An Overview of Bayesian Inference and Graphical Models

Abstract

The Bayesian view of statistics interprets probability as a measure of a state of knowledge or a degree of belief, and can be seen as an extension of the rules of logic to reasoning in the face of uncertainty [342]. The Bayesian view has many advantages [48, 342, 428, 606]: it has a firm axiomatic basis, coincides with the intuitive idea of probability, has a wide scope of applications and leads to efficient and tractable computational methods. The main aim of this book is to show that a Bayesian, probabilistic view on the problems that arise in the simulation, design and prediction of biomolecular structure and dynamics is extremely fruitful. This book is written for a mixed audience of computer scientists, bioinformaticians, and physicists with some background knowledge of protein structure. Throughout the book, the different authors will use a Bayesian viewpoint to address various questions related to biomolecular structure. Unfortunately, Bayesian statistics is still not a standard part of the university curriculum; most scientists are more familiar with the frequentist view on probability. Therefore, this chapter provides a quick, high level introduction to the subject, with an emphasis on introducing ideas rather than mathematical rigor. In order to explain the rather strange situation of two mainstream paradigms of statistics and two interpretations of the concept of probability existing next to each other, we start with explaining the historical background behind this schism, before sketching the main aspects of the Bayesian methodology. In the second part of this chapter, we will give an introduction to graphical models, which play a central role in many of the topics that are discussed in this book. We also discuss some useful concepts from information theory and statistical mechanics, because of their close ties to Bayesian statistics.