MCMC法

Transcript

1. MCMC๏ ੟࿏Ճࠃࡍେֶ ެऺӴੜେֶӃ ੜ෺౷ܭɾੜ෺৘ใֶ෼໺ ।ڭत ถԬ େี
2. .$.$ͱ͸ •.$.$
   
   .BSLPW
   $IBJO
   .POUF
   $BSMP Ϛϧίϑ࿈࠯ϞϯςΧϧϩ๏ • ղੳతʹಛఆͰ͖ͳ͍ؔ਺ͷۙࣅ஋ΛٻΊΔҰൠతͳख๏ ͷ૯শ • Ϛϧίϑ࿈࠯ͱϞϯςΧϧϩ๏ͷ૊Έ߹Θͤ • ౷ܭֶͷ෼໺ʹ͓͍ͯ͸ɺओʹύϥϝʔλͷࣄޙ෼෍ΛٻΊ Δࡍʹ༻͍Δɻ
3. Ϛϧίϑ࿈࠯ͷΠϝʔδ •̍ͭલͷঢ়ଶʹͷΈґଘ͢Δ֬཰઴ԽࣜΈ͍ͨͳ an = pan 1 + qbn 1 + rcn 1 bn = p0 an 1 + q0 bn 1 + r0 cn 1 cn = p00 an 1 + q00 bn 1 + r00 cn 1 <latexit sha1_base64="iFDV/XjgtO3T93Uw/89jlEDN89c=">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</latexit> ⇡n = P⇡n 1 ⇡n = 0 @ an bn cn 1 A , P = 0 @ p q r p0 q0 r0 p00 q00 r00 1 A <latexit sha1_base64="l7p1koIGjPO7BIMnM43NYKYObtk=">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</latexit>
4. ྫ͑͹ɺʮ͕Μηϯλʔ໰୊ʯ ࠓɺਓ͕શ෦Ͱਓ͍ͯɺݱࡏͦΕͧΕ݈߁ɺපؾɺ*$6ਓͷ ׂ߹Ͱ͍·͢ɻ िؒʹҰճɺঢ়ଶ͕มΘΓ·͕͢ɺ͕Μηϯλʔͷૉ੖Β͍͠ಇ͖ͷ͓ ͔͛ͰભҠ͢Δׂ߹͸දͷΑ͏ʹ੍ޚ͞Ε͍ͯ·͢ɻ ࣍ͷঢ়ଶ U ݈߁ පؾ *$6 ݱࡏͷঢ় ଶ U ݈߁    පؾ    *$6    *$6ͩͬͨͱ͖ʹҰिؒޙʹ݈߁ʹͳΔ֬཰͸ P(Xt 1 = ݈߁ |Xt = ICU) = 0.2 <latexit sha1_base64="yJ8r2D1Vamflzrzjlzk6cu1TvYY=">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</latexit>
5. O
   िؒޙͷ෼෍͸ •ॳظঢ়ଶͷ঱ঢ়෼෍͕ •͜ͷͱ͖िؒޙͷ঱ঢ়෼෍͸ •O
   िؒޙͷ঱ঢ়෼෍͸ ⇡(0) = (0.6, 0.25, 0.15) <latexit sha1_base64="aKe3PFOixaMhsZhOS3wHDvNuQeg=">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</latexit> ⇡(1) = ⇡(0) 0 @ 0.3 0.3 0.4 0.1 0.5 0.4 0.2 0.6 0.2 1 A = (0.6, 0.25, 0.15) 0 @ 0.3 0.3 0.4 0.1 0.5 0.4 0.2 0.6 0.2 1 A = (0.235, 0.395, 0.370) <latexit sha1_base64="1AGCgvP/DXypYOks9VW676EXLNU=">AAADrXicrVJdb9MwFHUWPkaBscEjLxYVVVtNJUlXBg+TJuCBxyGt26SmmxznprWWOMF2gMjKK3+CV/hR/BucNGOh2yOWfH1yzv2IfW+QxUwqx/ltbdh37t67v/mg8/DR460n2ztPT2SaCwpTmsapOAuIhJhxmCqmYjjLBJAkiOE0uHxf6adfQEiW8mNVZDBPyIKziFGiDHWxY235ASwY1/CZEyFIMSw7fpBoP2Plue67gxL3Dnq4RTmDsgnJEqIE+1Z2nNEY9/CV3fN9w7g1nrQYr8ava+t1fODh3wwHfSPsVvyksu5k8P9LYFPDG9f5x29Xx74zWDldX/5iu+uMnHrhm8BtQBc168i84Hc/TGmeAFc0JlLOXCdTc02EYjQG85q5hIzQS7KAmYGcJCDnuu5ciV8aJsRRKszmCtdsO0KTRMoiCYynucdSrmsVuRskt8mzXEVv5prxLFfA6apWlMdYpbiaBBwyAVTFhQGECmZ+F9MlEYQqMy/rhdQyMVdRS0gFmK8iBh1CxDirxsgoHL42om7OUh83oK0Or+Th7Xo766zh5voDRGtZrt1Molo2nXPX+3QTnHgjd280+eR1D981PdxEz9EL1Ecu2keH6CM6QlNErdz6Yf20ftmv7Knt2+cr1w2riXmG/ln24g9wUx2u</latexit> ⇡(n) = (0.6, 0.25, 0.15) 0 @ 0.3 0.3 0.4 0.1 0.5 0.4 0.2 0.6 0.2 1 A 0 @ 0.3 0.3 0.4 0.1 0.5 0.4 0.2 0.6 0.2 1 A . . . 0 @ 0.3 0.3 0.4 0.1 0.5 0.4 0.2 0.6 0.2 1 A <latexit sha1_base64="LJbsHUn4vQek7EeJlaFF8Np3AY8=">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</latexit> O
   ճֻ͚Δ
6. ཭ࢄ࣌ؒ Ϛϧίϑ࿈࠯  •࣌ؒͱͱ΋ʹ֬཰తʹมಈ͢ΔγεςϜΛهड़͢ΔϞσ ϧͷ͕̍ͭϚϧίϑ࿈࠯ •཭ࢄ࣌ؒ ʹ͓͚Δঢ়ଶΛ ͱ͢Δ ͱ͖ɺ֬཰աఔ͸ ͱදݱ •ͱΓಘΔঢ়ଶͷू߹ Λঢ়ଶۭؒ n 2 N = {0, 1, 2, ...} <latexit sha1_base64="ATIbiGJ0jUIErsBw8cKryF3CkpI=">AAACAHicbZDLSsNAFIYn9VbrLV52bgaL4CKEpAi6EYpuXEkF2wpNKJPppB06MwkzE6GGbnwSl+pG3PoeLnwbp20W2vrDwMd/zuGc+aOUUaU979sqLS2vrK6V1ysbm1vbO/buXkslmcSkiROWyPsIKcKoIE1NNSP3qSSIR4y0o+HVpN5+IFLRRNzpUUpCjvqCxhQjbayufSACKuDNRZB7ju/UHNd1g3HXrnquNxVcBL+AKijU6NpfQS/BGSdCY4aU6vheqsMcSU0xI+NKkCmSIjxEfdIxKBAnKsyn14/hsXF6ME6keULDqft7IkdcqRGPTCdHeqDmaxPTifh/5U6m4/MwpyLNNBF4tivOGNQJnKQBe1QSrNnIAMKSmnMhHiCJsDaZVUwO/vyvF6FVc33Dt6fV+mWRSBkcgiNwAnxwBurgGjRAE2DwCJ7BK3iznqwX6936mLWWrGJmH/yR9fkDHbCUHQ==</latexit> <latexit sha1_base64="ATIbiGJ0jUIErsBw8cKryF3CkpI=">AAACAHicbZDLSsNAFIYn9VbrLV52bgaL4CKEpAi6EYpuXEkF2wpNKJPppB06MwkzE6GGbnwSl+pG3PoeLnwbp20W2vrDwMd/zuGc+aOUUaU979sqLS2vrK6V1ysbm1vbO/buXkslmcSkiROWyPsIKcKoIE1NNSP3qSSIR4y0o+HVpN5+IFLRRNzpUUpCjvqCxhQjbayufSACKuDNRZB7ju/UHNd1g3HXrnquNxVcBL+AKijU6NpfQS/BGSdCY4aU6vheqsMcSU0xI+NKkCmSIjxEfdIxKBAnKsyn14/hsXF6ME6keULDqft7IkdcqRGPTCdHeqDmaxPTifh/5U6m4/MwpyLNNBF4tivOGNQJnKQBe1QSrNnIAMKSmnMhHiCJsDaZVUwO/vyvF6FVc33Dt6fV+mWRSBkcgiNwAnxwBurgGjRAE2DwCJ7BK3iznqwX6936mLWWrGJmH/yR9fkDHbCUHQ==</latexit> <latexit sha1_base64="ATIbiGJ0jUIErsBw8cKryF3CkpI=">AAACAHicbZDLSsNAFIYn9VbrLV52bgaL4CKEpAi6EYpuXEkF2wpNKJPppB06MwkzE6GGbnwSl+pG3PoeLnwbp20W2vrDwMd/zuGc+aOUUaU979sqLS2vrK6V1ysbm1vbO/buXkslmcSkiROWyPsIKcKoIE1NNSP3qSSIR4y0o+HVpN5+IFLRRNzpUUpCjvqCxhQjbayufSACKuDNRZB7ju/UHNd1g3HXrnquNxVcBL+AKijU6NpfQS/BGSdCY4aU6vheqsMcSU0xI+NKkCmSIjxEfdIxKBAnKsyn14/hsXF6ME6keULDqft7IkdcqRGPTCdHeqDmaxPTifh/5U6m4/MwpyLNNBF4tivOGNQJnKQBe1QSrNnIAMKSmnMhHiCJsDaZVUwO/vyvF6FVc33Dt6fV+mWRSBkcgiNwAnxwBurgGjRAE2DwCJ7BK3iznqwX6936mLWWrGJmH/yR9fkDHbCUHQ==</latexit> <latexit sha1_base64="ATIbiGJ0jUIErsBw8cKryF3CkpI=">AAACAHicbZDLSsNAFIYn9VbrLV52bgaL4CKEpAi6EYpuXEkF2wpNKJPppB06MwkzE6GGbnwSl+pG3PoeLnwbp20W2vrDwMd/zuGc+aOUUaU979sqLS2vrK6V1ysbm1vbO/buXkslmcSkiROWyPsIKcKoIE1NNSP3qSSIR4y0o+HVpN5+IFLRRNzpUUpCjvqCxhQjbayufSACKuDNRZB7ju/UHNd1g3HXrnquNxVcBL+AKijU6NpfQS/BGSdCY4aU6vheqsMcSU0xI+NKkCmSIjxEfdIxKBAnKsyn14/hsXF6ME6keULDqft7IkdcqRGPTCdHeqDmaxPTifh/5U6m4/MwpyLNNBF4tivOGNQJnKQBe1QSrNnIAMKSmnMhHiCJsDaZVUwO/vyvF6FVc33Dt6fV+mWRSBkcgiNwAnxwBurgGjRAE2DwCJ7BK3iznqwX6936mLWWrGJmH/yR9fkDHbCUHQ==</latexit> Xn <latexit sha1_base64="HJvkZNZUNRNPD5R1JGYb05lqNwE=">AAAB7XicbVDLSgNBEOz1GeMr6tHLYBA8SNiViB6DXjxGNA9IljA7mU2GzGOZmRXCkk/wqF7Eq1/kwb9xkuxBEwsaiqpuuruihDNjff/bW1ldW9/YLGwVt3d29/ZLB4dNo1JNaIMornQ7woZyJmnDMstpO9EUi4jTVjS6nfqtJ6oNU/LRjhMaCjyQLGYEWyc9tHuyVyr7FX8GtEyCnJQhR71X+ur2FUkFlZZwbEwn8BMbZlhbRjidFLupoQkmIzygHUclFtSE2ezUCTp1Sh/FSruSFs3U3xMZFsaMReQ6BbZDs+hNxfNI/Gd3UhtfhxmTSWqpJPNdccqRVWj6OuozTYnlY0cw0cydi8gQa0ysC6jocggWv14mzYtKUK1c3lfLtZs8kQIcwwmcQQBXUIM7qEMDCAzgGV7hzVPei/fufcxbV7x85gj+wPv8ASakjtI=</latexit> {X0, X1, X2, ...} <latexit sha1_base64="k32e4FnPv/0VIGwAdp4sQDJ6zAY=">AAAB/3icbVBNS8NAEN3Ur1q/oj16WSyChxKSUtFj0YvHCrYNNCFstpt26W4SdjdCCD34SzyqF/HqD/Hgv3Hb5qCtDwYe780wMy9MGZXKtr+Nysbm1vZOdbe2t39weGQen/RlkglMejhhiXBDJAmjMekpqhhxU0EQDxkZhNPbuT94JELSJH5QeUp8jsYxjShGSkuBWfcKN7CbbuDoajUty/JmgdmwLXsBuE6ckjRAiW5gfnmjBGecxAozJOXQsVPlF0goihmZ1bxMkhThKRqToaYx4kT6xeL4GTzXyghGidAVK7hQf08UiEuZ81B3cqQmctWbi82Q/2cPMxVd+wWN00yRGC93RRmDKoHzMOCICoIVyzVBWFB9LsQTJBBWOrKazsFZ/Xqd9FuW07Yu79uNzk2ZSBWcgjNwARxwBTrgDnRBD2CQg2fwCt6MJ+PFeDc+lq0Vo5ypgz8wPn8AuZeT9A==</latexit> S <latexit sha1_base64="CvOQ6/ocfNYHTVfp9t6B6mLnzM4=">AAAB63icbVDLSgNBEOyNrxhfUY9eBoPgQcKuRPQY9OIxQfOAZAmzk95kyMzuMjMrhJAv8KhexKuf5MG/cZLsQRMLGoqqbrq7gkRwbVz328mtrW9sbuW3Czu7e/sHxcOjpo5TxbDBYhGrdkA1Ch5hw3AjsJ0opDIQ2ApGdzO/9YRK8zh6NOMEfUkHEQ85o8ZK9YdeseSW3TnIKvEyUoIMtV7xq9uPWSoxMkxQrTuemxh/QpXhTOC00E01JpSN6AA7lkZUovYn80On5MwqfRLGylZkyFz9PTGhUuuxDGynpGaol72ZeBHI/+xOasIbf8KjJDUYscWuMBXExGT2OOlzhcyIsSWUKW7PJWxIFWXGxlOwOXjLX6+S5mXZq5Sv6pVS9TZLJA8ncArn4ME1VOEeatAABgjP8ApvjnRenHfnY9Gac7KZY/gD5/MHmumN7A==</latexit> ྫ͑͹ɺ4͸\ճ෮ɺॏ঱Խɺࢮ๢^
7. ཭ࢄ࣌ؒ Ϛϧίϑ࿈࠯  Theorem 1. ֬཰աఔ {Xn; n 2 N} ͕࣍ͷੑ࣭Λຬͨ͢ͱ͖ɺϚϧίϑաఔ (S ͕͔͔ͨͩՄࢉແݶݸͷ৔߹͸཭ࢄ࣌ؒϚϧίϑ࿈࠯) ͱݺͿɻ ͢΂ͯͷ n 2 N, x0, x1, ..., xn, xn+1 2 S ʹର͠ P(Xn+1 = xn+1 |X0 = x0, X1 = x1, ..., Xn = xn) = P(Xn+1 = xn+1 |Xn = xn) (1) ͕੒Γཱͭɻ <latexit sha1_base64="Qu1SNBQc/d7uFgra1JdL4jLKMcA=">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</latexit> Ϛϧίϑੑ
8. ఆৗϚϧίϑ࿈࠯ͱ$,ํఔࣜ •ఆৗϚϧίϑ࿈࠯ ͨ·ʹ੪࣌Ϛϧίϑ࿈࠯ͱ΋ ͱ͸ɺ ਪҠ֬཰ ͕ O ʹґଘ͠ͳ͍ɺ͢ͳΘͪ •N࣌ؒޙʹJ ͔ΒK
   ʹҠಈ͢Δ֬཰Λ ͱ͓͘ͱɺνϟοϓϚϯɾίϩϞΰϩϑํఔ͕ࣜ੒ཱ Pij(i, j 2 S) <latexit sha1_base64="Nk4z9F05wtNgKpSFHuQF42PBApU=">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</latexit> Pij = P(Xn+1 = j|Xn = i) = P(X1 = j|X0 = i) <latexit sha1_base64="NHrG3U3YTIsNlgetRiTtX5Pjksw=">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</latexit> P(m) ij = P(Xn+m = j|Xn = i) = P(Xm = j|X0 = i) <latexit sha1_base64="Zoc0s2Q+3Ew2S82vaD1X+ZOZZFc=">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</latexit> P(m) ij = X k2S P(l) ik P(m l) kj (0 < l < m) <latexit sha1_base64="wzngRU6xar/HVDnZOZsKyDeeuB8=">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</latexit>
9. ਪҠ֬཰ͱO࣌ؒޙ •ਪҠ֬཰ߦྻΛ •ศརͳؔ܎ •ॳظ֬཰ϕΫτϧ •O
   ࣌ؒޙʹͲ͜ʹ͍Δ͔͕෼͔Δ ఆৗϚϧίϑ࿈࠯ͷ֬཰๏ଇ
   P = 0 B @ P00 P01 . . . P10 P11 . . . . . . . . . . . . 1 C A <latexit sha1_base64="GzYAZosMJfs6LIVNpO4tW004uIU=">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</latexit> Pm ij = (Pm)ij <latexit sha1_base64="6PHJgoLY/dCq9jU+4nH+npzlyso=">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</latexit> ⇡(n) i = P(Xn = i) <latexit sha1_base64="AqDcRAgluuQqrQfN1mvgG4kV3Pc=">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</latexit> ⇡(0) = (⇡(0) 0 , ⇡(0) 1 , ...) <latexit sha1_base64="J3lZnXwTRugV2lDJV4MNGmU0JfU=">AAACzHicbVHNThsxEHa2f5T+hfbIxSKqFBBa7SKq9lIJlR44VSARQEq2kdeZJRa2d2XPtoqsvfIEfRqu7Uv0bepNjEgDI1n+5vvmx57JKyksJsnfTvTo8ZOnz9aer794+er1m+7G2zNb1obDgJeyNBc5syCFhgEKlHBRGWAql3CeXx22+vkPMFaU+hRnFWSKXWpRCM7QU+NuPMqVG1Xiu+sn201DP9O+98bJwt9tcRpwHMfb424viZO50fsgDaBHgh2PNzrXo0nJawUauWTWDtOkwswxg4JLaNZHtYWK8St2CUMPNVNgMzf/WEPfe2ZCi9L4o5HO2eUMx5S1M5X7SMVwale1ltzN1UPysMbiU+aErmoEzRe9ilpSLGk7KDoRBjjKmQeMG+GfS/mUGcbRj3O1EU6V/wpOoTTgvZkEN4FCaNFO2SsafgbRhbtxpwEsqzu38s7D+nLVYeAy9xWKlSp3Yb7QXPabS1f3dB+c7cXpfvzhZL938CXscI1ski3SJyn5SA7IETkmA8LJL3JDfpM/0bcIIxc1i9CoE3Lekf8suv4HqSvjJQ==</latexit> ͨͩ͠ ⇡(n) = ⇡(n 1)P = ⇡(n 2)P2 = ... = ⇡(0)Pn <latexit sha1_base64="DTljlTZQ0oDriUgO3cgszUDqSKo=">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</latexit>
10. ఆৗ֬཰ n ! 1 <latexit sha1_base64="02cR3i97RtOXYLzEwYdxkqVLy9k=">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</latexit> Def. ϕΫτϧ ⇡ = (⇡0, ⇡1, ⇡2, ...) ͕ ⇡ = ⇡P Λຬ଍͢Δͱ͖ɺ⇡ Λఆৗ֬཰ (stationary probability) ͱ͍͏ɻ·ͨɺۃݶ֬཰ ͕ଘࡏ͢Ε͹ͦΕ͸ఆৗ֬཰Ͱ͋Δɻ <latexit sha1_base64="RO2zwepC2t9HjHaZIEcZeE9BBIA=">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</latexit> Def. ঢ়ଶʹؔ͢Δॳظঢ়ଶ ⇡(0) ͕༩͑ΒΕ͍ͯΔͱ͢Δɻ ⇡(1) i = lim n!1 ⇡(n) i ͱͳΔ ⇡(1) = (⇡(1) i , i 2 S) ͕ଘࡏ͢ΔͳΒ͹ɺ⇡(1) Λۃݶ֬཰ (limiting prob- ability)(΋͘͠͸ฏߧ֬཰, steady state probability) ͱݺͿɻ <latexit sha1_base64="60LWrJWgLLs3FtEjO9jcgGwIQUU=">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</latexit> े෼ʹ௕͍Ϛϧίϑ࿈࠯Λ؍ଌ͢Ε͹ɺͲͷ ঢ়ଶʹ͍Δ܏޲͕͋Δͷ͔Λఆৗ෼෍ʹΑͬ ͯ஌Δ͜ͱ͕Ͱ͖Δɻ
11. Τϧΰʔτੑ FSHPEJD • ط໿Ͱ ਖ਼ ࠶ؼతͰඇपظతͳఆৗϚϧίϑ࿈࠯ΛΤϧΰʔυత • ط໿త JSSFEVDJCMF 
    ༗ݶճͷਪҠͰ4ͷཁૉશ͕ͯޓ͍ʹ౸ୡՄೳ üFY͋Δঢ়ଶ"ʹͳͬͯ͠·͏ͱೋ౓ͱผͷঢ়ଶʹ͸ͳΕͳ͍ɺͱ͍͏͜ͱ ͕ͳ͍ঢ়ଶ • ਖ਼ ࠶ؼత QPTJUJWF
    SFDVSSFOU 
    4ͷ೚ҙͷཁૉ͸ɺԿ౓Ͱ΋౸ୡՄೳ üFY͋Δ࣌ظҎ߱ɺ͋Δঢ়ଶʹͳΔ͜ͱ͸ͳ͍ɺͱ͍͏͜ͱ͕ͳ͍ঢ়ଶ • ඇपظత BQFSJPEJD 
    ࿈࠯ͷঢ়ଶ͕ҰఆͷपظΛ༗͍ͯ͠ͳ͍ üFY͋Δঢ়ଶ"ͷ࣍ʹ͸ඞͣ#ʹͳΔɺΈ͍ͨͳ͜ͱ͕ͳ͍ঢ়ଶ
12. Ϛϧίϑ࿈࠯ͷऩଋ Theorem. Ϛϧίϑ࿈࠯͕ط໿Ͱ͋Δͱ͢Δɻ • ঢ়ଶ͕ਖ਼࠶ؼతͰ͋ΔͳΒ͹ʢपظʹΑΒͣʣ།Ұͷఆৗ֬཰Λ΋ͭɻߋ ʹɺඇपظతͳΒ͹ɺۃݶ֬཰ͱҰக͢Δɻ • ঢ়ଶ͕ྵ࠶ؼతɺ·ͨ͸Ұ࣌తͰ͋ΔͳΒ͹ఆৗ֬཰͸ଘࡏ͠ͳ͍ɻ <latexit sha1_base64="AfV8G9jxNENb9hhlTkYrtTJehHA=">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</latexit> ཁ͸ΤϧΰʔτతͰ͋Δ࣌ʹɺϚϧίϑ ࿈࠯͸ఆৗ෼෍ʹऩଋ͢Δɻ
13. Ϛϧίϑ࿈࠯ϞϯςΧϧϩ๏ .$.$
     • .$.$ͱ͸
    ଟมྔ֬཰෼෍͔Βཚ਺Λੜ੒͢ΔͨΊͷΞϧΰ ϦζϜ ؠ೾σʔλαΠΤϯε • ࣄޙ෼෍ʹै͏ཚ਺Λ Ϛϧίϑ࿈࠯͔Β େྔʹൃੜɺۙࣅ͢Δ • े෼ʹ௕͍Ϛϧίϑ࿈࠯Λ؍ଌ͢Ε͹ɺͲͷঢ়ଶʹ͍Δ܏޲ ͕͋Δͷ͔Λఆৗ෼෍ʹΑͬͯ஌Δ͜ͱ͕Ͱ͖Δɻ Def (ϕΠζͷఆཧ). x 2 RD Λσʔλ, ✓ 2 RP Λύϥϝʔλͱ͢Δͱ͖ɺϕΠ ζͷఆཧ͸ f(✓|x) = f(x|✓)f(✓) f(x) Ͱද͞ΕΔɻ͜ͷͱ͖ f(x|✓) Λ໬౓ɺf(✓) Λࣄલ෼෍ͱݺͿɻ <latexit sha1_base64="OuSUz4kN3Cm9nJNip5fTCb/iqvM=">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</latexit>
14. Ϛϧίϑ࿈࠯ϞϯςΧϧϩ๏ .$.$
     •͜Ε·Ͱͷٞ࿦Λ·ͱΊΔͱ üϚϧίϑ࿈࠯͕ΤϧΰʔυతͰ͋Ε͹αϯϓϦϯά͕ఆৗ෼෍ʹै͏ ü࣍͸ભҠ֬཰ͷઃܭ͕໰୊ͱͳΔ üભҠ֬཰ΛΤϧΰʔτੑΛຬͨ͢Α͏ʹઃఆ͢Δͷ͸༰қͰ͋Δ͕ɺ ͦΕ͚ͩͰ͸ఆৗ෼෍ͷଘࡏͷΈΛอূ üͦͷఆৗ෼෍͕ر๬͢Δ ࣄޙ ෼෍ʹҰக͢Δͱ͸ݶΒͳ͍ˠৄࡉ ௼Γ߹͍৚݅ がんセンター問題は遷移確率が既知で定常分布が未知 取り組みたい問題は、遷移確率が未知で定常分布(事後分布)が既知 ٯʂ
15. ৄࡉ௼Γ߹͍৚݅ ʮ๬Ή໨ඪ෼෍ΛಘΔͨΊʹͲͷΑ͏ʹਪҠ֬཰ͷϚϧ ίϑ࿈࠯Λઃܭ͢Ε͹͍͍͔ʁʯͱ͍͏໰͍ʹର͢Δ̍ ͭͷղͱͯ͠ৄࡉ௼Γ߹͍৚݅ े෼৚݅Ͱ͋Γඞཁ৚݅Ͱ͸ͳ͍ Def (ৄࡉ௼Γ߹͍৚݅). ໨ඪ෼෍ r ͱભҠ֬཰ P ͕࣍ͷ৚݅Λຬͨ͢ͱ͖ɺͦ ͷϚϧίϑ࿈࠯ͷఆৗ෼෍͸ r ʹҰக͢Δɻ P(X0 = j|X = i)P(X = i) = P(X = i|X0 = j)P(X0 = j) <latexit sha1_base64="G5Vl7Ji7CT3G79dvtWHTQC3PZDg=">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</latexit> Pji <latexit sha1_base64="6xCmJO2HSmbzGaSOtFMYVVq/Dr8=">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</latexit> Pij <latexit sha1_base64="cM8cltIP+38+MoQN7BK81kGs1ZE=">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</latexit> ri <latexit sha1_base64="U6VWxBt1HPDQNO55sz2L4fptflo=">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</latexit> rj <latexit sha1_base64="Omxy1QfrB3r1jpdfJcu+4G1WgIw=">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</latexit> ະ஌਺1͕̎ͭʹํఔ͕ࣜͻͱͭͳͷͰɺ 1͕ҰҙʹܾఆͰ͖ͳ͍ ܾΊํͱͯ͠ • ΪϒεαϯϓϦϯά ೤ཋ๏ • ϝτϩϙϦεɾϔΠεςΟϯά • ϋϛϧτχΞϯϞϯςΧϧϩͳͲ
16. ݁ہɺɺɺ αϯϓϦϯά͍ͨ͠෼෍ ࣄޙ෼෍ ʹରͯ͠ɺͦΕΛఆৗ ෼෍ͱ͢ΔϚϧίϑ࿈࠯Λߏ੒͢Δํ๏ΛҰൠʹ Ϛϧίϑ࿈࠯ϞϯςΧϧϩ๏ ͱݺͿɻ
17. ϝτϩϙϦεɾϔΠεςΟϯάε๏ • ਪҠ֬཰ Λ ͷܗͰ༩͑Δ • ͨͩ͠ɺ • ࣮ࡍ͸ɺҰ༷ཚ਺ Λൃੜͤ͞ɺ ͳΒ ͦͷNPWFΛغ٫͠ɺ ͳΒ࠾୒͢Δɻ Pij = P(X0 = j|X = i) <latexit sha1_base64="/OdVOZ1EUK3s/KKZ4mUYoufFd9g=">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</latexit> Pij = qij↵ij <latexit sha1_base64="/aUoB/9im5dz4RuwGgK5yKyKVi8=">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</latexit> ↵ij = min{1, ⇡jqji ⇡iqij } <latexit sha1_base64="arMP1cByhHRWy61mEQxkNT4wLUI=">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</latexit> ࣍ͷͲͷঢ়ଶ ΛબͿ͔ બΜͩީิΛ ࠾୒͢Δ֬཰ v ⇠ Unif(0, 1) <latexit sha1_base64="YEgXZ4gnFgrGo+dnbLvhA9y9njg=">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</latexit> v > ↵ij <latexit sha1_base64="NccsxrSo0osp+IR+/voRxtf6E38=">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</latexit> v  ↵ij <latexit sha1_base64="H/J0TckTjkmtUfzsbc1Nl/+NTVY=">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</latexit>
18. ѥछ •ϋϛϧτχΞϯϞϯςΧϧϩ •ύϥϨϧςϯύϦϯά ϨϓϦΧަ׵๏ •ϚϧνΧϊχΧϧ :POFPLB
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