{"id":28921,"date":"2018-10-28T00:02:25","date_gmt":"2018-10-27T21:02:25","guid":{"rendered":"http:\/\/www.lecturesbureau.gr\/1\/?p=28921"},"modified":"2018-10-28T07:43:14","modified_gmt":"2018-10-28T05:43:14","slug":"the-bayes-theorem-1542","status":"publish","type":"post","link":"https:\/\/www.lecturesbureau.gr\/1\/the-bayes-theorem-1542\/","title":{"rendered":"\u03a4\u03bf \u03b8\u03b5\u03ce\u03c1\u03b7\u03bc\u03b1 \u03c4\u03bf\u03c5 Bayes: \u039f \u03b1\u03c0\u03bb\u03cc\u03c2 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc\u03c2 \u03c4\u03cd\u03c0\u03bf\u03c2 \u03c0\u03bf\u03c5 \u03bc\u03c0\u03bf\u03c1\u03b5\u03af \u03bd\u03b1 \u03b5\u03be\u03b7\u03b3\u03b5\u03af \u03c0\u03ce\u03c2 \u03bb\u03b5\u03b9\u03c4\u03bf\u03c5\u03c1\u03b3\u03b5\u03af \u03bf \u03b1\u03bd\u03b8\u03c1\u03ce\u03c0\u03b9\u03bd\u03bf\u03c2 \u03b5\u03b3\u03ba\u03ad\u03c6\u03b1\u03bb\u03bf\u03c2"},"content":{"rendered":"<div class=\"wpb-content-wrapper\"><p>\u0395\u03af\u03bd\u03b1\u03b9 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\u03b5\u03c0\u03b9\u03c3\u03c4\u03ae\u03bc\u03b7.<\/p>\n<p>\u03a0\u03c1\u03cc\u03ba\u03b5\u03b9\u03c4\u03b1\u03b9 \u03b3\u03b9\u03b1 \u03bc\u03b9\u03b1 \u03b1\u03c0\u03cc \u03c4\u03b9\u03c2 \u03b5\u03be\u03b9\u03c3\u03ce\u03c3\u03b5\u03b9\u03c2 \u03c0\u03bf\u03c5 \u03bf\u03b9 \u03c6\u03bf\u03b9\u03c4\u03b7\u03c4\u03ad\u03c2 \u03c4\u03c9\u03bd \u03b8\u03b5\u03c4\u03b9\u03ba\u03ce\u03bd \u03b5\u03c0\u03b9\u03c3\u03c4\u03b7\u03bc\u03ce\u03bd, \u03b1\u03c1\u03b3\u03ac \u03ae \u03b3\u03c1\u03ae\u03b3\u03bf\u03c1\u03b1, \u03b8\u03b1 \u03c3\u03c5\u03bd\u03b1\u03bd\u03c4\u03ae\u03c3\u03bf\u03c5\u03bd \u03bc\u03c0\u03c1\u03bf\u03c3\u03c4\u03ac \u03c4\u03bf\u03c5\u03c2. \u039c\u03ac\u03bb\u03b9\u03c3\u03c4\u03b1, \u03c3\u03c5\u03bd\u03ae\u03b8\u03c9\u03c2 \u03b1\u03c5\u03c4\u03cc \u03b3\u03af\u03bd\u03b5\u03c4\u03b1\u03b9 \u03c3\u03c4\u03b1 \u03c0\u03c1\u03ce\u03c4\u03b1 \u03c7\u03c1\u03cc\u03bd\u03b9\u03b1 \u03c6\u03bf\u03af\u03c4\u03b7\u03c3\u03b7\u03c2, \u03ba\u03b1\u03b8\u03ce\u03c2 \u03c4\u03bf\u00a0\u0398\u03b5\u03ce\u03c1\u03b7\u03bc\u03b1 \u03c4\u03bf\u03c5 Bayes\u00a0\u03b4\u03b5\u03bd \u03b5\u03af\u03bd\u03b1\u03b9 \u03bf\u03cd\u03c4\u03b5 \u03b1\u03ba\u03b1\u03c4\u03b1\u03bd\u03cc\u03b7\u03c4\u03bf, \u03bf\u03cd\u03c4\u03b5 \u03b4\u03cd\u03c3\u03bc\u03bf\u03c1\u03c6\u03bf \u03cc\u03c0\u03c9\u03c2 \u03bf\u03b9 \u03c0\u03b5\u03c1\u03b9\u03c3\u03c3\u03cc\u03c4\u03b5\u03c1\u03bf\u03b9 \u03c4\u03cd\u03c0\u03bf\u03b9. \u039c\u03b5 \u03bb\u03af\u03b3\u03b7 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ae \u03b4\u03b9\u03b1\u03af\u03c3\u03b8\u03b7\u03c3\u03b7, \u03b1\u03c5\u03c4\u03cc \u03c0\u03bf\u03c5 \u03b4\u03b9\u03b1\u03c4\u03cd\u03c0\u03c9\u03c3\u03b5 \u03ba\u03b1\u03b9 \u03b1\u03c0\u03ad\u03b4\u03b5\u03b9\u03be\u03b5 \u03bf \u0386\u03b3\u03b3\u03bb\u03bf\u03c2 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc\u03c2 \u03c3\u03c4\u03b9\u03c2 \u03b1\u03c1\u03c7\u03ad\u03c2 \u03c4\u03bf\u03c5 18\u03bf\u03c5 \u03b1\u03b9\u03ce\u03bd\u03b1, \u03b3\u03af\u03bd\u03b5\u03c4\u03b1\u03b9 \u03c0\u03bb\u03ae\u03c1\u03c9\u03c2 \u03b1\u03bd\u03c4\u03b9\u03bb\u03b7\u03c0\u03c4\u03cc.<\/p>\n<p>[vc_single_image image=&#8221;28910&#8243; img_size=&#8221;full&#8221; alignment=&#8221;center&#8221; qode_css_animation=&#8221;element_from_fade&#8221; css=&#8221;.vc_custom_1540705165952{padding-top: 20px !important;padding-bottom: 20px !important;}&#8221;][vc_column_text]\u0397 \u03c0\u03b1\u03c1\u03b1\u03c0\u03ac\u03bd\u03c9 \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7 \u03b5\u03ba\u03c6\u03c1\u03ac\u03b6\u03b5\u03b9 \u03c4\u03bf \u03b8\u03b5\u03ce\u03c1\u03b7\u03bc\u03b1 \u03c4\u03bf\u03c5 Bayes \u03c0\u03bf\u03c5 \u03bc\u03b1\u03b8\u03b1\u03af\u03bd\u03bf\u03c5\u03bd \u03cc\u03bb\u03bf\u03b9 \u03bf\u03b9 \u03c0\u03c1\u03c9\u03c4\u03bf\u03b5\u03c4\u03b5\u03af\u03c2 \u03c6\u03bf\u03b9\u03c4\u03b7\u03c4\u03ad\u03c2 \u03c4\u03c9\u03bd \u03b8\u03b5\u03c4\u03b9\u03ba\u03ce\u03bd \u03b5\u03c0\u03b9\u03c3\u03c4\u03b7\u03bc\u03ce\u03bd. \u0394\u03b9\u03b1\u03c4\u03c5\u03c0\u03ce\u03b8\u03b7\u03ba\u03b5 \u03b1\u03c0\u03cc \u03c4\u03bf\u03bd \u0386\u03b3\u03b3\u03bb\u03bf \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc \u03ba\u03b1\u03b9 \u03c0\u03c1\u03b5\u03c3\u03b2\u03c5\u03c4\u03b5\u03c1\u03b9\u03b1\u03bd\u03cc \u03b9\u03b5\u03c1\u03ad\u03b1 \u03a4\u03cc\u03bc\u03b1\u03c2 \u039c\u03c0\u03ad\u03c5\u03b6 (Thomas Bayes 1701\u20131761).<br \/>\n\u03a4\u03b9 \u03b5\u03be\u03b7\u03b3\u03b5\u03af \u03b1\u03c5\u03c4\u03cc\u03c2 \u03bf \u03b1\u03c0\u03bb\u03bf\u03cd\u03c3\u03c4\u03b1\u03c4\u03bf\u03c2 \u03bd\u03cc\u03bc\u03bf\u03c2; \u2013 \u03a0\u03ce\u03c2 \u03bd\u03b1 \u03c4\u03bf\u03bd \u03b1\u03c0\u03bf\u03b4\u03b5\u03af\u03be\u03b5\u03c4\u03b5, \u03c7\u03c1\u03b7\u03c3\u03b9\u03bc\u03bf\u03c0\u03bf\u03b9\u03ce\u03bd\u03c4\u03b1\u03c2 \u03ad\u03bd\u03b1 \u03b6\u03ac\u03c1\u03b9<br \/>\n\u03a4\u03bf \u03b8\u03b5\u03ce\u03c1\u03b7\u03bc\u03b1 \u03c4\u03bf\u03c5 Bayes \u03b1\u03bd\u03ae\u03ba\u03b5\u03b9 \u03c3\u03c4\u03b7\u03bd \u03bc\u03b5\u03b3\u03ac\u03bb\u03b7 \u03bf\u03b9\u03ba\u03bf\u03b3\u03ad\u03bd\u03b5\u03b9\u03b1 \u03c4\u03b7\u03c2 \u00ab\u0398\u03b5\u03c9\u03c1\u03af\u03b1\u03c2 \u03c4\u03c9\u03bd \u03a0\u03b9\u03b8\u03b1\u03bd\u03bf\u03c4\u03ae\u03c4\u03c9\u03bd\u00bb. \u0394\u03b5\u03bd \u03b5\u03af\u03bd\u03b1\u03b9 \u03cc\u03bc\u03c9\u03c2 \u03ad\u03bd\u03b1 \u03b1\u03c0\u03bb\u03cc \u03bc\u03ad\u03bb\u03bf\u03c2 \u03c4\u03b7\u03c2. \u039f Harold Jeffreys, \u03ad\u03bd\u03b1\u03c2 \u03b1\u03c0\u03cc \u03c4\u03bf\u03c5\u03c2 \u03c3\u03c0\u03bf\u03c5\u03b4\u03b1\u03b9\u03cc\u03c4\u03b5\u03c1\u03bf\u03c5\u03c2 \u0386\u03b3\u03b3\u03bb\u03bf\u03c5\u03c2 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03bf\u03cd\u03c2, \u03c0\u03bf\u03c5 \u03b1\u03c3\u03c7\u03bf\u03bb\u03ae\u03b8\u03b7\u03ba\u03b5 \u03bc\u03b5 \u03c4\u03b9\u03c2 \u00ab\u03bc\u03c0\u03b5\u03ca\u03b6\u03b9\u03b1\u03bd\u03ad\u03c2\u00bb \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b5\u03c2 \u03ba\u03b1\u03b9 \u03b5\u03b9\u03c3\u03ae\u03b3\u03b1\u03b3\u03b5 \u03c4\u03b7\u03bd \u03ad\u03bd\u03bd\u03bf\u03b9\u03b1 \u03c4\u03bf\u03c5 \u03b1\u03bb\u03b3\u03bf\u03c1\u03af\u03b8\u03bc\u03bf\u03c5 Bayes, \u03b5\u03af\u03c7\u03b5 \u03b4\u03b7\u03bb\u03ce\u03c3\u03b5\u03b9 \u03c0\u03c9\u03c2 \u03bf \u03c3\u03c5\u03b3\u03ba\u03b5\u03ba\u03c1\u03b9\u03bc\u03ad\u03bd\u03bf\u03c2 \u03c4\u03cd\u03c0\u03bf\u03c2 \u00ab\u03b5\u03af\u03bd\u03b1\u03b9 \u03c3\u03c4\u03b7 \u0398\u03b5\u03c9\u03c1\u03af\u03b1 \u03a0\u03b9\u03b8\u03b1\u03bd\u03bf\u03c4\u03ae\u03c4\u03c9\u03bd \u03cc\u03c0\u03c9\u03c2 \u03b1\u03bd\u03c4\u03af\u03c3\u03c4\u03bf\u03b9\u03c7\u03b1 \u03c4\u03bf \u03a0\u03c5\u03b8\u03b1\u03b3\u03cc\u03c1\u03b5\u03b9\u03bf \u0398\u03b5\u03ce\u03c1\u03b7\u03bc\u03b1 \u03c3\u03c4\u03b7 \u0393\u03b5\u03c9\u03bc\u03b5\u03c4\u03c1\u03af\u03b1\u00bb.<br \/>\n\u039f Bayes \u03b1\u03c3\u03c7\u03bf\u03bb\u03ae\u03b8\u03b7\u03ba\u03b5 \u03bc\u03b5 \u03c4\u03b9\u03c2\u00a0\u03b4\u03b5\u03c3\u03bc\u03b5\u03c5\u03bc\u03ad\u03bd\u03b5\u03c2 \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b5\u03c2\u00a0\u03ae \u03b1\u03bb\u03bb\u03b9\u03ce\u03c2 \u03c4\u03b9\u03c2 \u00ab\u03c5\u03c0\u03cc \u03c3\u03c5\u03bd\u03b8\u03ae\u03ba\u03b7\u00bb \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b5\u03c2. \u039f \u03bd\u03cc\u03bc\u03bf\u03c2 \u03c4\u03bf\u03c5, \u03bc\u03ad\u03c3\u03b1 \u03c3\u03c4\u03b7\u03bd \u03c3\u03c5\u03bd\u03bf\u03c0\u03c4\u03b9\u03ba\u03ae \u03c4\u03bf\u03c5 \u03b3\u03c1\u03b1\u03c6\u03ae, \u03ba\u03c1\u03cd\u03b2\u03b5\u03b9 \u03bc\u03c5\u03c3\u03c4\u03b9\u03ba\u03ac \u03c0\u03bf\u03c5 \u03b2\u03b1\u03c3\u03b1\u03bd\u03af\u03b6\u03bf\u03c5\u03bd \u03b1\u03c0\u03cc \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03bf\u03cd\u03c2 \u03ba\u03b1\u03b9 \u03c6\u03c5\u03c3\u03b9\u03ba\u03bf\u03cd\u03c2, \u03bc\u03ad\u03c7\u03c1\u03b9 \u03b3\u03b9\u03b1\u03c4\u03c1\u03bf\u03cd\u03c2 \u03ba\u03b1\u03b9 \u03c6\u03b9\u03bb\u03bf\u03c3\u03cc\u03c6\u03bf\u03c5\u03c2. \u0393\u03c1\u03ac\u03c6\u03bf\u03bd\u03c4\u03b1\u03c2 \u03c4\u03bf\u00a0\u00ab<strong>P(A|B) = P(B|A)*P(A)\/ P(B)<\/strong>\u00bb\u00a0\u03bf \u0391\u03b3\u03b3\u03bb\u03bf\u03c2 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc\u03c2 \u03b4\u03b5\u03bd \u03c0\u03b5\u03c1\u03af\u03bc\u03b5\u03bd\u03b5 \u03c0\u03c9\u03c2 \u03bf \u03c4\u03cd\u03c0\u03bf\u03c2 \u03c4\u03bf\u03c5, \u03bc\u03b5\u03c4\u03ac \u03b1\u03c0\u03cc 300 \u03c7\u03c1\u03cc\u03bd\u03b9\u03b1, \u03b8\u03b1 \u03ad\u03c7\u03b5\u03b9 \u03b4\u03b7\u03bc\u03b9\u03bf\u03c5\u03c1\u03b3\u03ae\u03c3\u03b5\u03b9 \u03bf\u03bb\u03cc\u03ba\u03bb\u03b7\u03c1\u03b1 \u03c6\u03b9\u03bb\u03bf\u03c3\u03bf\u03c6\u03b9\u03ba\u03ac \u03b5\u03c1\u03c9\u03c4\u03ae\u03bc\u03b1\u03c4\u03b1. \u03a0\u03c9\u03c2 \u03b8\u03b1 \u03ad\u03c7\u03b5\u03b9 \u03b5\u03c0\u03b7\u03c1\u03b5\u03ac\u03c3\u03b5\u03b9 \u03c4\u03b7\u03bd 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\u03b9\u03c3\u03bf\u03cd\u03c4\u03b1\u03b9 \u03bc\u03b5 \u03c4\u03b7\u03bd \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1 \u03bd\u03b1 \u03c3\u03c5\u03bc\u03b2\u03b5\u03af \u03c4\u03bf \u0392 \u03b4\u03b5\u03b4\u03bf\u03bc\u03ad\u03bd\u03bf\u03c5 \u03c4\u03bf\u03c5 \u0391, \u03b5\u03c0\u03af \u03c4\u03b7\u03bd \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1 \u03bd\u03b1 \u03c3\u03c5\u03bc\u03b2\u03b5\u03af \u03c4\u03bf \u0391, \u03b4\u03b9\u03ac \u03c4\u03b7\u03bd \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1 \u03bd\u03b1 \u03c3\u03c5\u03bc\u03b2\u03b5\u03af \u03c4\u03bf \u0392\u00bb. \u039f \u03bd\u03cc\u03bc\u03bf\u03c2 \u03c4\u03bf\u03c5 Bayes \u03b3\u03af\u03bd\u03b5\u03c4\u03b1\u03b9 \u03c0\u03bf\u03bb\u03cd \u03b5\u03cd\u03ba\u03bf\u03bb\u03b1 \u03b1\u03bd\u03c4\u03b9\u03bb\u03b7\u03c0\u03c4\u03cc\u03c2 \u03bc\u03b5 \u03ad\u03bd\u03b1 \u03b1\u03c0\u03bb\u03cc \u03c0\u03b1\u03c1\u03ac\u03b4\u03b5\u03b9\u03b3\u03bc\u03b1.<br 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\u039a\u03ac\u03b8\u03b5 \u03ad\u03bd\u03b1 \u03b1\u03c0\u03cc \u03b1\u03c5\u03c4\u03ac \u03ad\u03c7\u03b5\u03b9 1\/3 \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1 \u03bd\u03b1 \u03b9\u03c3\u03c7\u03cd\u03b5\u03b9.<br \/>\n\u0391\u03c2 \u03c4\u03bf \u03b4\u03bf\u03cd\u03bc\u03b5 \u03c4\u03ce\u03c1\u03b1 \u03bc\u03ad\u03c3\u03b1 \u03b1\u03c0\u03cc \u03c4\u03bf\u03bd \u03c4\u03cd\u03c0\u03bf \u03c4\u03bf\u03c5 Bayes: \u0397 \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1 \u03bd\u03b1 \u03ad\u03c7\u03c9 \u03c6\u03ad\u03c1\u03b5\u03b9 \u03b6\u03c5\u03b3\u03cc, \u03b1\u03bd \u03be\u03ad\u03c1\u03c9 \u03cc\u03c4\u03b9 \u03ad\u03c6\u03b5\u03c1\u03b1 2, \u03b5\u03af\u03bd\u03b1\u03b9 100%. \u0397 \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1 \u03bd\u03b1 \u03c6\u03ad\u03c1\u03c9 2, \u03c7\u03c9\u03c1\u03af\u03c2 \u03bd\u03b1 \u03be\u03ad\u03c1\u03c9 \u03c4\u03af\u03c0\u03bf\u03c4\u03b1, \u03b5\u03af\u03bd\u03b1\u03b9 1\/6 (\u03b5\u03c0\u03b5\u03b9\u03b4\u03ae \u03c4\u03bf \u03b6\u03ac\u03c1\u03b9 \u03ad\u03c7\u03b5\u03b9 6 \u03c0\u03bb\u03b5\u03c5\u03c1\u03ad\u03c2). \u0397 \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1 \u03bd\u03b1 \u03c6\u03ad\u03c1\u03c9 \u03b6\u03c5\u03b3\u03cc \u03b5\u03af\u03bd\u03b1\u03b9 1\/2. \u0392\u03ac\u03b6\u03bf\u03bd\u03c4\u03b1\u03c2 \u03c4\u03b1 \u03bd\u03bf\u03cd\u03bc\u03b5\u03c1\u03b1 \u03c0\u03ac\u03bd\u03c9 \u03c3\u03c4\u03b7\u03bd \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7 \u03ad\u03c7\u03bf\u03c5\u03bc\u03b5 \u03cc\u03c4\u03b9 P(A|B) = (1* 1\/6)\/1\/2 =1\/3.<br \/>\n\u039f \u03bd\u03cc\u03bc\u03bf\u03c2 \u03c4\u03bf\u03c5 Bayes \u03bc\u03c0\u03bf\u03c1\u03b5\u03af \u03bd\u03b1 \u03b3\u03af\u03bd\u03b5\u03b9 \u03b5\u03cd\u03ba\u03bf\u03bb\u03b1 \u03ba\u03b1\u03c4\u03b1\u03bd\u03bf\u03b7\u03c4\u03cc\u03c2. \u039f\u03b9 \u03c3\u03c5\u03bd\u03ad\u03c0\u03b5\u03b9\u03b5\u03c2 \u03c4\u03bf\u03c5 \u03cc\u03bc\u03c9\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 \u03c0\u03c1\u03b1\u03b3\u03bc\u03b1\u03c4\u03b9\u03ba\u03ac\u2026 \u03b1\u03c3\u03cd\u03bb\u03bb\u03b7\u03c0\u03c4\u03b5\u03c2.<\/p>\n<p>[\/vc_column_text][vc_single_image image=&#8221;28913&#8243; img_size=&#8221;full&#8221; alignment=&#8221;center&#8221; qode_css_animation=&#8221;element_from_fade&#8221; css=&#8221;.vc_custom_1540705173452{padding-top: 20px !important;padding-bottom: 20px !important;}&#8221;][vc_column_text]O Sheldon Cooper \u03c3\u03c4\u03bf \u03c4\u03b7\u03bb\u03b5\u03bf\u03c0\u03c4\u03b9\u03ba\u03cc \u03c3\u03af\u03c1\u03b9\u03b1\u03bb Big Bang Theory \u03c7\u03c1\u03b7\u03c3\u03b9\u03bc\u03bf\u03c0\u03bf\u03b9\u03b5\u03af \u03c4\u03bf \u03b8\u03b5\u03ce\u03c1\u03b7\u03bc\u03b1 \u03c4\u03bf\u03c5 Bayes<br \/>\n\u038c\u03c3\u03bf\u03bd \u03b1\u03c6\u03bf\u03c1\u03ac \u03c4\u03b7\u03bd \u03ba\u03b1\u03c4\u03b1\u03bd\u03cc\u03b7\u03c3\u03b7 \u03c4\u03bf\u03c5 \u03b8\u03b5\u03c9\u03c1\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2 \u03c4\u03bf\u03c5 Bayes, \u03bf Horgan \u03b8\u03b5\u03c9\u03c1\u03b5\u03af \u03c0\u03bf\u03bb\u03cd \u03c7\u03c1\u03ae\u03c3\u03b9\u03bc\u03bf \u03c4\u03bf \u03b4\u03bf\u03ba\u03af\u03bc\u03b9\u03bf,\u00a0 \u201cAn Intuitive Explanation of Bayes\u2019 Theorem\u201d, \u03c4\u03bf\u03c5 \u03b8\u03b5\u03c9\u03c1\u03b7\u03c4\u03b9\u03ba\u03bf\u03cd \u03c4\u03b7\u03c2 \u03c4\u03b5\u03c7\u03bd\u03b7\u03c4\u03ae\u03c2 \u03bd\u03bf\u03b7\u03bc\u03bf\u03c3\u03cd\u03bd\u03b7\u03c2 Eliezer Yudkowsky, \u03c4\u03b7\u03bd \u03c0\u03b1\u03c1\u03bf\u03c5\u03c3\u03af\u03b1\u03c3\u03b7 \u03c4\u03bf\u03c5 \u03b8\u03b5\u03c9\u03c1\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2 \u03c3\u03c4\u03b7\u00a0Wikipedia, \u03b1\u03bb\u03bb\u03ac \u03ba\u03b1\u03b9\u00a0\u03c4\u03b7\u03bd \u03c3\u03cd\u03bd\u03c4\u03bf\u03bc\u03b7 \u03c0\u03b1\u03c1\u03bf\u03c5\u03c3\u03af\u03b1\u03c3\u03b7 \u03c4\u03bf\u03c5 \u03c6\u03b9\u03bb\u03bf\u03c3\u03cc\u03c6\u03bf\u03c5 Curtis Brown.<br \/>\n\u0388\u03bd\u03b1\u03c2 \u03ba\u03c1\u03c5\u03bc\u03bc\u03ad\u03bd\u03bf\u03c2 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\u03b5\u03c5\u03b8\u03cd\u03bd\u03bf\u03bd\u03c4\u03b1\u03b9 \u03b3\u03b9\u03b1 \u03c4\u03bf 20%, 30%, \u03ba\u03b1\u03b9 50% \u03c4\u03b7\u03c2 \u03c0\u03b1\u03c1\u03b1\u03b3\u03c9\u03b3\u03ae\u03c2, \u03b1\u03bd\u03c4\u03af\u03c3\u03c4\u03bf\u03b9\u03c7\u03b1. \u03a4\u03bf \u03cc\u03c1\u03b9\u03bf \u03c4\u03c9\u03bd \u03b5\u03bb\u03b1\u03c4\u03c4\u03c9\u03bc\u03b1\u03c4\u03b9\u03ba\u03ce\u03bd \u03b1\u03bd\u03c4\u03b9\u03ba\u03b5\u03b9\u03bc\u03ad\u03bd\u03c9\u03bd \u03c0\u03bf\u03c5 \u03c0\u03b1\u03c1\u03ac\u03b3\u03b5\u03c4\u03b1\u03b9 \u03b5\u03af\u03bd\u03b1\u03b9: \u03b3\u03b9\u03b1 \u03c4\u03b7\u03bd \u03c0\u03c1\u03ce\u03c4\u03b7 \u03bc\u03b7\u03c7\u03b1\u03bd\u03ae, 5%; \u03b3\u03b9\u03b1 \u03c4\u03b7 \u03b4\u03b5\u03cd\u03c4\u03b5\u03c1\u03b7 \u03bc\u03b7\u03c7\u03b1\u03bd\u03ae, 3%; \u03b3\u03b9\u03b1 \u03c4\u03b7\u03bd \u03c4\u03c1\u03af\u03c4\u03b7 \u03bc\u03b7\u03c7\u03b1\u03bd\u03ae, 1%. \u0391\u03bd \u03ad\u03bd\u03b1 \u03b1\u03bd\u03c4\u03b9\u03ba\u03b5\u03af\u03bc\u03b5\u03bd\u03bf \u03b5\u03c0\u03b9\u03bb\u03ad\u03b3\u03b5\u03c4\u03b1\u03b9 \u03c4\u03c5\u03c7\u03b1\u03af\u03b1 \u03b1\u03c0\u03cc \u03c4\u03bf \u03c3\u03cd\u03bd\u03bf\u03bb\u03bf \u03c4\u03b7\u03c2 \u03c0\u03b1\u03c1\u03b1\u03b3\u03c9\u03b3\u03ae\u03c2 \u03ba\u03b1\u03b9 \u03b2\u03c1\u03b5\u03b8\u03b5\u03af \u03bd\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b5\u03bb\u03b1\u03c4\u03c4\u03c9\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc, \u03c0\u03bf\u03b9\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b7 \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1 \u03bd\u03b1 \u03ad\u03c7\u03b5\u03b9 \u03c0\u03b1\u03c1\u03b1\u03c7\u03b8\u03b5\u03af \u03b1\u03c0\u03cc \u03c4\u03b7\u03bd \u03c4\u03c1\u03af\u03c4\u03b7 \u03bc\u03b7\u03c7\u03b1\u03bd\u03ae?<br \/>\n\u0397 \u03bb\u03cd\u03c3\u03b7 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b7 \u03b1\u03ba\u03cc\u03bb\u03bf\u03c5\u03b8\u03b7. \u0388\u03c3\u03c4\u03c9\u00a0Ai\u00a0\u03b4\u03b7\u03bb\u03ce\u03bd\u03bf\u03c5\u03bc\u03b5 \u03c4\u03bf \u03b3\u03b5\u03b3\u03bf\u03bd\u03cc\u03c2 \u03cc\u03c4\u03b9 \u03c4\u03bf \u03b1\u03bd\u03c4\u03b9\u03ba\u03b5\u03af\u03bc\u03b5\u03bd\u03bf \u03c0\u03bf\u03c5 \u03b5\u03c0\u03b9\u03bb\u03ad\u03c7\u03b8\u03b7\u03ba\u03b5 \u03c4\u03c5\u03c7\u03b1\u03af\u03b1 \u03b5\u03af\u03c7\u03b5 \u03c0\u03b1\u03c1\u03b1\u03c7\u03b8\u03b5\u03af \u03b1\u03c0\u03cc \u03c4\u03b7\u03bd\u00a0i\u00a0\u03bc\u03b7\u03c7\u03b1\u03bd\u03ae (\u03b3\u03b9\u03b1\u00a0i\u00a0= 1,2,3). \u0388\u03c3\u03c4\u03c9\u00a0B\u03b4\u03b7\u03bb\u03ce\u03bd\u03bf\u03c5\u03bc\u03b5 \u03c4\u03bf \u03b3\u03b5\u03b3\u03bf\u03bd\u03cc\u03c2 \u03cc\u03c4\u03b9 \u03c4\u03bf \u03b1\u03bd\u03c4\u03b9\u03ba\u03b5\u03af\u03bc\u03b5\u03bd\u03bf \u03c0\u03bf\u03c5 \u03b5\u03c0\u03b9\u03bb\u03ad\u03c7\u03b8\u03b7\u03ba\u03b5 \u03c4\u03c5\u03c7\u03b1\u03af\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b5\u03bb\u03b1\u03c4\u03c4\u03c9\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc. \u03a4\u03cc\u03c4\u03b5 \u03b3\u03bd\u03c9\u03c1\u03af\u03b6\u03bf\u03c5\u03bc\u03b5 \u03c4\u03b1 \u03b1\u03ba\u03cc\u03bb\u03bf\u03c5\u03b8\u03b1:<br \/>\n<strong>P(A1) = 0.2,\u00a0\u00a0\u00a0\u00a0P(A2) = 0.3,\u00a0\u00a0\u00a0\u00a0P(A3) = 0.5.<\/strong><br \/>\n\u0391\u03bd \u03c4\u03bf \u03b1\u03bd\u03c4\u03b9\u03ba\u03b5\u03af\u03bc\u03b5\u03bd\u03bf \u03c0\u03b1\u03c1\u03ac\u03c7\u03b8\u03b7\u03ba\u03b5 \u03b1\u03c0\u03cc \u03c4\u03b7 \u03bc\u03b7\u03c7\u03b1\u03bd\u03ae\u00a0A1, \u03c4\u03cc\u03c4\u03b5 \u03b7 \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1 \u03bd\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b5\u03bb\u03b1\u03c4\u03c4\u03c9\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc \u03b5\u03af\u03bd\u03b1\u03b9 0.05 \u03b4\u03b7\u03bb\u03b1\u03b4\u03ae,\u00a0<strong>P(B\u00a0|\u00a0A1) = 0.05.<\/strong> \u03a3\u03c5\u03bd\u03b5\u03c0\u03ce\u03c2, \u03ad\u03c7\u03bf\u03c5\u03bc\u03b5<br \/>\n<strong>P(B\u00a0|\u00a0A1) = 0.05,\u00a0\u00a0\u00a0\u00a0P(B\u00a0|\u00a0A2) = 0.03,\u00a0\u00a0\u00a0\u00a0P(B\u00a0|\u00a0A3) = 0.01.<\/strong><br \/>\n\u0393\u03b9\u03b1 \u03bd\u03b1 \u03b1\u03c0\u03b1\u03bd\u03c4\u03ae\u03c3\u03bf\u03c5\u03bc\u03b5 \u03c4\u03bf \u03b5\u03c1\u03ce\u03c4\u03b7\u03bc\u03b1, \u03c0\u03c1\u03ad\u03c0\u03b5\u03b9 \u03c0\u03c1\u03ce\u03c4\u03b1 \u03bd\u03b1 \u03b2\u03c1\u03bf\u03cd\u03bc\u03b5\u00a0P(B). \u0391\u03c5\u03c4\u03cc \u03bc\u03c0\u03bf\u03c1\u03b5\u03af \u03bd\u03b1 \u03b3\u03af\u03bd\u03b5\u03b9 \u03bc\u03b5 \u03c4\u03bf\u03bd \u03b1\u03ba\u03cc\u03bb\u03bf\u03c5\u03b8\u03bf \u03c4\u03c1\u03cc\u03c0\u03bf:<br \/>\n<strong>P(B) = \u03a3i\u00a0P(B\u00a0|\u00a0Ai)\u202fP(Ai) = (0.05)(0.2) + (0.03)(0.3) + (0.01)(0.5) = 0.024.<\/strong><br \/>\n\u03a9\u03c2 \u03b5\u03ba \u03c4\u03bf\u03cd\u03c4\u03bf\u03c5 2.4% \u03b1\u03c0\u03cc \u03c4\u03b7 \u03c3\u03c5\u03bd\u03bf\u03bb\u03b9\u03ba\u03ae \u03c0\u03b1\u03c1\u03b1\u03b3\u03c9\u03b3\u03ae \u03c4\u03bf\u03c5 \u03b5\u03c1\u03b3\u03bf\u03c3\u03c4\u03b1\u03c3\u03af\u03bf\u03c5 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b5\u03bb\u03b1\u03c4\u03c4\u03c9\u03bc\u03b1\u03c4\u03b9\u03ba\u03ae.<br \/>\n\u0394\u03b7\u03bb\u03ce\u03c3\u03b1\u03bc\u03b5 \u03c4\u03bf\u00a0B\u00a0\u03c0\u03c9\u03c2 \u03c0\u03c1\u03bf\u03ad\u03ba\u03c5\u03c8\u03b5, \u03ba\u03b1\u03b9 \u03b8\u03ad\u03bb\u03bf\u03c5\u03bc\u03b5 \u03bd\u03b1 \u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03af\u03c3\u03bf\u03c5\u03bc\u03b5 \u03c4\u03b7 \u03b4\u03b5\u03c3\u03bc\u03b5\u03c5\u03bc\u03ad\u03bd\u03b7 \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1 \u03c4\u03bf\u03c5\u00a0A3. \u0391\u03c0\u03cc \u03c4\u03bf \u03b8\u03b5\u03ce\u03c1\u03b7\u03bc\u03b1 \u03c4\u03bf\u03c5 \u039c\u03c0\u03ad\u03c5\u03b6,<br \/>\n<strong>P(A3\u00a0|\u00a0B) =\u00a0P(B\u00a0|\u00a0A3)\u202fP(A3)\/P(B) = (0.01)(0.50)\/(0.024) = 5\/24.<\/strong><br \/>\n\u0394\u03b5\u03b4\u03bf\u03bc\u03ad\u03bd\u03bf\u03c5 \u03cc\u03c4\u03b9 \u03c4\u03bf \u03b1\u03bd\u03c4\u03b9\u03ba\u03b5\u03af\u03bc\u03b5\u03bd\u03bf \u03b5\u03af\u03bd\u03b1\u03b9 \u03b5\u03bb\u03b1\u03c4\u03c4\u03c9\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc, \u03b7 \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1 \u03bd\u03b1 \u03c0\u03b1\u03c1\u03ac\u03c7\u03b8\u03b7\u03ba\u03b5 \u03b1\u03c0\u03cc \u03c4\u03b7\u03bd \u03c4\u03c1\u03af\u03c4\u03b7 \u03bc\u03b7\u03c7\u03b1\u03bd\u03ae \u03b5\u03af\u03bd\u03b1\u03b9 \u03bc\u03cc\u03bd\u03bf <strong>5\/24<\/strong>. \u0391\u03bd \u03ba\u03b1\u03b9 \u03b7 \u03c4\u03c1\u03af\u03c4\u03b7 \u03bc\u03b7\u03c7\u03b1\u03bd\u03ae \u03c0\u03b1\u03c1\u03ac\u03b3\u03b5\u03b9 \u03c4\u03bf \u03bc\u03b9\u03c3\u03cc \u03b1\u03c0\u03cc \u03c4\u03b7 \u03c3\u03c5\u03bd\u03bf\u03bb\u03b9\u03ba\u03ae \u03c0\u03b1\u03c1\u03b1\u03b3\u03c9\u03b3\u03ae, \u03c0\u03b1\u03c1\u03ac\u03b3\u03b5\u03b9 \u03ad\u03bd\u03b1 \u03c0\u03bf\u03bb\u03cd \u03bc\u03b9\u03ba\u03c1\u03cc\u03c4\u03b5\u03c1\u03bf \u03c0\u03bf\u03c3\u03bf\u03c3\u03c4\u03cc \u03b1\u03c0\u03cc \u03c4\u03b1 \u03b5\u03bb\u03b1\u03c4\u03c4\u03c9\u03bc\u03b1\u03c4\u03b9\u03ba\u03ac \u03b1\u03bd\u03c4\u03b9\u03ba\u03b5\u03af\u03bc\u03b5\u03bd\u03b1. \u03a9\u03c2 \u03b5\u03ba \u03c4\u03bf\u03cd\u03c4\u03bf\u03c5, \u03c4\u03bf \u03cc\u03c4\u03b9 \u03b3\u03bd\u03c9\u03c1\u03af\u03b6\u03bf\u03c5\u03bc\u03b5 \u03c0\u03c9\u03c2 \u03c4\u03bf \u03b1\u03bd\u03c4\u03b9\u03ba\u03b5\u03af\u03bc\u03b5\u03bd\u03bf \u03c0\u03bf\u03c5 \u03b5\u03c0\u03b9\u03bb\u03ad\u03c7\u03b8\u03b7\u03ba\u03b5 \u03ae\u03c4\u03b1\u03bd \u03b5\u03bb\u03b1\u03c4\u03c4\u03c9\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc \u03bc\u03b1\u03c2 \u03b4\u03af\u03bd\u03b5\u03b9 \u03c4\u03b7 \u03b4\u03c5\u03bd\u03b1\u03c4\u03cc\u03c4\u03b7\u03c4\u03b1 \u03bd\u03b1 \u03b1\u03bd\u03c4\u03b9\u03ba\u03b1\u03c4\u03b1\u03c3\u03c4\u03ae\u03c3\u03bf\u03c5\u03bc\u03b5 \u03c4\u03b7\u03bd \u03b1\u03c1\u03c7\u03b9\u03ba\u03ae \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1<strong>\u00a0P(A3) = 1\/2<\/strong> \u03bc\u03b5 \u03c4\u03b7 \u03bc\u03b9\u03ba\u03c1\u03cc\u03c4\u03b5\u03c1\u03b7 \u03b4\u03b5\u03c3\u03bc\u03b5\u03c5\u03bc\u03ad\u03bd\u03b7 \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1<strong>\u00a0P(A3\u00a0|\u00a0B) = 5\/24<\/strong>.<\/p>\n<p>\u0394\u03b9\u03b1\u03b2\u03ac\u03c3\u03c4\u03b5 \u03c0\u03b5\u03c1\u03b9\u03c3\u03c3\u03cc\u03c4\u03b5\u03c1\u03b1 http:\/\/blogs.scientificamerican.com\/cross-check\/bayes-s-theorem-what-s-the-big-deal\/<\/p>\n<p>&nbsp;<\/p>\n<p><em>\u03a0\u03b7\u03b3\u03ae:\u00a0<strong> Wikipedia\u00a0iefimerida.gr<\/strong><\/em>[\/vc_column_text][\/vc_column][\/vc_row]<\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>\u0395\u03af\u03bd\u03b1\u03b9 \u03ad\u03bd\u03b1\u03c2 \u03b1\u03c0\u03cc \u03c4\u03bf\u03c5\u03c2 \u03c0\u03b9\u03bf \u03b1\u03c0\u03bb\u03bf\u03cd\u03c2 \u03c4\u03cd\u03c0\u03bf\u03c5\u03c2 \u03c0\u03bf\u03c5 \u03b8\u03b1 \u03bc\u03ac\u03b8\u03b5\u03b9 \u03ad\u03bd\u03b1\u03c2 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\u03c6\u03bf\u03b9\u03c4\u03b7\u03c4\u03ad\u03c2 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