Bayesian Models

Document Type

Book Chapter

Publication Title

Springer Handbooks

Abstract

Bayesian modelling has come a long way from the first appearance of the Bayes theorem. Now it is being applied in almost every scientific field. Scientists and practitioners are choosing to use Bayesian methodologies over the classical frequentist framework because of its rigour mathematical framework and the ability to combine prior information to define a prior distribution on the possible values of the unknown parameter. Here in this chapter we briefly discuss various aspects of Bayesian modelling. Starting from a short introduction on conditional probability, the Bayes theorem, different types of prior distributions, hierarchical and empirical Bayes and point and interval estimation, we describe Bayesian regression modelling with more detail. Then we mention an array of Bayesian computational techniques, viz. Laplace approximations, E-M algorithm, Monte Carlo sampling, importance sampling, Markov chain Monte Carlo algorithms, Gibbs sampler and Metropolis-Hastings algorithm. We also discuss model selection tools (e.g. DIC, WAIC, cross-validation, Bayes factor, etc.) and convergence diagnostics of the MCMC algorithm (e.g. Geweke diagnostics, effective sample size, Gelman-Rubin diagnostic, etc.). We end the chapter with some applications of Bayesian modelling and discuss some of the drawbacks in using Bayesian modelling in practice.

First Page

763

Last Page

793

DOI

10.1007/978-1-4471-7503-2_37

Publication Date

1-1-2023

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