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. TOC:Conditional Specification.- Basic Theorems.- Exact and Almost-Exact Compatibility in Discrete Distributions.- Distributions with Normal Conditionals.- Conditionals in Exponential Families.- Other Conditionally Specified Families.- Impossible Models.- Characterizations Involving Conditional Moments.- Multivariate Extensions.- Parameter Estimation in Conditionally Specified Models.- Simulations.- Marginal and Conditional Specification of Distributions.- Conditional Survival Models.- Bivariate Extreme Models Based on CS.- Bayesian Analysis Using Conditionally Specified Models.- Conditional Specification of Simultaneous Equation Models.- Other Conditional Specification Cases.
