Bayesian Analysis of Stochastic Process Models

2

Bayesian analysis

2.1 Introduction

In this chapter, we briefly address the first part of this book’s title, that is, Bayesian Analysis, providing a summary of the key results, methods and tools that are used throughout the rest of the book. Most of the ideas are illustrated through several worked examples showcasing the relevant models. The chapter also sets up the basic notation that we shall follow later on.

In the last few years numerous books dealing with various aspects of Bayesian analysis have been published. Some of the most relevant literature is referenced in the discussion at the end of this chapter. However, in contrast to the majority of these books, and given the emphasis of our later treatment of stochastic processes, we shall here stress two issues that are central to our book, that is, decision-making and computational issues.

The chapter is organized as follows. First, in Section 2.2 we outline the basics of the Bayesian approach to inference, estimation, hypothesis testing, and prediction. We also consider briefly problems of sensitivity to the prior distribution and the use of noninformative prior distributions. In Section 2.3, we outline Bayesian decision analysis. Then, in Section 2.4, we briefly review Bayesian computational methods. We finish with a discussion in Section 2.5.

2.2 Bayesian statistics

The Bayesian framework for inference and prediction is easily described. Indeed, at a conceptual level, one of the major advantages of the Bayesian approach ...