Probability and Bayesian Modeling

Jim Albert

ISBN 10: 1138492566 / ISBN 13: 9781138492561

Editore: CRC Press Dez 2019, 2019

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Neuware - Bayesian statistics has been advancing in many aspects in recent years. Bayesian learning provides a natural framework for students to solve scientific problems. This book provides an introduction to Bayesian analysis for undergraduate students with calculus, statistics, and a computational background.

Codice articolo 9781138492561

Dati bibliografici

• Titolo: Probability and Bayesian Modeling
• Editore: CRC Press Dez 2019
• Data di pubblicazione: 2019
• Lingua: Inglese
• ISBN 10: 1138492566
• ISBN 13: 9781138492561
• Rilegatura: Buch
• Condizione: Neu
• Dimensioni: 241 L x 164 A x 32 P (millimetri) 241 millimetri di larghezza per 164 millimetri di altezza per 32 millimetri di profondità
• Peso: 1026 grammi

Descrizione articolo

Riassunto

Probability and Bayesian Modeling is an introduction to probability and Bayesian thinking for undergraduate students with a calculus background. The first part of the book provides a broad view of probability including foundations, conditional probability, discrete and continuous distributions, and joint distributions. Statistical inference is presented completely from a Bayesian perspective. The text introduces inference and prediction for a single proportion and a single mean from Normal sampling. After fundamentals of Markov Chain Monte Carlo algorithms are introduced, Bayesian inference is described for hierarchical and regression models including logistic regression. The book presents several case studies motivated by some historical Bayesian studies and the authors’ research.

This text reflects modern Bayesian statistical practice. Simulation is introduced in all the probability chapters and extensively used in the Bayesian material to simulate from the posterior and predictive distributions. One chapter describes the basic tenets of Metropolis and Gibbs sampling algorithms; however several chapters introduce the fundamentals of Bayesian inference for conjugate priors to deepen understanding. Strategies for constructing prior distributions are described in situations when one has substantial prior information and for cases where one has weak prior knowledge. One chapter introduces hierarchical Bayesian modeling as a practical way of combining data from different groups. There is an extensive discussion of Bayesian regression models including the construction of informative priors, inference about functions of the parameters of interest, prediction, and model selection.

The text uses JAGS (Just Another Gibbs Sampler) as a general-purpose computational method for simulating from posterior distributions for a variety of Bayesian models. An R package ProbBayes is available containing all of the book datasets and special functions for illustrating concepts from the book.

A complete solutions manual is available for instructors who adopt the book in the Additional Resources section.

Informazioni sull?autore

Jim Albert is a Distinguished University Professor of Statistics at Bowling Green State University. His research interests include Bayesian modeling and applications of statistical thinking in sports. He has authored or coauthored several books including Ordinal Data Modeling, Bayesian Computation with R, and Workshop Statistics: Discovery with Data, A Bayesian Approach.

Jingchen (Monika) Hu is an Assistant Professor of Mathematics and Statistics at Vassar College. She teaches an undergraduate-level Bayesian Statistics course at Vassar, which is shared online across several liberal arts colleges. Her research focuses on dealing with data privacy issues by releasing synthetic data.