Bayesian inference

ABSTRACT

Bayesian statistical methods have become more popular in different applications of scientific research over the past several decades. This is mainly due to the computing capacity of modern machines and the recent advances in Bayesian computational methodologies. In this chapter, we give a brief introduction to Bayesian analysis and discuss the difference between Bayesian and classical frequentist statistics. To illustrate Bayesian methodologies, a diagnostic COVID-19 test is used to present the basic principles of the Bayesian approach, prior distribution, likelihood function, and posterior distribution. As an application of the Bayesian methodologies, we introduce Bayesian linear regression and Gaussian process regression and their Bayesian inference framework.