Appendix: Distribution Theory and Linear Algebra

Abstract

This Chapter contains a review and discussion of some of the basic results in distribution theory used throughout the book. Many of these results are stated without proofs and the reader is referred to a standard text on multivariate analysis, such as Mardia, Kent and Bibby (1979) for further details. The exceptions to this general rule are some of the results relating to Bayesian prior to posterior calculations in multivariate normal and joint normal/gamma models. Press (1985) is an excellent reference for such results in addition to standard, non-Bayesian multivariate theory. These results are discussed in detail as they are of some importance and should be clearly understood. For a comprehensive reference to all the distribution theory, see Johnson and Kotz (1972). For distribution theory specifically within the contexts of Bayesian analyses, see Aitchison and Dunsmore (1976), Box and Tiao (1973), and De Groot (1971).