Encyclopedia of Financial Models I

Introduction to Bayesian Inference

BILIANA S. GÜNER, PhD

Assistant Professor of Statistics and Econometrics, Ozyegin University, Turkey

SVETLOZAR T. RACHEV, PhD, Dr Sci

Frey Family Foundation Chair Professor, Department of Applied Mathematics and Statistics, Stony Brook University, and Chief Scientist, FinAnalytica

JOHN S. J. HSU, PhD

Professor of Statistics and Applied Probability, University of California, Santa Barbara

FRANK J. FABOZZI, PhD, CFA, CPA

Professor of Finance, EDHEC Business School

Abstract: Bayesian inference is the process of arriving at estimates of the model parameters reflecting the blending of information from different sources. Most commonly, two sources of information are considered: prior knowledge or beliefs and observed data. The discrepancy (or lack thereof) between them and their relative strength determines how far away the resulting Bayesian estimate is from the corresponding classical estimate. Along with the point estimate, which most often is the posterior mean, in the Bayesian setting one has available the whole posterior distribution, allowing for a richer analysis.

In this entry, we focus on the essentials of Bayesian inference. Formalizing the practitioner’s knowledge and intuition into prior distributions is a key part of the inferential process. Especially when the data records are not abundant, the choice of prior distributions can influence greatly posterior conclusions. After presenting an overview of some approaches to prior specification, ...