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Cmput 651 - Particle-based Inference 7/11/2008 !#1":*03&(-'1&#0&#-9*)-#-T&.*+)-*95)*'0& >NO&!W*::&AAPAB ;*Y%0&8>fB&> G<*$<&1#T&9%&.*((*$5:)&)'&+#1":%&(-'1&.*-%$):TB #0.&a>fBh&G<%-%&a>FBeI&G<%0%Y%-&8>FBeI #0.& &&&&&&&&&&&&&&&&&&&&&&&&&&&>#0.&k&*+&%#+T&)'&+#1":%&(-'1B C 3454(#)%"-.,/01)"2 C `V_[C&NO&G-'03:T& Q ( x ) 5+%+&a>FB&<%-% *P%P&5+%&k&#+&"-'FT&('-&+#1":*03&8&#0.&$'--%$)&l+W%Gm&9T& +)'$<#+)*$#::T&-%n%$)*03&%F$%++*Y%:T&:#-3%&+#1":%+ AS M%n%$)*'0&+#1":*03& >NO&!W*::&AAPAB H:#$WC&+51&'(&Z& ;#5++*#0+ De&<#-.%-&)'& +#1":% M%n%$)*'0& +#1":*03&'0&-%.& >+*1":%&;#5++*#0B AZ

Cmput 651 - Particle-based Inference 7/11/2008 8''-&$<'*$%&'(&"-'"'+#:&.*+)-*95)*'0 60&)<*+&-%3*'0 p ( x ) Q ( x ) ≪ 1 +'&1#0T& -%n%$)*'0+ De& $'--%$)+&('-& .*((%-%0$%+& 9%)G%%0&-%.&#0.& 9:#$W A@ [+)*1#)*03&)<*03+&(-'1&"#-)*$:%+ >#:+'&+%%&NO&[a5#)*'0+&AAPAh&AAP7B ;*Y%0&"#-)*$:%+ D = { ξ [1] , ..., ξ [ M ] } G%&$#0&%+)*1#)% M E D ( f ) = 1 %F"%$)#)*'0&'(&(50$)*'0&(C ˆ � f ( ξ [ m ]) M m =1 *0.*$#)'-&(50$)*'0 M P D ( y ) = 1 &&&&&&&&&&&&&&&&&&&&&&&&1#-3*0#:+C ˆ � I { ξ [ m ] � Y � = y } M c m =1 ,%0')%+&#++*301%0)& )'&o&*0&"#-)*$:% ξ [ m ] A?

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