A Defense of the Bayesian Choice

Abstract

A series of steps, each taken for good cause or pure necessity, each seeming so reasonable at the time, and each leading to things he had never imagined. He always seemed to find himself caught in that sort of dance. Robert Jordan, Lord of Chaos, Book VI of the Wheel of Time. This book has presented the main aspects of Bayesian inference in Statistics from a decision-theoretic point of view. Our coverage has scarcely been exhaustive: on one hand, the topics we consider are often treated in more detail. On the other hand, Bayesian analysis can be applied to many fields, and is increasingly done, thanks to the computational advances described in Chapter 6. Among these fields, we can mention biostatistics (see, e. for additional references.) Nonetheless, we found it important to consider Bayesian statistical analysis primarily from this theoretical and decisional perspective, before paying more attention to its potential for applications. Firstly, this study exhibits the inherent coherence of the Bayesian approach in comparison with alternative classical theories. Secondly, to develop an efficient approach for the processing of applications requires a solid background in theoretical issues.