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Probability Matching Priors: Higher Order Asymptotics

The remainder of the book turns to more statistical and applied issues but is relatively short in comparison to the foregoing material. Chapter 10 discusses estimation of the parameters of a multivariate t distribution including the use of the expectation maximization algorithm or one of its variants to obtain maximum likelihood estimates. Chapter 11 deals with classical and Bayesian inference in regression models when the errors are assumed to come from an uncorrelated multivariate t distribution. The implications of this model are that the errors are identically distributed but statistically dependent despite their lack of correlation. The applications in Chapter 12 are really notes for further reading. Projection pursuit, portfolio optimization, cluster analysis, and multiple decision problems are mentioned. In summary, this book is a useful reference work for anyone with an interest in non-Gaussian continuous multivariate distributions. Some form of heavytailed multivariate t distribution is often a natural alternative model to the normal distribution, and this book successfully summarizes what is known about such distributions. No doubt there are some omissions, as is to be expected when the relevant literature is very scattered, but the authors have done a useful service in bringing together a lot of useful material in one compact volume.