Bayesian Statistics for Beginners

Therese Donovan is a wildlife biologist with the U.S. Geological Survey, Vermont Cooperative Fish and Wildlife Research Unit. Based in the Rubenstein School of Environment and Natural Resources at the University of Vermont, Therese teaches graduate courses on ecological modeling and conservation biology. She works with a variety of student and professional collaborators on research problems focused on the conservation of vertebrates. Therese is the Director of the Vermont Cooperative Fish and Wildlife Unit Spreadsheet Project, a suite of on-line tutorials in Excel and R for modeling and analysis of wildlife populations. She lives in Vermont with her husband, Peter, and two children, Evan and Ana. Ruth Mickey is a Professor Emerita of Statistics at the University of Vermont. Most of Ruth's career was spent in the Department of Mathematics and Statistics, where she taught courses in Applied Multivariate Analysis, Categorical Data, Survey Sampling, Analysis of Variance and Regression, and Probability. She served as an advisor or committee member of numerous MS and PhD committees over a broad range of academic disciplines. She worked on the development of statistical methods and applications to advance public health and natural resources issues throughout her career.

While reading this book, I joined the authors on a learning endeavor thanks to their honesty and intellectual vulnerability. Their lack of experience with Bayesian statistics helps them to be effective communicators . . . If you are interested in starting your Bayesian journey, then Bayesian Statistics for Beginners is an excellent place to begin.

• Section 1 Basics of Probability 1: Introduction to Probability 2: Joint, Marginal, and Conditional Probability Section 2 Bayes' Theorem and Bayesian Inference 3: Bayes' Theorem 4: Bayesian Inference 5: The Author Problem - Bayesian Inference with Two Hypotheses 6: The Birthday Problem: Bayesian Inference with Multiple Discrete Hypotheses 7: The Portrait Problem: Bayesian Inference with Joint Likelihood Section 3 Probability Functions 8: Probability Mass Functions 9: Probability Density Functions Section 4 Bayesian Conjugates 10: The White House Problem: The Beta-Binomial Conjugate 11: The Shark Attack Problem: The Gamma-Poisson Conjugate 12: The Maple Syrup Problem: The Normal-Normal Conjugate Section 5 Markov Chain Monte Carlo 13: The Shark Attack Problem Revisited: MCMC with the Metropolis Algorithm 14: MCMC Diagnostic Approaches 15: The White House Problem Revisited: MCMC with the Metropolis-Hastings Algorithm 16: The Maple Syrup Problem Revisited: MCMC with Gibbs Sampling Section 6 Applications 17: The Survivor Problem: Simple Linear Regression with MCMC 18: The Survivor Problem Continued: Introduction to Bayesian Model Selection 19: The Lorax Problem: Introduction to Bayesian Networks 20: The Once-ler Problem: Introduction to Decision Trees Appendices Appendix 1: The Beta-Binomial Conjugate Solution Appendix 2: The Gamma-Poisson Conjugate Solution Appendix 3: The Normal-Normal Conjugate Solution Appendix 4: Conjugate Solutions for Simple Linear Regression Appendix 5: The Standardization of Regression Data