AMDA-2008-Session 23 - Bayesian Inference Prior...

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Bayesian Inference
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Prior Distribution density. prior the called be It will ). ( by on distributi prior the of density the denote will We . space parameter on the on distributi prior a through captured is idea' ' This . parameter the of value about the idea some has or investigat the that assumed is it approach Bayesian In the θ π Θ
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Posterior Distribution ) ( ) | ( ) | ( , of t independen is ) ( ) ( ) | ( Since . data the of light in the of values possible about the belief revised the gives on distributi posterior The ) ( ) | ( ) ( ) | ( ) | ( by given is observed been has data after the of density posterior The ) | f( by denoted is is parameter the of value true the when ) x ,..., (x data the of likelihood The n 1 θ π x x x x x x x x x x f m d f d f f = = = Θ Θ
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A simple example 056 . 0 data) | 0.6 P(p , 516 . 0 data) | 0.5 P(p , 428 . 0 data) | 0.4 P(p ) 4 . 0 )( 2 . 0 ( ) 5 . 0 )( 6 . 0 ( (0.2)(0.6) k where k (0.2)(0.4) data) | 0.6 P(p , k (0.6)(0.5) data) | 0.5 P(p , k (0.2)(0.6) data) | 0.4 P(p is n informatio above given the p of on distributi posterior The Tails in result
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AMDA-2008-Session 23 - Bayesian Inference Prior...

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