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by Therese M. Donovan (Author), Ruth M. Mickey (Author)
About the Author
Therese Donovan, Wildlife Biologist, U.S. Geological Survey, Vermont Cooperative Fish and Wildlife Research Unit, University of Vermont, USA,Ruth M. Mickey, Professor Emerita, Department of Mathematics and Statistics, University of Vermont, USA
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.
About this book
Bayesian statistics is currently undergoing something of a renaissance. At its heart is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available. It is an approach that is ideally suited to making initial assessments based on incomplete or imperfect information; as that information is gathered and disseminated, the Bayesian approach corrects or replaces the assumptions and alters its decision-making accordingly to generate a new set of probabilities. As new data/evidence becomes available the probability for a particular hypothesis can therefore be steadily refined and revised. It is very well-suited to the scientific method in general and is widely used across the social, biological, medical, and physical sciences. Key to this book's novel and informal perspective is its unique pedagogy, a question and answer approach that utilizes accessible language, humor, plentiful illustrations, and frequent reference to on-line resources.
Bayesian Statistics for Beginners is an introductory textbook suitable for senior undergraduate and graduate students, professional researchers, and practitioners seeking to improve their understanding of the Bayesian statistical techniques they routinely use for data analysis in the life and medical sciences, psychology, public health, business, and other fields.
Brief contents
SECTION 1 Basics of Probability
1 Introduction to Probability 3
2 Joint, Marginal, and Conditional Probability 11
SECTION 2 Bayes’ Theorem and Bayesian Inference
3 Bayes’ Theorem 29
4 Bayesian Inference 37
5 The Author Problem: Bayesian Inference with Two Hypotheses 48
6 The Birthday Problem: Bayesian Inference with Multiple Discrete Hypotheses 61
7 The Portrait Problem: Bayesian Inference with Joint Likelihood 73
SECTION 3 Probability Functions
8 Probability Mass Functions 87
9 Probability Density Functions 108
SECTION 4 Bayesian Conjugates
10 The White House Problem: The Beta-Binomial Conjugate 133
11 The Shark Attack Problem: The Gamma-Poisson Conjugate 150
12 The Maple Syrup Problem: The Normal-Normal Conjugate 172
SECTION 5 Markov Chain Monte Carlo
13 The Shark Attack Problem Revisited: MCMC with the Metropolis Algorithm 193
14 MCMC Diagnostic Approaches 212
15 The White House Problem Revisited: MCMC with the Metropolis–Hastings Algorithm 224
16 The Maple Syrup Problem Revisited: MCMC with Gibbs Sampling 247
SECTION 6 Applications
17 The Survivor Problem: Simple Linear Regression with MCMC 269
18 The Survivor Problem Continued: Introduction to Bayesian Model Selection 308
19 The Lorax Problem: Introduction to Bayesian Networks 325
20 The Once-ler Problem: Introduction to Decision Trees 353
Appendices
A.1 The Beta-Binomial Conjugate Solution 369
A.2 The Gamma-Poisson Conjugate Solution 373
A.3 The Normal-Normal Conjugate Solution 379
A.4 Conjugate Solutions for Simple Linear Regression 385
A.5 The Standardization of Regression Data 395
Bibliography 399
Hyperlinks 403
Name Index 413
Subject Index 414
Pages: 432 pages
Publisher: Oxford University Press (July 23, 2019)
Language: English
ISBN-10: 0198841302
ISBN-13: 978-0198841302
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