Appendix H Basic Results from Bayesian Inference Models
Introduction
This appendix describes and provides background information and results used mainly in the construction of Bayesian intervals in Chapters 15–17. The appendix contains:
 Some useful technical results that are used to obtain the posterior distributions and posterior predictive distributions in this appendix (Section H.1).
 A formal presentation of Bayes’ theorem (Section H.2).
 The definition of conjugate prior distributions with examples for the binomial, Poisson, and normal distributions (Section H.3).
 The definition of Jeffreys prior distributions with examples for the binomial, Poisson, and normal distributions. Also a modified Jeffreys prior distribution for the normal distribution (Section H.4).
 The definition of posterior predictive distributions with examples, using conjugate prior distributions, for the binomial, Poisson, and normal distributions (Section H.5).
 Posterior predictive distributions for the binomial and the Poisson distributions using Jeffreys prior distributions. Also a posterior predictive distribution for the normal distributions using a modified Jeffreys prior distribution (Section H.6).
H.1 Basic Results Used in This Appendix
In this appendix we use the following results:

We frequently need to compute the marginal distribution corresponding to a mixture of two normal distributions. The following result is useful in making those computations.
Consider the continuous normalnormal ...
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