25
Likelihoods, Priors, and Posteriors
13
✓
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<latexit sha1_base64="ldTChBJmjtlLCtT4XaCHdmQrWdk=">AAAB7nicdZDLSgMxFIYz9VbrrerSTbAVXJXMYG27K7pxWcFeoB1KJs20oZkLyRmhDH0JF25U3Po6Ln0bM20FFf0h8PGfc8g5vxdLoYGQDyu3tr6xuZXfLuzs7u0fFA+POjpKFONtFslI9TyquRQhb4MAyXux4jTwJO960+us3r3nSosovINZzN2AjkPhC0bBWL3yACYcaHlYLJGKUyWNWh2TSpXYjQvHACH1xiXBtoFMJbRSa1h8H4wilgQ8BCap1n2bxOCmVIFgks8Lg0TzmLIpHfO+wZAGXLvpYt85PjPOCPuRMi8EvHC/T6Q00HoWeKYzoDDRv2uZ+Vetn4Bfd1MRxgnwkC0/8hOJIcLZ8XgkFGcgZwYoU8LsitmEKsrARGQy+DoU/w8dp2IbvnVKzatVGnl0gk7RObJRDTXRDWqhNmJIogf0hJ6t2Hq0XqzXZWvOWs0cox+y3j4BRRuPvQ==</latexit>
<latexit sha1_base64="ldTChBJmjtlLCtT4XaCHdmQrWdk=">AAAB7nicdZDLSgMxFIYz9VbrrerSTbAVXJXMYG27K7pxWcFeoB1KJs20oZkLyRmhDH0JF25U3Po6Ln0bM20FFf0h8PGfc8g5vxdLoYGQDyu3tr6xuZXfLuzs7u0fFA+POjpKFONtFslI9TyquRQhb4MAyXux4jTwJO960+us3r3nSosovINZzN2AjkPhC0bBWL3yACYcaHlYLJGKUyWNWh2TSpXYjQvHACH1xiXBtoFMJbRSa1h8H4wilgQ8BCap1n2bxOCmVIFgks8Lg0TzmLIpHfO+wZAGXLvpYt85PjPOCPuRMi8EvHC/T6Q00HoWeKYzoDDRv2uZ+Vetn4Bfd1MRxgnwkC0/8hOJIcLZ8XgkFGcgZwYoU8LsitmEKsrARGQy+DoU/w8dp2IbvnVKzatVGnl0gk7RObJRDTXRDWqhNmJIogf0hJ6t2Hq0XqzXZWvOWs0cox+y3j4BRRuPvQ==</latexit>
<latexit sha1_base64="ldTChBJmjtlLCtT4XaCHdmQrWdk=">AAAB7nicdZDLSgMxFIYz9VbrrerSTbAVXJXMYG27K7pxWcFeoB1KJs20oZkLyRmhDH0JF25U3Po6Ln0bM20FFf0h8PGfc8g5vxdLoYGQDyu3tr6xuZXfLuzs7u0fFA+POjpKFONtFslI9TyquRQhb4MAyXux4jTwJO960+us3r3nSosovINZzN2AjkPhC0bBWL3yACYcaHlYLJGKUyWNWh2TSpXYjQvHACH1xiXBtoFMJbRSa1h8H4wilgQ8BCap1n2bxOCmVIFgks8Lg0TzmLIpHfO+wZAGXLvpYt85PjPOCPuRMi8EvHC/T6Q00HoWeKYzoDDRv2uZ+Vetn4Bfd1MRxgnwkC0/8hOJIcLZ8XgkFGcgZwYoU8LsitmEKsrARGQy+DoU/w8dp2IbvnVKzatVGnl0gk7RObJRDTXRDWqhNmJIogf0hJ6t2Hq0XqzXZWvOWs0cox+y3j4BRRuPvQ==</latexit>
<latexit sha1_base64="6zfLjapaAqmlCwdMvpksV/zSof0=">AAAB6XicdZDLTgIxFIbP4A3xhrp00wgmrkiHiMCO6MYlRrkkMCGd0oGGziVtx0gmPIILN2rc+kQufRs7gIka/ZMmX/5zTnrO70aCK43xh5VZWV1b38hu5ra2d3b38vsHbRXGkrIWDUUouy5RTPCAtTTXgnUjyYjvCtZxJ5dpvXPHpOJhcKunEXN8Mgq4xynRxrop3hcH+QIulSu4Xq0hXKpgu35WNoBxrX6OkW0gVQGWag7y7/1hSGOfBZoKolTPxpF2EiI1p4LNcv1YsYjQCRmxnsGA+Ew5yXzVGToxzhB5oTQv0Gjufp9IiK/U1HdNp0/0WP2upeZftV6svZqT8CCKNQvo4iMvFkiHKL0bDblkVIupAUIlN7siOiaSUG3SMRl8HYr+h3a5ZBu+LhcaF8s0snAEx3AKNlShAVfQhBZQGMEDPMGzNbEerRfrddGasZYzh/BD1tsnhpqNkQ==</latexit>
<latexit sha1_base64="6zfLjapaAqmlCwdMvpksV/zSof0=">AAAB6XicdZDLTgIxFIbP4A3xhrp00wgmrkiHiMCO6MYlRrkkMCGd0oGGziVtx0gmPIILN2rc+kQufRs7gIka/ZMmX/5zTnrO70aCK43xh5VZWV1b38hu5ra2d3b38vsHbRXGkrIWDUUouy5RTPCAtTTXgnUjyYjvCtZxJ5dpvXPHpOJhcKunEXN8Mgq4xynRxrop3hcH+QIulSu4Xq0hXKpgu35WNoBxrX6OkW0gVQGWag7y7/1hSGOfBZoKolTPxpF2EiI1p4LNcv1YsYjQCRmxnsGA+Ew5yXzVGToxzhB5oTQv0Gjufp9IiK/U1HdNp0/0WP2upeZftV6svZqT8CCKNQvo4iMvFkiHKL0bDblkVIupAUIlN7siOiaSUG3SMRl8HYr+h3a5ZBu+LhcaF8s0snAEx3AKNlShAVfQhBZQGMEDPMGzNbEerRfrddGasZYzh/BD1tsnhpqNkQ==</latexit>
<latexit sha1_base64="6zfLjapaAqmlCwdMvpksV/zSof0=">AAAB6XicdZDLTgIxFIbP4A3xhrp00wgmrkiHiMCO6MYlRrkkMCGd0oGGziVtx0gmPIILN2rc+kQufRs7gIka/ZMmX/5zTnrO70aCK43xh5VZWV1b38hu5ra2d3b38vsHbRXGkrIWDUUouy5RTPCAtTTXgnUjyYjvCtZxJ5dpvXPHpOJhcKunEXN8Mgq4xynRxrop3hcH+QIulSu4Xq0hXKpgu35WNoBxrX6OkW0gVQGWag7y7/1hSGOfBZoKolTPxpF2EiI1p4LNcv1YsYjQCRmxnsGA+Ew5yXzVGToxzhB5oTQv0Gjufp9IiK/U1HdNp0/0WP2upeZftV6svZqT8CCKNQvo4iMvFkiHKL0bDblkVIupAUIlN7siOiaSUG3SMRl8HYr+h3a5ZBu+LhcaF8s0snAEx3AKNlShAVfQhBZQGMEDPMGzNbEerRfrddGasZYzh/BD1tsnhpqNkQ==</latexit>
<latexit sha1_base64="6zfLjapaAqmlCwdMvpksV/zSof0=">AAAB6XicdZDLTgIxFIbP4A3xhrp00wgmrkiHiMCO6MYlRrkkMCGd0oGGziVtx0gmPIILN2rc+kQufRs7gIka/ZMmX/5zTnrO70aCK43xh5VZWV1b38hu5ra2d3b38vsHbRXGkrIWDUUouy5RTPCAtTTXgnUjyYjvCtZxJ5dpvXPHpOJhcKunEXN8Mgq4xynRxrop3hcH+QIulSu4Xq0hXKpgu35WNoBxrX6OkW0gVQGWag7y7/1hSGOfBZoKolTPxpF2EiI1p4LNcv1YsYjQCRmxnsGA+Ew5yXzVGToxzhB5oTQv0Gjufp9IiK/U1HdNp0/0WP2upeZftV6svZqT8CCKNQvo4iMvFkiHKL0bDblkVIupAUIlN7siOiaSUG3SMRl8HYr+h3a5ZBu+LhcaF8s0snAEx3AKNlShAVfQhBZQGMEDPMGzNbEerRfrddGasZYzh/BD1tsnhpqNkQ==</latexit>
We define as the posterior probability of given
(or alternatively, as the likelihood of the event )
Pr(✓|x)
<latexit sha1_base64="i56FXmAT7/Tje9rZ37Rgc55SYec=">AAAB/XicdVDLSgMxFM34rPVVFVdugq1QNyUzWNvuim5cVrAP6JSSSdM2NPMguSOWofgtLtyouPU7XPo3pg9BRQ8EDuecy705XiSFBkI+rKXlldW19dRGenNre2c3s7ff0GGsGK+zUIaq5VHNpQh4HQRI3ooUp74nedMbXU795i1XWoTBDYwj3vHpIBB9wSgYqZs5zLk1lXdhyIFi1yQB353mupksKThFUimVMSkUiV05cwwhpFw5J9g2ZIosWqDWzby7vZDFPg+ASap12yYRdBKqQDDJJ2k31jyibEQHvG1oQH2uO8ns/Ak+MUoP90NlXgB4pn6fSKiv9dj3TNKnMNS/van4l9eOoV/uJCKIYuABmy/qxxJDiKdd4J5QnIEcG0KZEuZWzIZUUQamMdPB10fx/6ThFGzDr51s9WLRRgodoWOURzYqoSq6QjVURwwl6AE9oWfr3nq0XqzXeXTJWswcoB+w3j4BTw6UtA==</latexit>
<latexit sha1_base64="i56FXmAT7/Tje9rZ37Rgc55SYec=">AAAB/XicdVDLSgMxFM34rPVVFVdugq1QNyUzWNvuim5cVrAP6JSSSdM2NPMguSOWofgtLtyouPU7XPo3pg9BRQ8EDuecy705XiSFBkI+rKXlldW19dRGenNre2c3s7ff0GGsGK+zUIaq5VHNpQh4HQRI3ooUp74nedMbXU795i1XWoTBDYwj3vHpIBB9wSgYqZs5zLk1lXdhyIFi1yQB353mupksKThFUimVMSkUiV05cwwhpFw5J9g2ZIosWqDWzby7vZDFPg+ASap12yYRdBKqQDDJJ2k31jyibEQHvG1oQH2uO8ns/Ak+MUoP90NlXgB4pn6fSKiv9dj3TNKnMNS/van4l9eOoV/uJCKIYuABmy/qxxJDiKdd4J5QnIEcG0KZEuZWzIZUUQamMdPB10fx/6ThFGzDr51s9WLRRgodoWOURzYqoSq6QjVURwwl6AE9oWfr3nq0XqzXeXTJWswcoB+w3j4BTw6UtA==</latexit>
<latexit sha1_base64="i56FXmAT7/Tje9rZ37Rgc55SYec=">AAAB/XicdVDLSgMxFM34rPVVFVdugq1QNyUzWNvuim5cVrAP6JSSSdM2NPMguSOWofgtLtyouPU7XPo3pg9BRQ8EDuecy705XiSFBkI+rKXlldW19dRGenNre2c3s7ff0GGsGK+zUIaq5VHNpQh4HQRI3ooUp74nedMbXU795i1XWoTBDYwj3vHpIBB9wSgYqZs5zLk1lXdhyIFi1yQB353mupksKThFUimVMSkUiV05cwwhpFw5J9g2ZIosWqDWzby7vZDFPg+ASap12yYRdBKqQDDJJ2k31jyibEQHvG1oQH2uO8ns/Ak+MUoP90NlXgB4pn6fSKiv9dj3TNKnMNS/van4l9eOoV/uJCKIYuABmy/qxxJDiKdd4J5QnIEcG0KZEuZWzIZUUQamMdPB10fx/6ThFGzDr51s9WLRRgodoWOURzYqoSq6QjVURwwl6AE9oWfr3nq0XqzXeXTJWswcoB+w3j4BTw6UtA==</latexit>
<latexit sha1_base64="i56FXmAT7/Tje9rZ37Rgc55SYec=">AAAB/XicdVDLSgMxFM34rPVVFVdugq1QNyUzWNvuim5cVrAP6JSSSdM2NPMguSOWofgtLtyouPU7XPo3pg9BRQ8EDuecy705XiSFBkI+rKXlldW19dRGenNre2c3s7ff0GGsGK+zUIaq5VHNpQh4HQRI3ooUp74nedMbXU795i1XWoTBDYwj3vHpIBB9wSgYqZs5zLk1lXdhyIFi1yQB353mupksKThFUimVMSkUiV05cwwhpFw5J9g2ZIosWqDWzby7vZDFPg+ASap12yYRdBKqQDDJJ2k31jyibEQHvG1oQH2uO8ns/Ak+MUoP90NlXgB4pn6fSKiv9dj3TNKnMNS/van4l9eOoV/uJCKIYuABmy/qxxJDiKdd4J5QnIEcG0KZEuZWzIZUUQamMdPB10fx/6ThFGzDr51s9WLRRgodoWOURzYqoSq6QjVURwwl6AE9oWfr3nq0XqzXeXTJWswcoB+w3j4BTw6UtA==</latexit>
<latexit sha1_base64="6zfLjapaAqmlCwdMvpksV/zSof0=">AAAB6XicdZDLTgIxFIbP4A3xhrp00wgmrkiHiMCO6MYlRrkkMCGd0oGGziVtx0gmPIILN2rc+kQufRs7gIka/ZMmX/5zTnrO70aCK43xh5VZWV1b38hu5ra2d3b38vsHbRXGkrIWDUUouy5RTPCAtTTXgnUjyYjvCtZxJ5dpvXPHpOJhcKunEXN8Mgq4xynRxrop3hcH+QIulSu4Xq0hXKpgu35WNoBxrX6OkW0gVQGWag7y7/1hSGOfBZoKolTPxpF2EiI1p4LNcv1YsYjQCRmxnsGA+Ew5yXzVGToxzhB5oTQv0Gjufp9IiK/U1HdNp0/0WP2upeZftV6svZqT8CCKNQvo4iMvFkiHKL0bDblkVIupAUIlN7siOiaSUG3SMRl8HYr+h3a5ZBu+LhcaF8s0snAEx3AKNlShAVfQhBZQGMEDPMGzNbEerRfrddGasZYzh/BD1tsnhpqNkQ==</latexit>
<latexit sha1_base64="6zfLjapaAqmlCwdMvpksV/zSof0=">AAAB6XicdZDLTgIxFIbP4A3xhrp00wgmrkiHiMCO6MYlRrkkMCGd0oGGziVtx0gmPIILN2rc+kQufRs7gIka/ZMmX/5zTnrO70aCK43xh5VZWV1b38hu5ra2d3b38vsHbRXGkrIWDUUouy5RTPCAtTTXgnUjyYjvCtZxJ5dpvXPHpOJhcKunEXN8Mgq4xynRxrop3hcH+QIulSu4Xq0hXKpgu35WNoBxrX6OkW0gVQGWag7y7/1hSGOfBZoKolTPxpF2EiI1p4LNcv1YsYjQCRmxnsGA+Ew5yXzVGToxzhB5oTQv0Gjufp9IiK/U1HdNp0/0WP2upeZftV6svZqT8CCKNQvo4iMvFkiHKL0bDblkVIupAUIlN7siOiaSUG3SMRl8HYr+h3a5ZBu+LhcaF8s0snAEx3AKNlShAVfQhBZQGMEDPMGzNbEerRfrddGasZYzh/BD1tsnhpqNkQ==</latexit>
<latexit sha1_base64="6zfLjapaAqmlCwdMvpksV/zSof0=">AAAB6XicdZDLTgIxFIbP4A3xhrp00wgmrkiHiMCO6MYlRrkkMCGd0oGGziVtx0gmPIILN2rc+kQufRs7gIka/ZMmX/5zTnrO70aCK43xh5VZWV1b38hu5ra2d3b38vsHbRXGkrIWDUUouy5RTPCAtTTXgnUjyYjvCtZxJ5dpvXPHpOJhcKunEXN8Mgq4xynRxrop3hcH+QIulSu4Xq0hXKpgu35WNoBxrX6OkW0gVQGWag7y7/1hSGOfBZoKolTPxpF2EiI1p4LNcv1YsYjQCRmxnsGA+Ew5yXzVGToxzhB5oTQv0Gjufp9IiK/U1HdNp0/0WP2upeZftV6svZqT8CCKNQvo4iMvFkiHKL0bDblkVIupAUIlN7siOiaSUG3SMRl8HYr+h3a5ZBu+LhcaF8s0snAEx3AKNlShAVfQhBZQGMEDPMGzNbEerRfrddGasZYzh/BD1tsnhpqNkQ==</latexit>
<latexit sha1_base64="6zfLjapaAqmlCwdMvpksV/zSof0=">AAAB6XicdZDLTgIxFIbP4A3xhrp00wgmrkiHiMCO6MYlRrkkMCGd0oGGziVtx0gmPIILN2rc+kQufRs7gIka/ZMmX/5zTnrO70aCK43xh5VZWV1b38hu5ra2d3b38vsHbRXGkrIWDUUouy5RTPCAtTTXgnUjyYjvCtZxJ5dpvXPHpOJhcKunEXN8Mgq4xynRxrop3hcH+QIulSu4Xq0hXKpgu35WNoBxrX6OkW0gVQGWag7y7/1hSGOfBZoKolTPxpF2EiI1p4LNcv1YsYjQCRmxnsGA+Ew5yXzVGToxzhB5oTQv0Gjufp9IiK/U1HdNp0/0WP2upeZftV6svZqT8CCKNQvo4iMvFkiHKL0bDblkVIupAUIlN7siOiaSUG3SMRl8HYr+h3a5ZBu+LhcaF8s0snAEx3AKNlShAVfQhBZQGMEDPMGzNbEerRfrddGasZYzh/BD1tsnhpqNkQ==</latexit>
✓
<latexit sha1_base64="ldTChBJmjtlLCtT4XaCHdmQrWdk=">AAAB7nicdZDLSgMxFIYz9VbrrerSTbAVXJXMYG27K7pxWcFeoB1KJs20oZkLyRmhDH0JF25U3Po6Ln0bM20FFf0h8PGfc8g5vxdLoYGQDyu3tr6xuZXfLuzs7u0fFA+POjpKFONtFslI9TyquRQhb4MAyXux4jTwJO960+us3r3nSosovINZzN2AjkPhC0bBWL3yACYcaHlYLJGKUyWNWh2TSpXYjQvHACH1xiXBtoFMJbRSa1h8H4wilgQ8BCap1n2bxOCmVIFgks8Lg0TzmLIpHfO+wZAGXLvpYt85PjPOCPuRMi8EvHC/T6Q00HoWeKYzoDDRv2uZ+Vetn4Bfd1MRxgnwkC0/8hOJIcLZ8XgkFGcgZwYoU8LsitmEKsrARGQy+DoU/w8dp2IbvnVKzatVGnl0gk7RObJRDTXRDWqhNmJIogf0hJ6t2Hq0XqzXZWvOWs0cox+y3j4BRRuPvQ==</latexit>
<latexit sha1_base64="ldTChBJmjtlLCtT4XaCHdmQrWdk=">AAAB7nicdZDLSgMxFIYz9VbrrerSTbAVXJXMYG27K7pxWcFeoB1KJs20oZkLyRmhDH0JF25U3Po6Ln0bM20FFf0h8PGfc8g5vxdLoYGQDyu3tr6xuZXfLuzs7u0fFA+POjpKFONtFslI9TyquRQhb4MAyXux4jTwJO960+us3r3nSosovINZzN2AjkPhC0bBWL3yACYcaHlYLJGKUyWNWh2TSpXYjQvHACH1xiXBtoFMJbRSa1h8H4wilgQ8BCap1n2bxOCmVIFgks8Lg0TzmLIpHfO+wZAGXLvpYt85PjPOCPuRMi8EvHC/T6Q00HoWeKYzoDDRv2uZ+Vetn4Bfd1MRxgnwkC0/8hOJIcLZ8XgkFGcgZwYoU8LsitmEKsrARGQy+DoU/w8dp2IbvnVKzatVGnl0gk7RObJRDTXRDWqhNmJIogf0hJ6t2Hq0XqzXZWvOWs0cox+y3j4BRRuPvQ==</latexit>
<latexit sha1_base64="ldTChBJmjtlLCtT4XaCHdmQrWdk=">AAAB7nicdZDLSgMxFIYz9VbrrerSTbAVXJXMYG27K7pxWcFeoB1KJs20oZkLyRmhDH0JF25U3Po6Ln0bM20FFf0h8PGfc8g5vxdLoYGQDyu3tr6xuZXfLuzs7u0fFA+POjpKFONtFslI9TyquRQhb4MAyXux4jTwJO960+us3r3nSosovINZzN2AjkPhC0bBWL3yACYcaHlYLJGKUyWNWh2TSpXYjQvHACH1xiXBtoFMJbRSa1h8H4wilgQ8BCap1n2bxOCmVIFgks8Lg0TzmLIpHfO+wZAGXLvpYt85PjPOCPuRMi8EvHC/T6Q00HoWeKYzoDDRv2uZ+Vetn4Bfd1MRxgnwkC0/8hOJIcLZ8XgkFGcgZwYoU8LsitmEKsrARGQy+DoU/w8dp2IbvnVKzatVGnl0gk7RObJRDTXRDWqhNmJIogf0hJ6t2Hq0XqzXZWvOWs0cox+y3j4BRRuPvQ==</latexit>
<latexit sha1_base64="ldTChBJmjtlLCtT4XaCHdmQrWdk=">AAAB7nicdZDLSgMxFIYz9VbrrerSTbAVXJXMYG27K7pxWcFeoB1KJs20oZkLyRmhDH0JF25U3Po6Ln0bM20FFf0h8PGfc8g5vxdLoYGQDyu3tr6xuZXfLuzs7u0fFA+POjpKFONtFslI9TyquRQhb4MAyXux4jTwJO960+us3r3nSosovINZzN2AjkPhC0bBWL3yACYcaHlYLJGKUyWNWh2TSpXYjQvHACH1xiXBtoFMJbRSa1h8H4wilgQ8BCap1n2bxOCmVIFgks8Lg0TzmLIpHfO+wZAGXLvpYt85PjPOCPuRMi8EvHC/T6Q00HoWeKYzoDDRv2uZ+Vetn4Bfd1MRxgnwkC0/8hOJIcLZ8XgkFGcgZwYoU8LsitmEKsrARGQy+DoU/w8dp2IbvnVKzatVGnl0gk7RObJRDTXRDWqhNmJIogf0hJ6t2Hq0XqzXZWvOWs0cox+y3j4BRRuPvQ==</latexit>
<latexit sha1_base64="6zfLjapaAqmlCwdMvpksV/zSof0=">AAAB6XicdZDLTgIxFIbP4A3xhrp00wgmrkiHiMCO6MYlRrkkMCGd0oGGziVtx0gmPIILN2rc+kQufRs7gIka/ZMmX/5zTnrO70aCK43xh5VZWV1b38hu5ra2d3b38vsHbRXGkrIWDUUouy5RTPCAtTTXgnUjyYjvCtZxJ5dpvXPHpOJhcKunEXN8Mgq4xynRxrop3hcH+QIulSu4Xq0hXKpgu35WNoBxrX6OkW0gVQGWag7y7/1hSGOfBZoKolTPxpF2EiI1p4LNcv1YsYjQCRmxnsGA+Ew5yXzVGToxzhB5oTQv0Gjufp9IiK/U1HdNp0/0WP2upeZftV6svZqT8CCKNQvo4iMvFkiHKL0bDblkVIupAUIlN7siOiaSUG3SMRl8HYr+h3a5ZBu+LhcaF8s0snAEx3AKNlShAVfQhBZQGMEDPMGzNbEerRfrddGasZYzh/BD1tsnhpqNkQ==</latexit>
<latexit sha1_base64="6zfLjapaAqmlCwdMvpksV/zSof0=">AAAB6XicdZDLTgIxFIbP4A3xhrp00wgmrkiHiMCO6MYlRrkkMCGd0oGGziVtx0gmPIILN2rc+kQufRs7gIka/ZMmX/5zTnrO70aCK43xh5VZWV1b38hu5ra2d3b38vsHbRXGkrIWDUUouy5RTPCAtTTXgnUjyYjvCtZxJ5dpvXPHpOJhcKunEXN8Mgq4xynRxrop3hcH+QIulSu4Xq0hXKpgu35WNoBxrX6OkW0gVQGWag7y7/1hSGOfBZoKolTPxpF2EiI1p4LNcv1YsYjQCRmxnsGA+Ew5yXzVGToxzhB5oTQv0Gjufp9IiK/U1HdNp0/0WP2upeZftV6svZqT8CCKNQvo4iMvFkiHKL0bDblkVIupAUIlN7siOiaSUG3SMRl8HYr+h3a5ZBu+LhcaF8s0snAEx3AKNlShAVfQhBZQGMEDPMGzNbEerRfrddGasZYzh/BD1tsnhpqNkQ==</latexit>
<latexit sha1_base64="6zfLjapaAqmlCwdMvpksV/zSof0=">AAAB6XicdZDLTgIxFIbP4A3xhrp00wgmrkiHiMCO6MYlRrkkMCGd0oGGziVtx0gmPIILN2rc+kQufRs7gIka/ZMmX/5zTnrO70aCK43xh5VZWV1b38hu5ra2d3b38vsHbRXGkrIWDUUouy5RTPCAtTTXgnUjyYjvCtZxJ5dpvXPHpOJhcKunEXN8Mgq4xynRxrop3hcH+QIulSu4Xq0hXKpgu35WNoBxrX6OkW0gVQGWag7y7/1hSGOfBZoKolTPxpF2EiI1p4LNcv1YsYjQCRmxnsGA+Ew5yXzVGToxzhB5oTQv0Gjufp9IiK/U1HdNp0/0WP2upeZftV6svZqT8CCKNQvo4iMvFkiHKL0bDblkVIupAUIlN7siOiaSUG3SMRl8HYr+h3a5ZBu+LhcaF8s0snAEx3AKNlShAVfQhBZQGMEDPMGzNbEerRfrddGasZYzh/BD1tsnhpqNkQ==</latexit>
<latexit sha1_base64="6zfLjapaAqmlCwdMvpksV/zSof0=">AAAB6XicdZDLTgIxFIbP4A3xhrp00wgmrkiHiMCO6MYlRrkkMCGd0oGGziVtx0gmPIILN2rc+kQufRs7gIka/ZMmX/5zTnrO70aCK43xh5VZWV1b38hu5ra2d3b38vsHbRXGkrIWDUUouy5RTPCAtTTXgnUjyYjvCtZxJ5dpvXPHpOJhcKunEXN8Mgq4xynRxrop3hcH+QIulSu4Xq0hXKpgu35WNoBxrX6OkW0gVQGWag7y7/1hSGOfBZoKolTPxpF2EiI1p4LNcv1YsYjQCRmxnsGA+Ew5yXzVGToxzhB5oTQv0Gjufp9IiK/U1HdNp0/0WP2upeZftV6svZqT8CCKNQvo4iMvFkiHKL0bDblkVIupAUIlN7siOiaSUG3SMRl8HYr+h3a5ZBu+LhcaF8s0snAEx3AKNlShAVfQhBZQGMEDPMGzNbEerRfrddGasZYzh/BD1tsnhpqNkQ==</latexit>
<latexit sha1_base64="6zfLjapaAqmlCwdMvpksV/zSof0=">AAAB6XicdZDLTgIxFIbP4A3xhrp00wgmrkiHiMCO6MYlRrkkMCGd0oGGziVtx0gmPIILN2rc+kQufRs7gIka/ZMmX/5zTnrO70aCK43xh5VZWV1b38hu5ra2d3b38vsHbRXGkrIWDUUouy5RTPCAtTTXgnUjyYjvCtZxJ5dpvXPHpOJhcKunEXN8Mgq4xynRxrop3hcH+QIulSu4Xq0hXKpgu35WNoBxrX6OkW0gVQGWag7y7/1hSGOfBZoKolTPxpF2EiI1p4LNcv1YsYjQCRmxnsGA+Ew5yXzVGToxzhB5oTQv0Gjufp9IiK/U1HdNp0/0WP2upeZftV6svZqT8CCKNQvo4iMvFkiHKL0bDblkVIupAUIlN7siOiaSUG3SMRl8HYr+h3a5ZBu+LhcaF8s0snAEx3AKNlShAVfQhBZQGMEDPMGzNbEerRfrddGasZYzh/BD1tsnhpqNkQ==</latexit>
<latexit sha1_base64="6zfLjapaAqmlCwdMvpksV/zSof0=">AAAB6XicdZDLTgIxFIbP4A3xhrp00wgmrkiHiMCO6MYlRrkkMCGd0oGGziVtx0gmPIILN2rc+kQufRs7gIka/ZMmX/5zTnrO70aCK43xh5VZWV1b38hu5ra2d3b38vsHbRXGkrIWDUUouy5RTPCAtTTXgnUjyYjvCtZxJ5dpvXPHpOJhcKunEXN8Mgq4xynRxrop3hcH+QIulSu4Xq0hXKpgu35WNoBxrX6OkW0gVQGWag7y7/1hSGOfBZoKolTPxpF2EiI1p4LNcv1YsYjQCRmxnsGA+Ew5yXzVGToxzhB5oTQv0Gjufp9IiK/U1HdNp0/0WP2upeZftV6svZqT8CCKNQvo4iMvFkiHKL0bDblkVIupAUIlN7siOiaSUG3SMRl8HYr+h3a5ZBu+LhcaF8s0snAEx3AKNlShAVfQhBZQGMEDPMGzNbEerRfrddGasZYzh/BD1tsnhpqNkQ==</latexit>
<latexit sha1_base64="6zfLjapaAqmlCwdMvpksV/zSof0=">AAAB6XicdZDLTgIxFIbP4A3xhrp00wgmrkiHiMCO6MYlRrkkMCGd0oGGziVtx0gmPIILN2rc+kQufRs7gIka/ZMmX/5zTnrO70aCK43xh5VZWV1b38hu5ra2d3b38vsHbRXGkrIWDUUouy5RTPCAtTTXgnUjyYjvCtZxJ5dpvXPHpOJhcKunEXN8Mgq4xynRxrop3hcH+QIulSu4Xq0hXKpgu35WNoBxrX6OkW0gVQGWag7y7/1hSGOfBZoKolTPxpF2EiI1p4LNcv1YsYjQCRmxnsGA+Ew5yXzVGToxzhB5oTQv0Gjufp9IiK/U1HdNp0/0WP2upeZftV6svZqT8CCKNQvo4iMvFkiHKL0bDblkVIupAUIlN7siOiaSUG3SMRl8HYr+h3a5ZBu+LhcaF8s0snAEx3AKNlShAVfQhBZQGMEDPMGzNbEerRfrddGasZYzh/BD1tsnhpqNkQ==</latexit>
<latexit sha1_base64="6zfLjapaAqmlCwdMvpksV/zSof0=">AAAB6XicdZDLTgIxFIbP4A3xhrp00wgmrkiHiMCO6MYlRrkkMCGd0oGGziVtx0gmPIILN2rc+kQufRs7gIka/ZMmX/5zTnrO70aCK43xh5VZWV1b38hu5ra2d3b38vsHbRXGkrIWDUUouy5RTPCAtTTXgnUjyYjvCtZxJ5dpvXPHpOJhcKunEXN8Mgq4xynRxrop3hcH+QIulSu4Xq0hXKpgu35WNoBxrX6OkW0gVQGWag7y7/1hSGOfBZoKolTPxpF2EiI1p4LNcv1YsYjQCRmxnsGA+Ew5yXzVGToxzhB5oTQv0Gjufp9IiK/U1HdNp0/0WP2upeZftV6svZqT8CCKNQvo4iMvFkiHKL0bDblkVIupAUIlN7siOiaSUG3SMRl8HYr+h3a5ZBu+LhcaF8s0snAEx3AKNlShAVfQhBZQGMEDPMGzNbEerRfrddGasZYzh/BD1tsnhpqNkQ==</latexit>
We define and as the prior probability of the event and the prior
probability of the event , respectively.
Pr(✓)
<latexit sha1_base64="nUh8bp4XV9BHVTOWmouXKSA5aes=">AAAB83icdZDLSgMxFIYzXmu9VV26CbZC3ZTMYG27K7pxWcFeoDOUTJq2oZmLyRmhDH0OF25U3PowLn0b04ugoj8EPv5zDufk92MpNBDyYa2srq1vbGa2sts7u3v7uYPDlo4SxXiTRTJSHZ9qLkXImyBA8k6sOA18ydv++GpWb99zpUUU3sIk5l5Ah6EYCEbBWF7BbaiiCyMO9KzQy+VJySmTWqWKSalM7Nq5Y4CQau2CYNvATHm0VKOXe3f7EUsCHgKTVOuuTWLwUqpAMMmnWTfRPKZsTIe8azCkAddeOj96ik+N08eDSJkXAp673ydSGmg9CXzTGVAY6d+1mflXrZvAoOqlIowT4CFbLBokEkOEZwngvlCcgZwYoEwJcytmI6ooA5OTyeDro/h/aDkl2/CNk69fLtPIoGN0gorIRhVUR9eogZqIoTv0gJ7Qs5VYj9aL9bpoXbGWM0foh6y3TziDkV4=</latexit>
<latexit sha1_base64="nUh8bp4XV9BHVTOWmouXKSA5aes=">AAAB83icdZDLSgMxFIYzXmu9VV26CbZC3ZTMYG27K7pxWcFeoDOUTJq2oZmLyRmhDH0OF25U3PowLn0b04ugoj8EPv5zDufk92MpNBDyYa2srq1vbGa2sts7u3v7uYPDlo4SxXiTRTJSHZ9qLkXImyBA8k6sOA18ydv++GpWb99zpUUU3sIk5l5Ah6EYCEbBWF7BbaiiCyMO9KzQy+VJySmTWqWKSalM7Nq5Y4CQau2CYNvATHm0VKOXe3f7EUsCHgKTVOuuTWLwUqpAMMmnWTfRPKZsTIe8azCkAddeOj96ik+N08eDSJkXAp673ydSGmg9CXzTGVAY6d+1mflXrZvAoOqlIowT4CFbLBokEkOEZwngvlCcgZwYoEwJcytmI6ooA5OTyeDro/h/aDkl2/CNk69fLtPIoGN0gorIRhVUR9eogZqIoTv0gJ7Qs5VYj9aL9bpoXbGWM0foh6y3TziDkV4=</latexit>
<latexit sha1_base64="nUh8bp4XV9BHVTOWmouXKSA5aes=">AAAB83icdZDLSgMxFIYzXmu9VV26CbZC3ZTMYG27K7pxWcFeoDOUTJq2oZmLyRmhDH0OF25U3PowLn0b04ugoj8EPv5zDufk92MpNBDyYa2srq1vbGa2sts7u3v7uYPDlo4SxXiTRTJSHZ9qLkXImyBA8k6sOA18ydv++GpWb99zpUUU3sIk5l5Ah6EYCEbBWF7BbaiiCyMO9KzQy+VJySmTWqWKSalM7Nq5Y4CQau2CYNvATHm0VKOXe3f7EUsCHgKTVOuuTWLwUqpAMMmnWTfRPKZsTIe8azCkAddeOj96ik+N08eDSJkXAp673ydSGmg9CXzTGVAY6d+1mflXrZvAoOqlIowT4CFbLBokEkOEZwngvlCcgZwYoEwJcytmI6ooA5OTyeDro/h/aDkl2/CNk69fLtPIoGN0gorIRhVUR9eogZqIoTv0gJ7Qs5VYj9aL9bpoXbGWM0foh6y3TziDkV4=</latexit>
<latexit sha1_base64="nUh8bp4XV9BHVTOWmouXKSA5aes=">AAAB83icdZDLSgMxFIYzXmu9VV26CbZC3ZTMYG27K7pxWcFeoDOUTJq2oZmLyRmhDH0OF25U3PowLn0b04ugoj8EPv5zDufk92MpNBDyYa2srq1vbGa2sts7u3v7uYPDlo4SxXiTRTJSHZ9qLkXImyBA8k6sOA18ydv++GpWb99zpUUU3sIk5l5Ah6EYCEbBWF7BbaiiCyMO9KzQy+VJySmTWqWKSalM7Nq5Y4CQau2CYNvATHm0VKOXe3f7EUsCHgKTVOuuTWLwUqpAMMmnWTfRPKZsTIe8azCkAddeOj96ik+N08eDSJkXAp673ydSGmg9CXzTGVAY6d+1mflXrZvAoOqlIowT4CFbLBokEkOEZwngvlCcgZwYoEwJcytmI6ooA5OTyeDro/h/aDkl2/CNk69fLtPIoGN0gorIRhVUR9eogZqIoTv0gJ7Qs5VYj9aL9bpoXbGWM0foh6y3TziDkV4=</latexit>
Pr(x)
<latexit sha1_base64="o+AJzGX0lQVrzOU9OhX8TwPclKU=">AAAB7nicdZDLSgMxFIbPeK31VnXpJtgKdVMyg7XtrujGZQV7gXYomTTThmYuJBmxlL6ECzcqbn0dl76NmbaCiv4Q+PjPOeSc34sFVxrjD2tldW19YzOzld3e2d3bzx0ctlSUSMqaNBKR7HhEMcFD1tRcC9aJJSOBJ1jbG1+l9fYdk4pH4a2exMwNyDDkPqdEG6tT6DVk8f6s0M/lcckp41qlinCpjO3auWMA42rtAiPbQKo8LNXo5957g4gmAQs1FUSpro1j7U6J1JwKNsv2EsViQsdkyLoGQxIw5U7n+87QqXEGyI+keaFGc/f7xJQESk0Cz3QGRI/U71pq/lXrJtqvulMexolmIV185CcC6Qilx6MBl4xqMTFAqORmV0RHRBKqTUQmg69D0f/Qckq24RsnX79cppGBYziBIthQgTpcQwOaQEHAAzzBsxVbj9aL9bpoXbGWM0fwQ9bbJ3F4jzI=</latexit>
<latexit sha1_base64="o+AJzGX0lQVrzOU9OhX8TwPclKU=">AAAB7nicdZDLSgMxFIbPeK31VnXpJtgKdVMyg7XtrujGZQV7gXYomTTThmYuJBmxlL6ECzcqbn0dl76NmbaCiv4Q+PjPOeSc34sFVxrjD2tldW19YzOzld3e2d3bzx0ctlSUSMqaNBKR7HhEMcFD1tRcC9aJJSOBJ1jbG1+l9fYdk4pH4a2exMwNyDDkPqdEG6tT6DVk8f6s0M/lcckp41qlinCpjO3auWMA42rtAiPbQKo8LNXo5957g4gmAQs1FUSpro1j7U6J1JwKNsv2EsViQsdkyLoGQxIw5U7n+87QqXEGyI+keaFGc/f7xJQESk0Cz3QGRI/U71pq/lXrJtqvulMexolmIV185CcC6Qilx6MBl4xqMTFAqORmV0RHRBKqTUQmg69D0f/Qckq24RsnX79cppGBYziBIthQgTpcQwOaQEHAAzzBsxVbj9aL9bpoXbGWM0fwQ9bbJ3F4jzI=</latexit>
<latexit sha1_base64="o+AJzGX0lQVrzOU9OhX8TwPclKU=">AAAB7nicdZDLSgMxFIbPeK31VnXpJtgKdVMyg7XtrujGZQV7gXYomTTThmYuJBmxlL6ECzcqbn0dl76NmbaCiv4Q+PjPOeSc34sFVxrjD2tldW19YzOzld3e2d3bzx0ctlSUSMqaNBKR7HhEMcFD1tRcC9aJJSOBJ1jbG1+l9fYdk4pH4a2exMwNyDDkPqdEG6tT6DVk8f6s0M/lcckp41qlinCpjO3auWMA42rtAiPbQKo8LNXo5957g4gmAQs1FUSpro1j7U6J1JwKNsv2EsViQsdkyLoGQxIw5U7n+87QqXEGyI+keaFGc/f7xJQESk0Cz3QGRI/U71pq/lXrJtqvulMexolmIV185CcC6Qilx6MBl4xqMTFAqORmV0RHRBKqTUQmg69D0f/Qckq24RsnX79cppGBYziBIthQgTpcQwOaQEHAAzzBsxVbj9aL9bpoXbGWM0fwQ9bbJ3F4jzI=</latexit>
<latexit sha1_base64="o+AJzGX0lQVrzOU9OhX8TwPclKU=">AAAB7nicdZDLSgMxFIbPeK31VnXpJtgKdVMyg7XtrujGZQV7gXYomTTThmYuJBmxlL6ECzcqbn0dl76NmbaCiv4Q+PjPOeSc34sFVxrjD2tldW19YzOzld3e2d3bzx0ctlSUSMqaNBKR7HhEMcFD1tRcC9aJJSOBJ1jbG1+l9fYdk4pH4a2exMwNyDDkPqdEG6tT6DVk8f6s0M/lcckp41qlinCpjO3auWMA42rtAiPbQKo8LNXo5957g4gmAQs1FUSpro1j7U6J1JwKNsv2EsViQsdkyLoGQxIw5U7n+87QqXEGyI+keaFGc/f7xJQESk0Cz3QGRI/U71pq/lXrJtqvulMexolmIV185CcC6Qilx6MBl4xqMTFAqORmV0RHRBKqTUQmg69D0f/Qckq24RsnX79cppGBYziBIthQgTpcQwOaQEHAAzzBsxVbj9aL9bpoXbGWM0fwQ9bbJ3F4jzI=</latexit>
✓
<latexit sha1_base64="ldTChBJmjtlLCtT4XaCHdmQrWdk=">AAAB7nicdZDLSgMxFIYz9VbrrerSTbAVXJXMYG27K7pxWcFeoB1KJs20oZkLyRmhDH0JF25U3Po6Ln0bM20FFf0h8PGfc8g5vxdLoYGQDyu3tr6xuZXfLuzs7u0fFA+POjpKFONtFslI9TyquRQhb4MAyXux4jTwJO960+us3r3nSosovINZzN2AjkPhC0bBWL3yACYcaHlYLJGKUyWNWh2TSpXYjQvHACH1xiXBtoFMJbRSa1h8H4wilgQ8BCap1n2bxOCmVIFgks8Lg0TzmLIpHfO+wZAGXLvpYt85PjPOCPuRMi8EvHC/T6Q00HoWeKYzoDDRv2uZ+Vetn4Bfd1MRxgnwkC0/8hOJIcLZ8XgkFGcgZwYoU8LsitmEKsrARGQy+DoU/w8dp2IbvnVKzatVGnl0gk7RObJRDTXRDWqhNmJIogf0hJ6t2Hq0XqzXZWvOWs0cox+y3j4BRRuPvQ==</latexit>
<latexit sha1_base64="ldTChBJmjtlLCtT4XaCHdmQrWdk=">AAAB7nicdZDLSgMxFIYz9VbrrerSTbAVXJXMYG27K7pxWcFeoB1KJs20oZkLyRmhDH0JF25U3Po6Ln0bM20FFf0h8PGfc8g5vxdLoYGQDyu3tr6xuZXfLuzs7u0fFA+POjpKFONtFslI9TyquRQhb4MAyXux4jTwJO960+us3r3nSosovINZzN2AjkPhC0bBWL3yACYcaHlYLJGKUyWNWh2TSpXYjQvHACH1xiXBtoFMJbRSa1h8H4wilgQ8BCap1n2bxOCmVIFgks8Lg0TzmLIpHfO+wZAGXLvpYt85PjPOCPuRMi8EvHC/T6Q00HoWeKYzoDDRv2uZ+Vetn4Bfd1MRxgnwkC0/8hOJIcLZ8XgkFGcgZwYoU8LsitmEKsrARGQy+DoU/w8dp2IbvnVKzatVGnl0gk7RObJRDTXRDWqhNmJIogf0hJ6t2Hq0XqzXZWvOWs0cox+y3j4BRRuPvQ==</latexit>
<latexit sha1_base64="ldTChBJmjtlLCtT4XaCHdmQrWdk=">AAAB7nicdZDLSgMxFIYz9VbrrerSTbAVXJXMYG27K7pxWcFeoB1KJs20oZkLyRmhDH0JF25U3Po6Ln0bM20FFf0h8PGfc8g5vxdLoYGQDyu3tr6xuZXfLuzs7u0fFA+POjpKFONtFslI9TyquRQhb4MAyXux4jTwJO960+us3r3nSosovINZzN2AjkPhC0bBWL3yACYcaHlYLJGKUyWNWh2TSpXYjQvHACH1xiXBtoFMJbRSa1h8H4wilgQ8BCap1n2bxOCmVIFgks8Lg0TzmLIpHfO+wZAGXLvpYt85PjPOCPuRMi8EvHC/T6Q00HoWeKYzoDDRv2uZ+Vetn4Bfd1MRxgnwkC0/8hOJIcLZ8XgkFGcgZwYoU8LsitmEKsrARGQy+DoU/w8dp2IbvnVKzatVGnl0gk7RObJRDTXRDWqhNmJIogf0hJ6t2Hq0XqzXZWvOWs0cox+y3j4BRRuPvQ==</latexit>
<latexit sha1_base64="ldTChBJmjtlLCtT4XaCHdmQrWdk=">AAAB7nicdZDLSgMxFIYz9VbrrerSTbAVXJXMYG27K7pxWcFeoB1KJs20oZkLyRmhDH0JF25U3Po6Ln0bM20FFf0h8PGfc8g5vxdLoYGQDyu3tr6xuZXfLuzs7u0fFA+POjpKFONtFslI9TyquRQhb4MAyXux4jTwJO960+us3r3nSosovINZzN2AjkPhC0bBWL3yACYcaHlYLJGKUyWNWh2TSpXYjQvHACH1xiXBtoFMJbRSa1h8H4wilgQ8BCap1n2bxOCmVIFgks8Lg0TzmLIpHfO+wZAGXLvpYt85PjPOCPuRMi8EvHC/T6Q00HoWeKYzoDDRv2uZ+Vetn4Bfd1MRxgnwkC0/8hOJIcLZ8XgkFGcgZwYoU8LsitmEKsrARGQy+DoU/w8dp2IbvnVKzatVGnl0gk7RObJRDTXRDWqhNmJIogf0hJ6t2Hq0XqzXZWvOWs0cox+y3j4BRRuPvQ==</latexit>
To simplify notation, we will refer to the event of the random variable X taking on
instance value x, i.e., X = x, simply with x