The concept of conditional specification of distributions is not new but, except in normal families, it has not been well developed in the literature. Computational difficulties undoubtedly hindered or discouraged developments in this direction. However, such roadblocks are of dimished importance today. Questions of compatibility of conditional and marginal specifications of distributions are of fundamental importance in modeling scenarios. Models with conditionals in exponential families are particularly tractable and provide useful models in a broad variety of settings.

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