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Full Description
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.
Contents
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
