{"id":419,"date":"2016-05-05T19:36:08","date_gmt":"2016-05-05T16:36:08","guid":{"rendered":"http:\/\/biostatistics.med.uoa.gr\/?p=419"},"modified":"2022-04-05T16:02:54","modified_gmt":"2022-04-05T13:02:54","slug":"bayes-advanced","status":"publish","type":"post","link":"https:\/\/biostatistics.med.uoa.gr\/en\/bayes-advanced\/","title":{"rendered":"\u039c\u03c0\u03b5\u03cb\u03b6\u03b9\u03b1\u03bd\u03ae \u03a3\u03c5\u03bc\u03c0\u03b5\u03c1\u03b1\u03c3\u03bc\u03b1\u03c4\u03bf\u03bb\u03bf\u03b3\u03af\u03b1 \u0399I"},"content":{"rendered":"<h1 style=\"text-align: left;\"><strong style=\"font-size: 16px; line-height: 1.5;\">\u0394\u03b9\u03b4\u03ac\u03c3\u03ba\u03bf\u03c5\u03c3\u03b1<\/strong><\/h1>\n<p><a href=\"http:\/\/biostatistics.med.uoa.gr\/index.php\/meligkotsidou\/\">L. Meligkotsidou<\/a><\/p>\n<p>&nbsp;<\/p>\n<p><strong>\u03a3\u03ba\u03bf\u03c0\u03cc\u03c2 \u03c4\u03bf\u03c5 \u03bc\u03b1\u03b8\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2<\/strong><\/p>\n<p>\u0397 \u03c0\u03b1\u03c1\u03bf\u03c5\u03c3\u03af\u03b1\u03c3\u03b7 \u03c4\u03c9\u03bd \u03b1\u03bb\u03b3\u03cc\u03c1\u03b9\u03b8\u03bc\u03c9\u03bd Markov chain Monte Carlo (MCMC) \u03ba\u03b1\u03b9 \u03b7 \u03c7\u03c1\u03ae\u03c3\u03b7 \u03c4\u03bf\u03c5\u03c2 \u03c9\u03c2 \u03b5\u03c1\u03b3\u03b1\u03bb\u03b5\u03af\u03b1 \u03b3\u03b9\u03b1 \u039c\u03c0\u03b5\u03cb\u03b6\u03b9\u03b1\u03bd\u03ae \u03c3\u03c5\u03bc\u03c0\u03b5\u03c1\u03b1\u03c3\u03bc\u03b1\u03c4\u03bf\u03bb\u03bf\u03b3\u03af\u03b1 \u03b3\u03b9\u03b1 \u03c0\u03bf\u03bb\u03cd\u03c0\u03bb\u03bf\u03ba\u03b1 \u03c0\u03bf\u03bb\u03c5\u03c0\u03b1\u03c1\u03b1\u03bc\u03b5\u03c4\u03c1\u03b9\u03ba\u03ac \u03bc\u03bf\u03bd\u03c4\u03ad\u03bb\u03b1. \u03a0\u03c1\u03cc\u03ba\u03b5\u03b9\u03c4\u03b1\u03b9 \u03b3\u03b9\u03b1 \u03ad\u03bd\u03b1 \u03bc\u03ac\u03b8\u03b7\u03bc\u03b1 \u03c0\u03bf\u03c5 \u03c3\u03c5\u03bc\u03c0\u03bb\u03b7\u03c1\u03ce\u03bd\u03b5\u03b9 \u03c4\u03bf \u03bc\u03ac\u03b8\u03b7\u03bc\u03b1 \u2018<a href=\"http:\/\/biostatistics.med.uoa.gr\/index.php\/bayes-one\/\">Bayesian Inference I<\/a>\u2019, \u03b4\u03af\u03bd\u03bf\u03bd\u03c4\u03b1\u03c2 \u03c3\u03c4\u03bf\u03c5\u03c2 \u03c6\u03bf\u03b9\u03c4\u03b7\u03c4\u03ad\u03c2 \u03c4\u03b7\u03bd \u03b5\u03c5\u03ba\u03b1\u03b9\u03c1\u03af\u03b1 \u03bd\u03b1 \u03b1\u03c0\u03bf\u03ba\u03c4\u03ae\u03c3\u03bf\u03c5\u03bd \u03c0\u03b9\u03bf \u03b5\u03be\u03b5\u03b9\u03b4\u03b9\u03ba\u03b5\u03c5\u03bc\u03ad\u03bd\u03b7 \u03b3\u03bd\u03ce\u03c3\u03b7 \u03c3\u03c4\u03bf \u03b1\u03bd\u03c4\u03b9\u03ba\u03b5\u03af\u03bc\u03b5\u03bd\u03bf \u03c4\u03b7\u03c2 \u039c\u03c0\u03b5\u03cb\u03b6\u03b9\u03b1\u03bd\u03ae\u03c2 \u03a3\u03c4\u03b1\u03c4\u03b9\u03c3\u03c4\u03b9\u03ba\u03ae\u03c2 \u03ba\u03b1\u03b9 \u03c4\u03b1 \u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03b9\u03c3\u03c4\u03b9\u03ba\u03ac \u03b5\u03c1\u03b3\u03b1\u03bb\u03b5\u03af\u03b1 \u03b3\u03b9\u03b1 \u03bd\u03b1 \u03c4\u03b7\u03bd \u03b5\u03c6\u03b1\u03c1\u03bc\u03cc\u03c3\u03bf\u03c5\u03bd \u03c3\u03c4\u03b7\u03bd \u03c0\u03c1\u03ac\u03be\u03b7. \u0397 \u03c5\u03bb\u03bf\u03c0\u03bf\u03af\u03b7\u03c3\u03b7 \u03ba\u03b1\u03b9 \u03b5\u03c6\u03b1\u03c1\u03bc\u03bf\u03b3\u03ae \u03c4\u03c9\u03bd \u03b1\u03bb\u03b3\u03bf\u03c1\u03af\u03b8\u03bc\u03c9\u03bd \u03c3\u03b5 \u0397\/\u03a5 \u03b3\u03af\u03bd\u03b5\u03c4\u03b1\u03b9 \u03bc\u03b5 \u03c4\u03b7 \u03c7\u03c1\u03ae\u03c3\u03b7 \u03c0\u03c1\u03bf\u03b3\u03c1\u03b1\u03bc\u03bc\u03b1\u03c4\u03b9\u03c3\u03bc\u03bf\u03cd \u03c3\u03b5 R.<\/p>\n<p><strong>\u0395\u03ba\u03c0\u03b1\u03b9\u03b4\u03b5\u03c5\u03c4\u03b9\u03ba\u03bf\u03af \u03c3\u03c4\u03cc\u03c7\u03bf\u03b9 \u03c4\u03bf\u03c5 \u03bc\u03b1\u03b8\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2<\/strong><\/p>\n<p>\u039c\u03b5\u03c4\u03ac \u03c4\u03b7 \u03b5\u03c0\u03b9\u03c4\u03c5\u03c7\u03ae \u03bf\u03bb\u03bf\u03ba\u03bb\u03ae\u03c1\u03c9\u03c3\u03b7 \u03c4\u03bf\u03c5 \u03bc\u03b1\u03b8\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2 \u03bf \u03c6\u03bf\u03b9\u03c4\u03b7\u03c4\u03ae\u03c2 \u03b8\u03b1 \u03ad\u03c7\u03b5\u03b9 \u03b1\u03c0\u03bf\u03ba\u03c4\u03ae\u03c3\u03b5\u03b9 \u03ba\u03ac\u03c0\u03bf\u03b9\u03b5\u03c2 \u03b2\u03b1\u03c3\u03b9\u03ba\u03ad\u03c2 \u03b3\u03bd\u03ce\u03c3\u03b5\u03b9\u03c2 \u03c3\u03c4\u03bf\u03c7\u03b1\u03c3\u03c4\u03b9\u03ba\u03ae\u03c2 \u03c0\u03c1\u03bf\u03c3\u03bf\u03bc\u03bf\u03af\u03c9\u03c3\u03b7\u03c2, \u03b8\u03b1 \u03ad\u03c7\u03b5\u03b9 \u03bc\u03ac\u03b8\u03b5\u03b9 \u03c4\u03bf\u03c5\u03c2 \u03b2\u03b1\u03c3\u03b9\u03ba\u03bf\u03cd\u03c2 \u03b1\u03bb\u03b3\u03cc\u03c1\u03b9\u03b8\u03bc\u03bf\u03c5\u03c2 MCMC \u03ba\u03b1\u03b9 \u03b8\u03b1 \u03ad\u03c7\u03b5\u03b9 \u03b1\u03c0\u03bf\u03ba\u03c4\u03ae\u03c3\u03b5\u03b9 \u03b5\u03be\u03bf\u03b9\u03ba\u03b5\u03af\u03c9\u03c3\u03b7 \u03bc\u03b5 \u03c4\u03bf\u03bd \u03c0\u03c1\u03bf\u03b3\u03c1\u03b1\u03bc\u03bc\u03b1\u03c4\u03b9\u03c3\u03bc\u03bf \u03c3\u03c4\u03b7\u03bd R \u03bc\u03ad\u03c3\u03b1 \u03b1\u03c0\u03cc \u03c4\u03b7\u03bd \u03b5\u03c6\u03b1\u03c1\u03bc\u03bf\u03b3\u03ae \u03c4\u03c9\u03bd \u03bc\u03b5\u03b8\u03cc\u03b4\u03c9\u03bd \u03ba\u03b1\u03b9 \u03c4\u03c9\u03bd \u03b1\u03bb\u03b3\u03bf\u03c1\u03af\u03b8\u03bc\u03c9\u03bd.<\/p>\n<p><strong>\u03a0\u03b5\u03c1\u03b9\u03b5\u03c7\u03cc\u03bc\u03b5\u03bd\u03bf<\/strong><\/p>\n<ol>\n<li>\u0395\u03b9\u03c3\u03b1\u03b3\u03c9\u03b3\u03ae \u03c3\u03c4\u03b7 \u03a3\u03c4\u03bf\u03c7\u03b1\u03c3\u03c4\u03b9\u03ba\u03ae \u03a0\u03c1\u03bf\u03c3\u03bf\u03bc\u03bf\u03af\u03c9\u03c3\u03b7 \u03ba\u03b1\u03b9 \u03c4\u03b9\u03c2 \u03bc\u03b5\u03b8\u03cc\u03b4\u03bf\u03c5\u03c2 Monte Carlo<\/li>\n<li>\u0394\u03b5\u03b9\u03b3\u03bc\u03b1\u03c4\u03bf\u03bb\u03ae\u03c0\u03c4\u03b7\u03c2 Gibbs<\/li>\n<li>\u03a4\u03b5\u03c7\u03bd\u03b9\u03ba\u03ae \u0391\u03cd\u03be\u03b7\u03c3\u03b7\u03c2 \u0394\u03b5\u03b4\u03bf\u03bc\u03ad\u03bd\u03c9\u03bd \u03b3\u03b9\u03b1 \u03c0\u03c1\u03bf\u03b2\u03bb\u03ae\u03bc\u03b1\u03c4\u03b1 \u03b5\u03bb\u03b9\u03c0\u03ce\u03bd \u03b4\u03b5\u03b4\u03bf\u03bc\u03ad\u03bd\u03c9\u03bd<\/li>\n<li>\u0391\u03bb\u03b3\u03cc\u03c1\u03b9\u03b8\u03bc\u03bf\u03c2 Metropolis-Hastings<\/li>\n<li>\u039c\u03c0\u03b5\u03cb\u03b6\u03b9\u03b1\u03bd\u03ae \u03c3\u03c5\u03bc\u03c0\u03b5\u03c1\u03b1\u03c3\u03bc\u03b1\u03c4\u03bf\u03bb\u03bf\u03b3\u03af\u03b1 \u03b3\u03b9\u03b1 \u0393\u03c1\u03b1\u03bc\u03bc\u03b9\u03ba\u03ac \u039c\u03bf\u03bd\u03c4\u03ad\u03bb\u03b1<\/li>\n<li>\u039c\u03c0\u03b5\u03cb\u03b6\u03b9\u03b1\u03bd\u03ae \u03c3\u03c5\u03bc\u03c0\u03b5\u03c1\u03b1\u03c3\u03bc\u03b1\u03c4\u03bf\u03bb\u03bf\u03b3\u03af\u03b1 \u03b3\u03b9\u03b1 \u0393\u03b5\u03bd\u03b9\u03ba\u03b5\u03c5\u03bc\u03ad\u03bd\u03b1 \u0393\u03c1\u03b1\u03bc\u03bc\u03b9\u03ba\u03ac \u039c\u03bf\u03bd\u03c4\u03ad\u03bb\u03b1<\/li>\n<li>\u0395\u03c6\u03b1\u03c1\u03bc\u03bf\u03b3\u03ad\u03c2 \u03c3\u03c4\u03b7\u03bd R<\/li>\n<\/ol>\n<p><strong>\u039c\u03ad\u03b8\u03bf\u03b4\u03bf\u03b9 \u03b4\u03b9\u03b4\u03b1\u03c3\u03ba\u03b1\u03bb\u03af\u03b1\u03c2<\/strong><\/p>\n<p>\u03a4\u03bf \u03c0\u03b5\u03c1\u03b9\u03b5\u03c7\u03cc\u03bc\u03b5\u03bd\u03bf \u03c4\u03bf\u03c5 \u03bc\u03b1\u03b8\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2 \u03ba\u03b1\u03bb\u03cd\u03c0\u03c4\u03b5\u03c4\u03b1\u03b9 \u03bc\u03ad\u03c3\u03b1 \u03b1\u03c0\u03cc 18 \u03ce\u03c1\u03b5\u03c2 \u03b8\u03b5\u03c9\u03c1\u03b7\u03c4\u03b9\u03ba\u03ae \u03b4\u03b9\u03b4\u03b1\u03c3\u03ba\u03b1\u03bb\u03af\u03b1 \u03ba\u03b1\u03b9 18 \u03ce\u03c1\u03b5\u03c2 \u03c0\u03c1\u03b1\u03ba\u03c4\u03b9\u03ba\u03ae \u03ac\u03c3\u03ba\u03b7\u03c3\u03b7 \u03c3\u03b5 \u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03b9\u03c3\u03c4\u03ad\u03c2 \u03bc\u03b5 \u03c4\u03b7 \u03c7\u03c1\u03ae\u03c3\u03b7 \u03c0\u03c1\u03bf\u03b3\u03c1\u03b1\u03bc\u03bc\u03b1\u03c4\u03b9\u03c3\u03bc\u03bf\u03cd \u03c3\u03c4\u03bf \u03c3\u03c4\u03b1\u03c4\u03b9\u03c3\u03c4\u03b9\u03ba\u03cc \u03c0\u03c1\u03cc\u03b3\u03c1\u03b1\u03bc\u03bc\u03b1 R.<\/p>\n<p><strong>\u039c\u03ad\u03b8\u03bf\u03b4\u03bf\u03c2 \u03b1\u03be\u03b9\u03bf\u03bb\u03cc\u03b3\u03b7\u03c3\u03b7\u03c2<\/strong><\/p>\n<p>\u0397 \u03b1\u03be\u03b9\u03bf\u03bb\u03cc\u03b3\u03b7\u03c3\u03b7 \u03c4\u03bf\u03c5 \u03c6\u03bf\u03b9\u03c4\u03b7\u03c4\u03ae \u03b3\u03af\u03bd\u03b5\u03c4\u03b1\u03b9\u00a0 \u03bc\u03b5 \u03c4\u03b7 \u03b2\u03b1\u03b8\u03bc\u03bf\u03bb\u03cc\u03b3\u03b7\u03c3\u03b7 \u03c4\u03c1\u03b9\u03ce\u03bd \u03b5\u03c1\u03b3\u03b1\u03c3\u03b9\u03ce\u03bd \u03c0\u03bf\u03c5 \u03b5\u03bc\u03c0\u03bb\u03ad\u03ba\u03bf\u03c5\u03bd \u03c0\u03c1\u03bf\u03b3\u03c1\u03b1\u03bc\u03bc\u03b1\u03c4\u03b9\u03c3\u03bc\u03cc \u03c3\u03b5 R \u03ba\u03b1\u03b9 \u03b1\u03bd\u03ac\u03bb\u03c5\u03c3\u03b7 \u03b4\u03b5\u03b4\u03bf\u03bc\u03ad\u03bd\u03c9\u03bd, \u03bf\u03b9 \u03bf\u03c0\u03bf\u03af\u03b5\u03c2 \u03b1\u03bd\u03b1\u03bb\u03bf\u03b3\u03bf\u03cd\u03bd\u00a0 \u03c3\u03c4\u03bf 30% \u00a0\u03c4\u03bf\u03c5 \u03c4\u03b5\u03bb\u03b9\u03ba\u03bf\u03cd \u03b2\u03b1\u03b8\u03bc\u03bf\u03cd, \u03b5\u03bd\u03ce \u03c4\u03bf \u03c5\u03c0\u03cc\u03bb\u03bf\u03b9\u03c0\u03bf 70% \u03c0\u03c1\u03bf\u03ad\u03c1\u03c7\u03b5\u03c4\u03b1\u03b9 \u03b1\u03c0\u03cc \u03c4\u03b7\u03bd \u03b1\u03c0\u03cc\u03b4\u03bf\u03c3\u03b7 \u03c4\u03bf\u03c5 \u03c6\u03bf\u03b9\u03c4\u03b7\u03c4\u03ae \u03c3\u03b5 \u03b3\u03c1\u03b1\u03c0\u03c4\u03ad\u03c2 \u03b5\u03be\u03b5\u03c4\u03ac\u03c3\u03b5\u03b9\u03c2.<\/p>","protected":false},"excerpt":{"rendered":"<p>\u0394\u03b9\u03b4\u03ac\u03c3\u03ba\u03bf\u03c5\u03c3\u03b1 \u039b. \u039c\u03b5\u03bb\u03b9\u03b3\u03ba\u03bf\u03c4\u03c3\u03af\u03b4\u03bf\u03c5 &nbsp; \u03a3\u03ba\u03bf\u03c0\u03cc\u03c2 \u03c4\u03bf\u03c5 \u03bc\u03b1\u03b8\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2 \u0397 \u03c0\u03b1\u03c1\u03bf\u03c5\u03c3\u03af\u03b1\u03c3\u03b7 \u03c4\u03c9\u03bd \u03b1\u03bb\u03b3\u03cc\u03c1\u03b9\u03b8\u03bc\u03c9\u03bd Markov chain Monte Carlo (MCMC) \u03ba\u03b1\u03b9 \u03b7 \u03c7\u03c1\u03ae\u03c3\u03b7 \u03c4\u03bf\u03c5\u03c2 \u03c9\u03c2 \u03b5\u03c1\u03b3\u03b1\u03bb\u03b5\u03af\u03b1 \u03b3\u03b9\u03b1 \u039c\u03c0\u03b5\u03cb\u03b6\u03b9\u03b1\u03bd\u03ae \u03c3\u03c5\u03bc\u03c0\u03b5\u03c1\u03b1\u03c3\u03bc\u03b1\u03c4\u03bf\u03bb\u03bf\u03b3\u03af\u03b1 \u03b3\u03b9\u03b1 \u03c0\u03bf\u03bb\u03cd\u03c0\u03bb\u03bf\u03ba\u03b1 \u03c0\u03bf\u03bb\u03c5\u03c0\u03b1\u03c1\u03b1\u03bc\u03b5\u03c4\u03c1\u03b9\u03ba\u03ac \u03bc\u03bf\u03bd\u03c4\u03ad\u03bb\u03b1. \u03a0\u03c1\u03cc\u03ba\u03b5\u03b9\u03c4\u03b1\u03b9 \u03b3\u03b9\u03b1 \u03ad\u03bd\u03b1 \u03bc\u03ac\u03b8\u03b7\u03bc\u03b1 \u03c0\u03bf\u03c5 \u03c3\u03c5\u03bc\u03c0\u03bb\u03b7\u03c1\u03ce\u03bd\u03b5\u03b9 \u03c4\u03bf \u03bc\u03ac\u03b8\u03b7\u03bc\u03b1 \u2018\u039c\u03c0\u03b5\u03cb\u03b6\u03b9\u03b1\u03bd\u03ae \u03a3\u03c5\u03bc\u03c0\u03b5\u03c1\u03b1\u03c3\u03bc\u03b1\u03c4\u03bf\u03bb\u03bf\u03b3\u03af\u03b1 \u0399\u2019, \u03b4\u03af\u03bd\u03bf\u03bd\u03c4\u03b1\u03c2 \u03c3\u03c4\u03bf\u03c5\u03c2 \u03c6\u03bf\u03b9\u03c4\u03b7\u03c4\u03ad\u03c2 \u03c4\u03b7\u03bd \u03b5\u03c5\u03ba\u03b1\u03b9\u03c1\u03af\u03b1 \u03bd\u03b1 \u03b1\u03c0\u03bf\u03ba\u03c4\u03ae\u03c3\u03bf\u03c5\u03bd \u03c0\u03b9\u03bf \u03b5\u03be\u03b5\u03b9\u03b4\u03b9\u03ba\u03b5\u03c5\u03bc\u03ad\u03bd\u03b7 \u03b3\u03bd\u03ce\u03c3\u03b7 \u03c3\u03c4\u03bf \u03b1\u03bd\u03c4\u03b9\u03ba\u03b5\u03af\u03bc\u03b5\u03bd\u03bf \u03c4\u03b7\u03c2 \u039c\u03c0\u03b5\u03cb\u03b6\u03b9\u03b1\u03bd\u03ae\u03c2 \u03a3\u03c4\u03b1\u03c4\u03b9\u03c3\u03c4\u03b9\u03ba\u03ae\u03c2 <a href=\"https:\/\/biostatistics.med.uoa.gr\/en\/bayes-advanced\/\" rel=\"nofollow\"><span class=\"sr-only\">Read more about \u039c\u03c0\u03b5\u03cb\u03b6\u03b9\u03b1\u03bd\u03ae \u03a3\u03c5\u03bc\u03c0\u03b5\u03c1\u03b1\u03c3\u03bc\u03b1\u03c4\u03bf\u03bb\u03bf\u03b3\u03af\u03b1 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