Bayesian computational methods in biomedical research

This article gives a survey of Bayesian techniques useful for biomedical applications. Given the extensive use of Bayesian methods, especially with the recent advent of Markov Chain Monte Carlo (MCMC), we can never do exhaustive justice. Nevertheless, we have made an attempt to present different Bayesian applications from different viewpoints and differing levels of complexity. We start with a brief introduction to the Bayesian paradigm in Section 8.2, and give some basic formulas. In Section 8.3, we review conjugate Bayesian analysis in both the static and dynamic inferential frameworks, and give references to some biomedical applications. The conjugate Bayesian approach is often insufficient for handling complex problems that arise in several applications. The advent of sampling-based Bayesian methods has opened the door to carrying out inference in a variety of settings. They must of course be used with care, and with sufficient understanding of the underlying stochastics. In Section 8.4, we present details on the algorithms most commonly used in Bayesian computing and provide exhaustive references. Sections 8.5–8.8 show illustrations of Bayesian computing in biomedical applications that are of current interest.