If the pp distribution is p(yrep | y) = \int p(yrep | theta) p(theta | y) dtheta, and we know just some (S) samples from the posterior then the pp distribution should be p(yrep | y) = mean( p(yrep | theta_s) ). If, for instance, the likelihood is gaussian, then the pp distribution is an average o…

p(yrep | y) is conceptually the integral over theta of the function p(y_rep | theta) * p(theta | y). We can draw from the distribution whose PDF is p(yrep | y) by repeating the following two steps many times: Draw theta_tilde from the distribution whose PDF is p(theta | y) Draw y_rep from the dis…

Thanks for your answer. I had misunderstood (almost) everything. I have to read more carefully next time :-) I have found another explanation to my doubts here , maybe it can help others. The integration is done in this case just looking to one side of the table, no summations at all.

Sampling from the posterior predictive distribution

General

Homer March 3, 2019, 1:53pm 4

Your thread is quite old by now, but perhaps this new thread could also help to clarify any open questions.

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Sampling from the posterior predictive distribution

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