Introduction.- Probability theory and classical statistics.- Basics of Bayesian statistics.- Modern model estimation part 1: Gibbs sampling.- Modern model estimation part 2: Metroplis-Hastings sampling.- Evaluating MCMC algorithms and model fit.- The linear regression model.- Generalized linear models.- Introduction to hierarchical models.- Introduction to multivariate regression models.- Conclusion.
This book outlines Bayesian statistical analysis in great detail, from the development of a model through the process of making statistical inference. The key feature of this book is that it covers models that are most commonly used in social science research - including the linear regression model, generalized linear models, hierarchical models, and multivariate regression models - and it thoroughly develops each real-data example in painstaking detail.
This book provides an introduction to the Bayesian approach to statistical analysis of data, written at a level that is accessible to a social science audience. The book covers the Bayesian approach from model development through the development and implementation of programs to estimate the model, through summation and interpretation of the output. The first part provides a detailed introduction to mathematical statistics and the Bayesian approach to statistics, as well as a thorough explanation of the rationale for using simulation methods to construct summaries of posterior distributions. Markov chain Monte Carlo (MCMC) methods-including the Gibbs sampler and the Metropolis-Hastings algorithm-are then introduced as general methods for simulating samples from distributions. Extensive discussion of programming Markov chain Monte Carlo algorithms, monitoring their performance, and improving them is provided before turning to the larger examples involving real social science models and data.