Bayesian Prediction(cont.)

• Given these observations, we can compute the posterior for each multinomial ? Xi | pai independently

  • The posterior is Dirichlet with parameters
    ?(Xi=1|pai)+N (Xi=1|pai),…, ?(Xi=k|pai)+N (Xi=k|pai)
    

• The predictive distribution is then represented by the parameters

which is what we expected!

The Bayesian analysis just made the assumptions explicit

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