Probability and Bayesian Modeling 1st Edition

Chance and Bayesian Modeling presents a prelude to chance and Bayesian contemplating for undergraduates with a calculus background. The preliminary part of the book provides an extensive perspective on chance, encompassing bedrock principles, contingent probability, discrete and uniform distributions, and combined distributions. Statistical assumption is entirely presented from a Bayesian standpoint. The text introduces surmise and prognosis for a lone fraction and a lone average from Common sampling. After foundational Markov Chain Monte Carlo algorithms are initiated, Bayesian surmise is delineated for hierarchical and regression models inclusive of logistic regression. The book offers various scenarios galvanized by historical Bayesian exploration and the authors’ investigation.

This manuscript showcases contemporary Bayesian statistical practice. Simulation is introduced throughout all the chance sections and extensively utilized within the Bayesian material to simulate from the posterior and omen distributions. One section details the fundamental doctrines of Metropolis and Gibbs sampling algorithms; however, several sections introduce the rudiments of Bayesian surmise for conjugate priors to intensify understanding. Approaches for establishing prior distributions are detailed in instances where one possesses ample prior knowledge and for scenarios where one has feeble prior data. A section introduces hierarchical Bayesian modeling as a pragmatic approach to amalgamating data from distinct groups. There is a comprehensive discourse on Bayesian regression models encompassing the construction of illuminating priors, surmise about functions of the parameters of interest, prognosis, and model selection.

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