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Bayesian Data Analysis, Third Edition, 3rd Edition by Donald B. Rubin, Aki Vehtari, David B. Dunson, Hal S. Stern, John B. Carlin, Andrew Gelman

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Appendix B

Outline of proofs of limit theorems

The basic result of large-sample Bayesian inference is that as more and more data arrive, the posterior distribution of the parameter vector approaches multivariate normal. If the likelihood model happens to be correct, then we can also prove that the limiting posterior distribution is centered at the true value of the parameter vector. In this appendix, we outline a proof of the main results. The practical relevance of the theorems is discussed in Chapter 4.

We derive the limiting posterior distribution ...

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