Elements of Bayesian Statistics

This important reference/text focuses on the theory of reduction of a Bayesian experiment considered as a (unique) probability measure on a product space (parameter space x sample space). Treating the basic model and its essential properties, it comprehensively examines sufficiency, including its applications to identification and to comparison of models, as well as ancillarity, with its application to exogeneity. In addition, Elements of Bayesian Statistics details three developments of the basic model, including sequential decomposition of the sample information, asymptotic development in properties of reduction, and invariance ... features numerous examples illustrating the essential properties of the most important statistical models, such as normal, regression, and nonparametric models, stationary processes, and models with incidental parameters ... introduces original treatments of analyses of joint reductions, optimality of reductions and identification, Bayesian analysis of standard stationary processes, systematic relationships between sampling and Bayesian results, and others ... discusses densities with virtually all basic results proved for abstract probability measures ... and integrates a large number of topics in statistical methods. Book jacket.