Bayesian inference : statistical and probabilistic Mathematics / Arthur Gray.

Includes bibliographical references and index.

Bayesian Inference: Statistical and Probabilistic Mathematics by Arthur Gray provides a structured introduction to Bayesian inference as a coherent framework for reasoning under uncertainty, contrasting it with frequentist approaches and emphasizing probability as a measure of belief. The book develops the core idea of using Bayes’ theorem to update prior beliefs with new evidence through prior distributions, likelihood functions, and posterior distributions, while also discussing both subjective and objective choices of priors. It further explores practical modeling techniques such as conjugate priors, hierarchical models, and predictive distributions, alongside computational methods like Markov Chain Monte Carlo (MCMC) for handling complex problems. Through applications in areas such as machine learning, decision theory, and scientific data analysis, the text highlights probabilistic interpretation over traditional point estimates, ultimately bridging theoretical foundations with practical implementation of Bayesian methods.