Bayesian analysis

The book Bayesian analysis: general framework deals with Bayesian inference within the framework of four stochastic models: the normal random sample the Gauss-Markov model the beta-binomial model and the Poisson-gamma model. For each of these models analytic expressions are presented for the posterior PDF the prior predictive PDF and the posterior predictive PDF under the Laplace prior PDF the Jeffreys prior PDF and the conjugate prior PDF. Topics such as the elicitation of hyper-parameter for the conjugate prior PDF the selection of models and prediction in multivariate regression analysis and the use of the Bayes factor in the test of hypothesis are dealt with more detail.