Prior vs Likelihood vs Posterior Posterior Predictive ...

Prior vs Likelihood vs PosteriorPosterior Predictive DistributionPoisson DataStatistics 220 Spring 2005 Copyrightc 2005 by Mark E. IrwinChoosing the Likelihood ModelWhile much thought is put into thinking about priors in a Bayesian Analysis,the data ( Likelihood ) model can have a big that need to be made involve Independence vs Exchangable vs More Complex Dependence Tail size, Normal vstdf Probability of eventsChoosing the Likelihood Model1 Example: Probability of God s ExistanceTwo different analyses - both using the priorP[God] =P[No God] = Ratio Components:Di=P[Datai|God]P[Datai|No God]Evidence (Datai)Di- UnwinDi- ShermerRecognition of of moral of natural miracles (prayers)21 Extranatural miracles (resurrection) the Likelihood Model2P[God|Data]: Unwin:23 Shermer: even starting with the same Prior , the difference beliefs about what thedata says gives quite different Posterior is based on an analysis published in an July 2004 Scientific Americanarticle.

Choosing the Likelihood Model While much thought is put into thinking about priors in a Bayesian Analysis, the data (likelihood) model can have a big efiect.

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