{"id":1396,"date":"2024-07-29T06:16:24","date_gmt":"2024-07-29T06:16:24","guid":{"rendered":"http:\/\/www.statdc.com\/?p=1396"},"modified":"2025-06-11T01:23:00","modified_gmt":"2025-06-11T01:23:00","slug":"%eb%b2%a0%ec%9d%b4%ec%a7%80%ec%95%88-%ed%86%b5%ea%b3%84bayesian-statistics","status":"publish","type":"post","link":"http:\/\/www.inmining.co.kr\/?p=1396","title":{"rendered":"\ubca0\uc774\uc9c0\uc548 \ud1b5\uacc4(Bayesian Statistics)"},"content":{"rendered":"\n

\ubca0\uc774\uc9c0\uc548 \ud1b5\uacc4(Bayesian Statistics)\ub294 \ud1b5\uacc4\uc801 \ucd94\ub860\uc758 \ud55c \ubc29\ubc95\uc73c\ub85c, \ud655\ub960\uc744 \uc8fc\uad00\uc801\uc778 \uc2e0\ub150\uc758 \uc815\ub3c4\ub85c \ud574\uc11d\ud558\uace0, \uc0c8\ub85c\uc6b4 \ub370\uc774\ud130\ub97c \uad00\ucc30\ud560 \ub54c \uc774 \uc2e0\ub150\uc744 \uac31\uc2e0\ud574 \ub098\uac00\ub294 \uc811\uadfc\ubc95\uc785\ub2c8\ub2e4. \ubca0\uc774\uc9c0\uc548 \ud1b5\uacc4\ub294 \ubca0\uc774\uc988 \uc815\ub9ac(Bayes’ Theorem)\ub97c \uae30\ubc18\uc73c\ub85c \ud558\uba70, \uc0ac\uc804 \ud655\ub960(prior probability)\uacfc \uc0ac\ud6c4 \ud655\ub960(posterior probability)\uc744 \uc0ac\uc6a9\ud558\uc5ec \ucd94\ub860\ud569\ub2c8\ub2e4. \ub2e4\uc74c\uc740 \ubca0\uc774\uc9c0\uc548 \ud1b5\uacc4\uc758 \uc8fc\uc694 \uac1c\ub150\uacfc \uacfc\uc815\uc5d0 \ub300\ud55c \uc124\uba85\uc785\ub2c8\ub2e4.<\/p>\n\n\n\n

\ucc38\uc870 : \uc0ac\ud6c4 \ud655\ub960http:\/\/www.statdc.com\/?p=774<\/a><\/p>\n\n\n\n

<\/span>\ubca0\uc774\uc988 \uc815\ub9ac (Bayes’ Theorem)<\/span><\/h3>\n\n\n\n

\ubca0\uc774\uc988 \uc815\ub9ac\ub294 \ub2e4\uc74c\uacfc \uac19\uc740 \ud615\ud0dc\ub85c \ud45c\ud604\ub429\ub2c8\ub2e4:\\(\\)<\/p>\n\n\n\n

\\[ P(A|B) = \\frac{P(B|A) \\cdot P(A)}{P(B)} \\]<\/p>\n\n\n\n

\uc5ec\uae30\uc11c,<\/p>\n\n\n\n

    \n
  • \\( P(A|B) \\): \uc0ac\uac74 B\uac00 \ubc1c\uc0dd\ud55c \ud6c4 \uc0ac\uac74 A\uac00 \ubc1c\uc0dd\ud560 \uc870\uac74\ubd80 \ud655\ub960 (\uc0ac\ud6c4 \ud655\ub960, posterior probability)<\/li>\n\n\n\n
  • \\( P(B|A) \\): \uc0ac\uac74 A\uac00 \ubc1c\uc0dd\ud55c \ud6c4 \uc0ac\uac74 B\uac00 \ubc1c\uc0dd\ud560 \uc870\uac74\ubd80 \ud655\ub960 (\uc6b0\ub3c4, likelihood)<\/li>\n\n\n\n
  • \\( P(A) \\): \uc0ac\uac74 A\uc758 \uc0ac\uc804 \ud655\ub960 (prior probability)<\/li>\n\n\n\n
  • \\( P(B) \\): \uc0ac\uac74 B\uc758 \uc804\uccb4 \ud655\ub960 (evidence)<\/li>\n<\/ul>\n\n\n\n

    <\/span>\ubca0\uc774\uc9c0\uc548 \ud1b5\uacc4\uc758 \uc8fc\uc694 \uac1c\ub150<\/span><\/h3>\n\n\n\n

    1.\uc0ac\uc804 \ud655\ub960 (Prior Probability)<\/strong>:<\/p>\n\n\n\n

      <\/ol>\n\n\n\n
        \n
      • \ub370\uc774\ud130 \uad00\ucc30 \uc774\uc804\uc5d0 \uc6b0\ub9ac\uac00 \uac00\uc9c0\uace0 \uc788\ub294 \ubbff\uc74c\uc774\ub098 \uc9c0\uc2dd\uc744 \ub098\ud0c0\ub0b4\ub294 \ud655\ub960\uc785\ub2c8\ub2e4.<\/li>\n\n\n\n
      • \uc608\ub97c \ub4e4\uc5b4, \uc9c8\ubcd1\uc758 \uc720\ubcd1\ub960, \uacfc\uac70 \uacbd\ud5d8 \ub4f1\uc744 \ubc14\ud0d5\uc73c\ub85c \uc124\uc815\ud569\ub2c8\ub2e4.<\/li>\n<\/ul>\n\n\n\n

        2.\uc6b0\ub3c4 (Likelihood)<\/strong>:<\/p>\n\n\n\n

          <\/ol>\n\n\n\n
            \n
          • \uc8fc\uc5b4\uc9c4 \ub370\uc774\ud130\uac00 \ud2b9\uc815 \ud30c\ub77c\ubbf8\ud130 \uac12\uc744 \uac00\uc9c8 \ud655\ub960\uc785\ub2c8\ub2e4.<\/li>\n\n\n\n
          • \ub370\uc774\ud130\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \uadf8 \ub370\uc774\ud130\uac00 \ud2b9\uc815 \uac00\uc124 \ud558\uc5d0\uc11c \uc5bc\ub9c8\ub098 \uc798 \uc124\uba85\ub418\ub294\uc9c0\ub97c \ub098\ud0c0\ub0c5\ub2c8\ub2e4.<\/li>\n<\/ul>\n\n\n\n

            3.\uc0ac\ud6c4 \ud655\ub960 (Posterior Probability)<\/strong>:<\/p>\n\n\n\n

              <\/ol>\n\n\n\n
                \n
              • \ub370\uc774\ud130\ub97c \uad00\ucc30\ud55c \ud6c4\uc5d0 \uc0ac\uc804 \ud655\ub960\uc744 \uc5c5\ub370\uc774\ud2b8\ud55c \uacb0\uacfc\ub85c \uc5bb\uc5b4\uc9c4 \ud655\ub960\uc785\ub2c8\ub2e4.<\/li>\n\n\n\n
              • \uc0c8\ub85c\uc6b4 \ub370\uc774\ud130\ub97c \ud1b5\ud574 \uc0ac\uc804 \ud655\ub960\uc744 \uac31\uc2e0\ud558\uc5ec \uc5bb\uc740 \ud655\ub960 \ubd84\ud3ec\uc785\ub2c8\ub2e4.<\/li>\n<\/ul>\n\n\n\n

                <\/span>\ubca0\uc774\uc9c0\uc548 \ucd94\ub860 \uacfc\uc815<\/span><\/h3>\n\n\n\n

                1.\uc0ac\uc804 \ud655\ub960 \uc124\uc815<\/strong>:<\/p>\n\n\n\n

                  <\/ol>\n\n\n\n
                    \n
                  • \ubb38\uc81c\uc5d0 \ub300\ud55c \ucd08\uae30 \ubbff\uc74c\uc774\ub098 \uc9c0\uc2dd\uc744 \ubc14\ud0d5\uc73c\ub85c \uc0ac\uc804 \ud655\ub960\uc744 \uc124\uc815\ud569\ub2c8\ub2e4.<\/li>\n<\/ul>\n\n\n\n

                    2.\ub370\uc774\ud130 \uc218\uc9d1 \ubc0f \uc6b0\ub3c4 \uacc4\uc0b0<\/strong>:<\/p>\n\n\n\n

                      <\/ol>\n\n\n\n
                        \n
                      • \ub370\uc774\ud130\ub97c \uc218\uc9d1\ud558\uace0, \uc8fc\uc5b4\uc9c4 \ub370\uc774\ud130\uac00 \ud2b9\uc815 \ud30c\ub77c\ubbf8\ud130 \uac12\uc77c \ub54c\uc758 \uc6b0\ub3c4\ub97c \uacc4\uc0b0\ud569\ub2c8\ub2e4.<\/li>\n<\/ul>\n\n\n\n

                        3.\uc0ac\ud6c4 \ud655\ub960 \uacc4\uc0b0<\/strong>:<\/p>\n\n\n\n

                          <\/ol>\n\n\n\n
                            \n
                          • \ubca0\uc774\uc988 \uc815\ub9ac\ub97c \uc0ac\uc6a9\ud558\uc5ec \uc0ac\uc804 \ud655\ub960\uacfc \uc6b0\ub3c4\ub97c \uacb0\ud569\ud558\uc5ec \uc0ac\ud6c4 \ud655\ub960\uc744 \uacc4\uc0b0\ud569\ub2c8\ub2e4.<\/li>\n<\/ul>\n\n\n\n

                            4.\uacb0\ub860 \ub3c4\ucd9c \ubc0f \uc758\uc0ac\uacb0\uc815<\/strong>:<\/p>\n\n\n\n

                              <\/ol>\n\n\n\n
                                \n
                              • \uc0ac\ud6c4 \ud655\ub960\uc744 \ubc14\ud0d5\uc73c\ub85c \ucd94\ub860\uc744 \ud558\uace0, \uc774\ub97c \ud1b5\ud574 \uc758\uc0ac\uacb0\uc815\uc744 \ub0b4\ub9bd\ub2c8\ub2e4.<\/li>\n<\/ul>\n\n\n\n

                                <\/span>\ubca0\uc774\uc9c0\uc548 \ud1b5\uacc4\uc758 \uc7a5\uc810<\/span><\/h3>\n\n\n\n
                                  \n
                                • \uc9c1\uad00\uc801 \ud574\uc11d<\/strong>: \uc0ac\uc804 \ud655\ub960\uacfc \uc0ac\ud6c4 \ud655\ub960\uc744 \ud1b5\ud574 \ubb38\uc81c\ub97c \uc9c1\uad00\uc801\uc73c\ub85c \ud574\uc11d\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/li>\n\n\n\n
                                • \uc815\ubcf4 \uac31\uc2e0 \uac00\ub2a5<\/strong>: \uc0c8\ub85c\uc6b4 \ub370\uc774\ud130\uac00 \ub4e4\uc5b4\uc62c \ub54c\ub9c8\ub2e4 \uc0ac\ud6c4 \ud655\ub960\uc744 \uac31\uc2e0\ud558\uc5ec \ub354 \uc815\ud655\ud55c \ucd94\ub860\uc774 \uac00\ub2a5\ud569\ub2c8\ub2e4.<\/li>\n\n\n\n
                                • \ubcf5\uc7a1\ud55c \ubb38\uc81c \ud574\uacb0<\/strong>: \ubcf5\uc7a1\ud55c \ubb38\uc81c\ub098 \ubd88\ud655\uc2e4\uc131\uc774 \ub192\uc740 \ubb38\uc81c\ub97c \ub2e4\ub8f0 \ub54c \uc720\uc6a9\ud569\ub2c8\ub2e4.<\/li>\n<\/ul>\n\n\n\n

                                  <\/span>\ubca0\uc774\uc9c0\uc548 \ud1b5\uacc4\uc758 \ub2e8\uc810<\/span><\/h3>\n\n\n\n
                                    \n
                                  • \uc0ac\uc804 \ud655\ub960\uc758 \uc8fc\uad00\uc131<\/strong>: \uc0ac\uc804 \ud655\ub960\uc744 \uc124\uc815\ud558\ub294 \ub370 \uc8fc\uad00\uc131\uc774 \uac1c\uc785\ub420 \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/li>\n\n\n\n
                                  • \uacc4\uc0b0 \ubcf5\uc7a1\uc131<\/strong>: \ubca0\uc774\uc9c0\uc548 \ucd94\ub860\uc740 \uacc4\uc0b0\uc774 \ubcf5\uc7a1\ud560 \uc218 \uc788\uc73c\uba70, \ud2b9\ud788 \uace0\ucc28\uc6d0 \ubb38\uc81c\uc5d0\uc11c\ub294 \uacc4\uc0b0 \ube44\uc6a9\uc774 \ub9ce\uc774 \ub4ed\ub2c8\ub2e4.<\/li>\n<\/ul>\n\n\n\n

                                    <\/span>\uc608\uc81c: \ubca0\uc774\uc9c0\uc548 \ucd94\ub860<\/span><\/h3>\n\n\n\n

                                    \ub2e4\uc74c\uc740 \ubca0\uc774\uc9c0\uc548 \ucd94\ub860\uc744 \uc0ac\uc6a9\ud558\uc5ec \ub3d9\uc804\uc744 \ub358\uc84c\uc744 \ub54c \ub3d9\uc804\uc774 \uacf5\uc815\ud55c\uc9c0 \uc5ec\ubd80\ub97c \ud310\ub2e8\ud558\ub294 \uc608\uc81c\uc785\ub2c8\ub2e4.<\/p>\n\n\n\n

                                    1.\uc0ac\uc804 \ud655\ub960<\/strong>:<\/p>\n\n\n\n

                                      <\/ol>\n\n\n\n
                                        \n
                                      • \uacf5\uc815\ud55c \ub3d9\uc804\uc77c \ud655\ub960 \\( P(Fair) = 0.5 \\)<\/li>\n\n\n\n
                                      • \uce58\uc6b0\uce5c \ub3d9\uc804\uc77c \ud655\ub960 \\( P(Biased) = 0.5 \\)<\/li>\n<\/ul>\n\n\n\n

                                        2.\uc6b0\ub3c4<\/strong>:<\/p>\n\n\n\n

                                          <\/ol>\n\n\n\n
                                            \n
                                          • 10\ubc88 \ub3d9\uc804\uc744 \ub358\uc838\uc11c 7\ubc88 \uc55e\uba74\uc774 \ub098\uc62c \ud655\ub960<\/li>\n\n\n\n
                                          • \uacf5\uc815\ud55c \ub3d9\uc804\uc758 \uacbd\uc6b0 \\( P(7 Heads | Fair) \\)<\/li>\n\n\n\n
                                          • \uce58\uc6b0\uce5c \ub3d9\uc804\uc758 \uacbd\uc6b0 \\( P(7 Heads | Biased) \\)<\/li>\n<\/ul>\n\n\n\n

                                            3.\uc0ac\ud6c4 \ud655\ub960 \uacc4\uc0b0<\/strong>:<\/p>\n\n\n\n

                                              <\/ol>\n\n\n\n
                                                \n
                                              • \ubca0\uc774\uc988 \uc815\ub9ac\ub97c \uc0ac\uc6a9\ud558\uc5ec \uacc4\uc0b0\ud569\ub2c8\ub2e4.<\/li>\n<\/ul>\n\n\n\n
                                                from scipy.stats import binom\n\n# \uc0ac\uc804 \ud655\ub960\nP_Fair = 0.5\nP_Biased = 0.5\n\n# \uc6b0\ub3c4 \uacc4\uc0b0\nn = 10  # \ub3d9\uc804\uc744 \ub358\uc9c4 \ud69f\uc218\nk = 7   # \uc55e\uba74\uc774 \ub098\uc628 \ud69f\uc218\n\nP_7Heads_Fair = binom.pmf(k, n, 0.5)  # \uacf5\uc815\ud55c \ub3d9\uc804\nP_7Heads_Biased = binom.pmf(k, n, 0.7)  # \uce58\uc6b0\uce5c \ub3d9\uc804 (\uc608: \uc55e\uba74 \ud655\ub960 0.7)\n\n# \uc0ac\ud6c4 \ud655\ub960 \uacc4\uc0b0\nP_7Heads = P_7Heads_Fair * P_Fair + P_7Heads_Biased * P_Biased\n\nP_Fair_7Heads = (P_7Heads_Fair * P_Fair) \/ P_7Heads\nP_Biased_7Heads = (P_7Heads_Biased * P_Biased) \/ P_7Heads\n\nprint(f\"\uacf5\uc815\ud55c \ub3d9\uc804\uc77c \uc0ac\ud6c4 \ud655\ub960: {P_Fair_7Heads:.4f}\")\nprint(f\"\uce58\uc6b0\uce5c \ub3d9\uc804\uc77c \uc0ac\ud6c4 \ud655\ub960: {P_Biased_7Heads:.4f}\")<\/code><\/pre>\n\n\n\n
                                                \uc774 \uc608\uc81c\ub294 10\ubc88\uc758 \ub3d9\uc804 \ub358\uc9c0\uae30\uc5d0\uc11c 7\ubc88 \uc55e\uba74\uc774 \ub098\uc628 \ub370\uc774\ud130\ub97c \ubc14\ud0d5\uc73c\ub85c, \ub3d9\uc804\uc774 \uacf5\uc815\ud55c\uc9c0 \uc5ec\ubd80\ub97c \ucd94\ub860\ud558\ub294 \uacfc\uc815\uc744 \ubcf4\uc5ec\uc90d\ub2c8\ub2e4. \ubca0\uc774\uc988 \uc815\ub9ac\ub97c \uc0ac\uc6a9\ud558\uc5ec \uc0ac\uc804 \ud655\ub960\uc744 \uc5c5\ub370\uc774\ud2b8\ud558\uace0, \uc0ac\ud6c4 \ud655\ub960\uc744 \uacc4\uc0b0\ud569\ub2c8\ub2e4.<\/p>\n","protected":false},"excerpt":{"rendered":"
                                                \ubca0\uc774\uc9c0\uc548 \ud1b5\uacc4(Bayesian Statistics)\ub294 \ud1b5\uacc4\uc801 \ucd94\ub860\uc758 \ud55c \ubc29\ubc95\uc73c\ub85c, \ud655\ub960\uc744 \uc8fc\uad00\uc801\uc778 \uc2e0\ub150\uc758 \uc815\ub3c4\ub85c \ud574\uc11d\ud558\uace0, \uc0c8\ub85c\uc6b4 \ub370\uc774\ud130\ub97c \uad00\ucc30\ud560 \ub54c \uc774 \uc2e0\ub150\uc744…<\/p>\n","protected":false},"author":1,"featured_media":1397,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[],"class_list":["post-1396","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-stat","wpcat-6-id"],"_links":{"self":[{"href":"http:\/\/www.inmining.co.kr\/index.php?rest_route=\/wp\/v2\/posts\/1396","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.inmining.co.kr\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.inmining.co.kr\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.inmining.co.kr\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.inmining.co.kr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1396"}],"version-history":[{"count":2,"href":"http:\/\/www.inmining.co.kr\/index.php?rest_route=\/wp\/v2\/posts\/1396\/revisions"}],"predecessor-version":[{"id":1400,"href":"http:\/\/www.inmining.co.kr\/index.php?rest_route=\/wp\/v2\/posts\/1396\/revisions\/1400"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/www.inmining.co.kr\/index.php?rest_route=\/wp\/v2\/media\/1397"}],"wp:attachment":[{"href":"http:\/\/www.inmining.co.kr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1396"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.inmining.co.kr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1396"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.inmining.co.kr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1396"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}