlara dayan\u0131r. Daha detayl\u0131 bilgi i\u00e7in fatihsoysal.com<\/a> sitesini ziyaret edebilirsiniz.<\/p>\n

Temel Olas\u0131l\u0131k Kavramlar\u0131: Ba\u015flang\u0131\u00e7 \u0130\u00e7in Gerekli Bilgiler<\/h2>\n

Probabilistik ak\u0131l y\u00fcr\u00fctmeye ba\u015flamadan \u00f6nce, baz\u0131 temel kavramlar\u0131 anlamak gerekir. Bunlar aras\u0131nda olas\u0131l\u0131k, ko\u015fullu olas\u0131l\u0131k, ba\u011f\u0131ms\u0131z olaylar ve Bayes teoremi yer al\u0131r. Olas\u0131l\u0131k, bir olay\u0131n ger\u00e7ekle\u015fme ihtimalini 0 ile 1 aras\u0131nda bir say\u0131 ile ifade eder. 0, olay\u0131n asla ger\u00e7ekle\u015fmeyece\u011fi, 1 ise kesinlikle ger\u00e7ekle\u015fece\u011fi anlam\u0131na gelir. Ko\u015fullu olas\u0131l\u0131k, bir olay\u0131n ba\u015fka bir olay\u0131n ger\u00e7ekle\u015fmesi durumunda ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131d\u0131r. \u00d6rne\u011fin, ya\u011fmur ya\u011fmas\u0131 ko\u015fuluyla \u015femsiyenizi yan\u0131n\u0131zda ta\u015f\u0131ma olas\u0131l\u0131\u011f\u0131 ko\u015fullu olas\u0131l\u0131kt\u0131r. Ba\u011f\u0131ms\u0131z olaylar, birbirlerini etkilemeyen olaylard\u0131r. \u00d6rne\u011fin, iki zar at\u0131ld\u0131\u011f\u0131nda birinin sonucu di\u011ferini etkilemez. Bayes teoremi ise, ko\u015fullu olas\u0131l\u0131klar\u0131 kullanarak bir olay\u0131n olas\u0131l\u0131\u011f\u0131n\u0131 g\u00fcncellememize olanak tan\u0131r. Yeni bilgiler edinildik\u00e7e \u00f6nceden belirlenmi\u015f olas\u0131l\u0131klar\u0131 revize eder. Bu kavramlar, probabilistik ak\u0131l y\u00fcr\u00fctmenin temelini olu\u015fturur ve daha karma\u015f\u0131k konular\u0131 anlaman\u0131z i\u00e7in olmazsa olmazd\u0131r.<\/p>\n

Bayes Teoremi: Nas\u0131l \u00c7al\u0131\u015f\u0131r ve Nerede Kullan\u0131l\u0131r?<\/h2>\n

Bayes teoremi, probabilistik ak\u0131l y\u00fcr\u00fctmenin kalbinde yer alan g\u00fc\u00e7l\u00fc bir ara\u00e7t\u0131r. Bu teorem, yeni kan\u0131tlar \u0131\u015f\u0131\u011f\u0131nda bir hipotezin olas\u0131l\u0131\u011f\u0131n\u0131 nas\u0131l g\u00fcncelleyece\u011fimizi g\u00f6sterir. Form\u00fcl\u00fc \u015fu \u015fekildedir: P(A|B) = [P(B|A) * P(A)] \/ P(B). Burada P(A|B), B olay\u0131n\u0131n ger\u00e7ekle\u015fmesi ko\u015fuluyla A olay\u0131n\u0131n olas\u0131l\u0131\u011f\u0131d\u0131r (posterior olas\u0131l\u0131k); P(B|A), A olay\u0131n\u0131n ger\u00e7ekle\u015fmesi ko\u015fuluyla B olay\u0131n\u0131n olas\u0131l\u0131\u011f\u0131d\u0131r (likelihood); P(A), A olay\u0131n\u0131n \u00f6nceden belirlenmi\u015f olas\u0131l\u0131\u011f\u0131d\u0131r (prior olas\u0131l\u0131k); ve P(B), B olay\u0131n\u0131n olas\u0131l\u0131\u011f\u0131d\u0131r (marginal olas\u0131l\u0131k). Bayes teoremi, t\u0131bbi te\u015fhis, spam filtreleme ve finansal modelleme gibi bir\u00e7ok alanda kullan\u0131l\u0131r. \u00d6rne\u011fin, bir doktorun bir hastan\u0131n belirli bir hastal\u0131\u011fa sahip olma olas\u0131l\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in Bayes teoremini kullanmas\u0131 olas\u0131d\u0131r. Yeni te\u015fhis test sonu\u00e7lar\u0131 elde edildik\u00e7e, doktor bu sonu\u00e7lara dayanarak hastan\u0131n hastal\u0131\u011f\u0131 olma olas\u0131l\u0131\u011f\u0131n\u0131 g\u00fcncelleyebilir. Bu g\u00fcncelleme, daha do\u011fru bir te\u015fhis koymas\u0131na yard\u0131mc\u0131 olur. Uygulamada, Bayes teoremi genellikle karma\u015f\u0131k hesaplamalar gerektirir ve genellikle bilgisayar programlar\u0131 kullan\u0131larak uygulan\u0131r.<\/p>\n

Olas\u0131l\u0131k Da\u011f\u0131l\u0131mlar\u0131: Verileri Anlamak ve Modellemek<\/h2>\n

Olas\u0131l\u0131k da\u011f\u0131l\u0131mlar\u0131, bir de\u011fi\u015fkenin olas\u0131 de\u011ferlerinin olas\u0131l\u0131klar\u0131n\u0131 tan\u0131mlar. Bir\u00e7ok farkl\u0131 olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131 t\u00fcr\u00fc vard\u0131r, bunlar\u0131n en yayg\u0131n olanlar\u0131 normal da\u011f\u0131l\u0131m, Bernoulli da\u011f\u0131l\u0131m\u0131 ve Poisson da\u011f\u0131l\u0131m\u0131d\u0131r. Normal da\u011f\u0131l\u0131m, \u00e7an e\u011frisi olarak da bilinen, simetrik bir da\u011f\u0131l\u0131md\u0131r ve bir\u00e7ok do\u011fal fenomeni modellemek i\u00e7in kullan\u0131l\u0131r. Bernoulli da\u011f\u0131l\u0131m\u0131, yaln\u0131zca iki olas\u0131 sonucu olan (\u00f6rne\u011fin, ba\u015far\u0131 veya ba\u015far\u0131s\u0131zl\u0131k) olaylar i\u00e7in kullan\u0131l\u0131r. Poisson da\u011f\u0131l\u0131m\u0131 ise, belirli bir zaman veya alanda ger\u00e7ekle\u015fen olaylar\u0131n say\u0131s\u0131n\u0131 modellemek i\u00e7in kullan\u0131l\u0131r. Do\u011fru olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131 se\u00e7mek, verileri do\u011fru bir \u015fekilde analiz etmek ve anlaml\u0131 sonu\u00e7lar \u00e7\u0131karmak i\u00e7in \u00e7ok \u00f6nemlidir. Yanl\u0131\u015f bir da\u011f\u0131l\u0131m se\u00e7imi, hatal\u0131 sonu\u00e7lara ve yanl\u0131\u015f kararlara yol a\u00e7abilir. Do\u011fru da\u011f\u0131l\u0131m\u0131 se\u00e7mek i\u00e7in, verilerin \u00f6zelliklerini dikkatlice incelemek ve uygun istatistiksel testleri uygulamak gerekir. Bu genellikle verilerin g\u00f6rsel incelenmesi, histogram olu\u015fturulmas\u0131 ve \u00e7e\u015fitli istatistiksel \u00f6l\u00e7\u00fctlerin hesaplanmas\u0131 ile yap\u0131l\u0131r.<\/p>\n

Probabilistik Ak\u0131l Y\u00fcr\u00fctmenin Ger\u00e7ek D\u00fcnya Uygulamalar\u0131: Vaka \u00c7al\u0131\u015fmalar\u0131<\/h2>\n

Probabilistik ak\u0131l y\u00fcr\u00fctme, ger\u00e7ek d\u00fcnyada bir\u00e7ok farkl\u0131 alanda kullan\u0131l\u0131r. Birka\u00e7 \u00f6rnek verelim: T\u0131pta, hastal\u0131k te\u015fhisi koymak ve tedavi planlar\u0131 geli\u015ftirmek i\u00e7in kullan\u0131l\u0131r. Finansta, risk de\u011ferlendirmesi ve yat\u0131r\u0131m kararlar\u0131 almak i\u00e7in kullan\u0131l\u0131r. Hava tahmininde, hava olaylar\u0131n\u0131n olas\u0131l\u0131\u011f\u0131n\u0131 tahmin etmek i\u00e7in kullan\u0131l\u0131r. Makine \u00f6\u011frenmesinde, modellerin do\u011frulu\u011funu de\u011ferlendirmek ve yeni verilerle modelleri g\u00fcncellemek i\u00e7in kullan\u0131l\u0131r. \u00d6rne\u011fin, bir kredi kurulu\u015funun kredi ba\u015fvurusunda bulunan bir ki\u015finin \u00f6deme g\u00fcc\u00fcn\u00fc de\u011ferlendirmesi i\u00e7in probabilistik modeller kullanmas\u0131 olas\u0131d\u0131r. Ba\u015fvuran\u0131n ge\u00e7mi\u015f bor\u00e7 \u00f6deme ge\u00e7mi\u015fi, gelir d\u00fczeyi ve di\u011fer fakt\u00f6rler dikkate al\u0131narak, ki\u015finin \u00f6deme g\u00fcc\u00fcn\u00fcn olas\u0131l\u0131\u011f\u0131 hesaplan\u0131r. Bu hesaplama, kredi onay veya red karar\u0131n\u0131 vermede etkili olur. Bir ba\u015fka \u00f6rnek ise spam filtreleme sistemleridir. Bu sistemler, bir e-postan\u0131n spam olma olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in probabilistik y\u00f6ntemler kullan\u0131r. E-postan\u0131n i\u00e7eri\u011fi, g\u00f6nderenin adresi ve di\u011fer fakt\u00f6rler dikkate al\u0131narak, e-postan\u0131n spam olma olas\u0131l\u0131\u011f\u0131 hesaplan\u0131r. Bu hesaplama, e-postan\u0131n spam klas\u00f6r\u00fcne ta\u015f\u0131nmas\u0131 veya gelen kutusunda kalmas\u0131 karar\u0131n\u0131 belirler.<\/p>\n

Probabilistik Programlama: Kod \u00d6rnekleri<\/h3>\n

Probabilistik programlama, probabilistik ak\u0131l y\u00fcr\u00fctmeyi kodlaman\u0131n bir yoludur. Bu dilde, olas\u0131l\u0131k da\u011f\u0131l\u0131mlar\u0131n\u0131 ve Bayes teoremini do\u011frudan kullanarak modeller olu\u015fturabilirsiniz. \u00d6rnek olarak, Python'da PyMC3 k\u00fct\u00fcphanesi kullan\u0131larak basit bir Bayes modelini nas\u0131l olu\u015fturabilece\u011finizi g\u00f6steren bir kod \u00f6rne\u011fi a\u015fa\u011f\u0131dad\u0131r:<\/p>\n

<\/code><\/p>\n

python\nimport pymc3 as pm\n\nwith pm.Model() as model:\n    # Prior da\u011f\u0131l\u0131m\u0131\n    theta = pm.Beta(\"theta\", alpha=1, beta=1)\n\n    # Likelihood\n    y = pm.Binomial(\"y\", p=theta, n=10, observed=6)\n\n    # Posterior da\u011f\u0131l\u0131m\u0131n\u0131 \u00f6rnekleme\n    trace = pm.sample(1000)\n\npm.summary(trace)<\/pre>\n
<\/code><\/p>\n
Bu kod, bir madeni paran\u0131n adil olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in Bayes teoremini kullan\u0131r.  theta<\/code>, paran\u0131n yaz\u0131 gelme olas\u0131l\u0131\u011f\u0131n\u0131 temsil eder.  y<\/code>, 10 denemede 6 yaz\u0131 geldi\u011fini g\u00f6zlemlenmi\u015f veridir.  pm.sample()<\/code> fonksiyonu, posterior da\u011f\u0131l\u0131mdan \u00f6rnekler olu\u015fturur ve bu \u00f6rnekler kullan\u0131larak theta<\/code>'n\u0131n olas\u0131 de\u011ferleri tahmin edilebilir.  Daha geli\u015fmi\u015f uygulamalar i\u00e7in  fatihsoysal.com<\/a> sitesinden daha detayl\u0131 bilgi alabilirsiniz.<\/p>\n
\u0130leri D\u00fczey Probabilistik Ak\u0131l Y\u00fcr\u00fctme Teknikleri<\/h2>\n
Temel kavramlar\u0131 \u00f6\u011frendikten sonra, daha geli\u015fmi\u015f probabilistik ak\u0131l y\u00fcr\u00fctme tekniklerini ke\u015ffedebilirsiniz. Bunlar aras\u0131nda Markov zincirleri Monte Carlo (MCMC) y\u00f6ntemleri, varyasyonel \u00e7\u0131kar\u0131m ve derin probabilistik modeller yer al\u0131r.  MCMC y\u00f6ntemleri, y\u00fcksek boyutlu posterior da\u011f\u0131l\u0131mlardan \u00f6rnek olu\u015fturmak i\u00e7in kullan\u0131l\u0131r ve Bayes teoremini karma\u015f\u0131k modellerde uygulamay\u0131 m\u00fcmk\u00fcn k\u0131lar.  Varyasyonel \u00e7\u0131kar\u0131m ise, posterior da\u011f\u0131l\u0131m\u0131 daha basit bir da\u011f\u0131l\u0131mla yakla\u015ft\u0131r\u0131r ve bu sayede hesaplama maliyetini d\u00fc\u015f\u00fcr\u00fcr. Derin probabilistik modeller ise, derin \u00f6\u011frenme tekniklerini probabilistik modellerle birle\u015ftirir ve b\u00fcy\u00fck miktarda veriyi analiz etmek i\u00e7in kullan\u0131l\u0131r.  Bu teknikler, daha karma\u015f\u0131k problemleri \u00e7\u00f6zmek ve daha do\u011fru sonu\u00e7lar elde etmek i\u00e7in kullan\u0131l\u0131r. Ancak, bu y\u00f6ntemlerin uygulanmas\u0131 daha ileri d\u00fczey istatistiksel ve programlama becerileri gerektirir. Bu konuda uzmanla\u015fmak, ileri seviye matematik ve istatistiksel analiz bilgisi gerektirir.<\/p>\n
\u00d6\u011frenme Yol Haritas\u0131<\/h2>\n\n\n\n\n\n
Konu<\/th>\nYeni Ba\u015flayan<\/th>\nOrta Seviye<\/th>\n\u0130leri Seviye<\/th>\n<\/tr>\n
Temel Olas\u0131l\u0131k<\/td>\nOlas\u0131l\u0131k, ko\u015fullu olas\u0131l\u0131k, ba\u011f\u0131ms\u0131z olaylar<\/td>\nBayes teoremi, olas\u0131l\u0131k da\u011f\u0131l\u0131mlar\u0131 (normal, Bernoulli, binomial)<\/td>\nDaha karma\u015f\u0131k olas\u0131l\u0131k da\u011f\u0131l\u0131mlar\u0131, ileri istatistiksel testler<\/td>\n<\/tr>\n
Uygulama<\/td>\nBasit olas\u0131l\u0131k problemleri \u00e7\u00f6zme<\/td>\nBayes teoremini ger\u00e7ek d\u00fcnya problemlerine uygulama<\/td>\nMCMC, varyasyonel \u00e7\u0131kar\u0131m, derin probabilistik modeller<\/td>\n<\/tr>\n
Ara\u00e7lar<\/td>\nHesap makinesi, el ile hesaplama<\/td>\nPython, R gibi programlama dilleri<\/td>\n\u00d6zel yaz\u0131l\u0131mlar, geli\u015fmi\u015f istatistik paketleri<\/td>\n<\/tr>\n<\/table>\n
Sonu\u00e7<\/h2>\n
Probabilistik ak\u0131l y\u00fcr\u00fctme, belirsizli\u011fin oldu\u011fu durumlarda karar vermeyi m\u00fcmk\u00fcn k\u0131lan g\u00fc\u00e7l\u00fc bir ara\u00e7t\u0131r.  Bu makale, bu alana giri\u015f yapman\u0131z\u0131 ve olas\u0131l\u0131klar\u0131n gizemli d\u00fcnyas\u0131n\u0131 ke\u015ffetmenizi sa\u011flad\u0131.  Temel kavramlar\u0131 \u00f6\u011frendikten sonra, daha geli\u015fmi\u015f tekniklere ge\u00e7ebilir ve bu g\u00fc\u00e7l\u00fc ara\u00e7lar\u0131 ger\u00e7ek d\u00fcnya problemlerine uygulayabilirsiniz.  Daha fazla bilgi i\u00e7in fatihsoysal.com<\/a> sitesini ziyaret edebilirsiniz.<\/p>\n
S\u0131k\u00e7a Sorulan Sorular<\/h3>\n
    \n
  • Probabilistik ak\u0131l y\u00fcr\u00fctme neden \u00f6nemlidir?<\/strong> \u00c7\u00fcnk\u00fc belirsizli\u011fin oldu\u011fu durumlarda en iyi karar\u0131 almam\u0131za yard\u0131mc\u0131 olur.<\/li>\n
  • Bayes teoremini nas\u0131l uygular\u0131m?<\/strong>  Bayes teoremini uygulamak i\u00e7in prior olas\u0131l\u0131klar\u0131, likelihood ve marginal olas\u0131l\u0131\u011f\u0131 bilmeniz gerekir.  Bu de\u011ferleri kullanarak posterior olas\u0131l\u0131\u011f\u0131 hesaplayabilirsiniz.<\/li>\n
  • Hangi olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131 kullanmal\u0131y\u0131m?<\/strong>  Kullanaca\u011f\u0131n\u0131z olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131 verilerinize ve \u00e7\u00f6zmeye \u00e7al\u0131\u015ft\u0131\u011f\u0131n\u0131z probleme ba\u011fl\u0131d\u0131r.<\/li>\n
  • Probabilistik programlama nedir?<\/strong> Probabilistik programlama, probabilistik modeller olu\u015fturmak ve analiz etmek i\u00e7in kullan\u0131lan bir programlama paradigmas\u0131d\u0131r.<\/li>\n
  • Probabilistik ak\u0131l y\u00fcr\u00fctmeyi nerede \u00f6\u011frenebilirim?<\/strong>  \u00dcniversitelerin istatistik ve olas\u0131l\u0131k derslerinde veya online kurslarda \u00f6\u011frenebilirsiniz.  Ayr\u0131ca, bu konuyla ilgili bir\u00e7ok kitap ve kaynak mevcuttur.<\/li>\n<\/ul>\n
    Yazar: Fatih Soysal<\/p>\n
    <\/code><\/p>\n","protected":false},"excerpt":{"rendered":"Probabilistik Ak\u0131l Y\u00fcr\u00fctme: Bir Ba\u015flang\u0131\u00e7 Rehberi Ya\u015fam\u0131m\u0131zda her g\u00fcn y\u00fczlerce karar al\u0131r\u0131z. Hava durumuna g\u00f6re \u015femsiye al\u0131p almamak,…","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"csco_page_header_type":"","csco_page_load_nextpost":"","csco_page_subscribe_form":"","csco_page_contact_form":"","footnotes":""},"categories":[1],"tags":[],"class_list":{"0":"post-29423","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-genel","7":"cs-entry","8":"cs-video-wrap"},"yoast_head":"\nProbabilistik Ak\u0131l Y\u00fcr\u00fctme: Bir Ba\u015flang\u0131\u00e7 Rehberi<\/title>\n<meta name=\"description\" content=\"Ya\u015fam\u0131m\u0131zda her g\u00fcn y\u00fczlerce karar al\u0131r\u0131z. 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