Conditionals in Exponential Families
Following our careful analysis of the normal conditionals example in the last chapter and our brief mention of the exponential conditionals distribution in Chapter 2, it is natural to seek out more general results regarding distributions whose conditionals are posited to be members of quite general exponential families. Indeed the discussion leading up to Theorem 2.4, suggests that things should work well when conditionals are from exponential families. The key reference for the present chapter is Arnold and Strauss (1991). However, it should be mentioned that results due to Besag (1974) in a stochastic process setting anticipate some of the observations in this chapter.
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