Introduction to Applied Bayesian Statistics and Estimation for Social Scientists

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) methodsincluding the Gibbs sampler and the Metropolis-Hastings algorithmare 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.

First book written at an introductory level for social scientists interested in learning about MCMC Includes supplementary material: sn.pub/extras

Contenu
Probability Theory and Classical Statistics.- Basics of Bayesian Statistics.- Modern Model Estimation Part 1: Gibbs Sampling.- Modern Model Estimation Part 2: MetroplisHastings Sampling.- Evaluating Markov Chain Monte Carlo Algorithms and Model Fit.- The Linear Regression Model.- Generalized Linear Models.- to Hierarchical Models.- to Multivariate Regression Models.- Conclusion.