In this article, we aim to provide a thorough review of the Bayesian-inference-based methods applied to Hepatitis B Virus（HBV）, Hepatitis C Virus（HCV）, and Human Immunodeficiency Virus（HIV） studies with a focus on the detection of the viral mutations and various problems which are correlated to these mutations. It is particularly difficult to detect and interpret these interacting mutation patterns, but by using Bayesian statistical modeling, it provides a groundbreaking opportunity to solve these problems. Here we summarize Bayesian-based statistical approaches, including the Bayesian Variable Partition（BVP） model, Bayesian Network（BN）, and the Recursive Model Selection（RMS） procedure, which are designed to detect the mutations and to make further inferences to the comprehensive dependence structure among the interactions. BVP, BN, and RMS in which Markov Chain Monte Carlo（MCMC） methods are used have been widely applied in HBV, HCV, and HIV studies in the recent years.We also provide a summary of the Bayesian methods’ applications toward these viruses’ studies, where several important and useful results have been discovered. We envisage the applications of more modified Bayesian methods to other infectious diseases and cancer cells that will be following with critical medical results before long.
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