Pattern Recognition and Machine Learning by Bishop
Bayesian inference Gaussian variables. { To estimate N (˙2 is assumed known), use Gaussian prior. { To estimate = 1=˙2, use Gamma function as prior, i.e. Gam( ja;b) = ba a 1 ( a) exp( b ) since it has the same functional form as the likelihood. The Student-t distribution may be motivated by: { Adding an in nite number of Gaussians with ...
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Pattern Classi cation by Duda et al. - Home | tommyodland.com
tommyodland.comThe Bayesian framework is analytically tractable when using Gaussians. For in-stance, we can compute p( jD) if we assume p( ) ˘N( 0; 0). The distribution p( ) is called a conjugate prior and p( jD) is a reproducing density, since a normal prior transforms to a normal posterior (with di erent parameters) when new data is observed.
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