Bayesian Analysis for the Social Sciences
List of Tables.
Part I: Introducing Bayesian Analysis.
1. The foundations of Bayesian inference.
1.1 What is probability?
1.2 Subjective probability in Bayesian statistics.
1.3 Bayes theorem, discrete case.
1.4 Bayes theorem, continuous parameter.
1.5 Parameters as random variables, beliefs as distributions.
1.6 Communicating the results of a Bayesian analysis.
1.7 Asymptotic properties of posterior distributions.
1.8 Bayesian hypothesis testing.
1.9 From subjective beliefs to parameters and models.
1.10 Historical note.
2. Getting started: Bayesian analysis for simple models.
2.1 Learning about probabilities, rates and proportions.
2.2 Associations between binary variables.
2.3 Learning from counts.
2.4 Learning about a normal mean and variance.
2.5 Regression models.
2.6 Further reading.
Part II: Simulation Based Bayesian Analysis.
3. Monte Carlo methods.
3.1 Simulation consistency.
3.2 Inference for functions of parameters.
3.3 Marginalization via Monte Carlo integration.
3.4 Sampling algorithms.
3.5 Further reading.
4. Markov chains.
4.1 Notation and definitions.
4.2 Properties of Markov chains.
4.3 Convergence of Markov chains.
4.4 Limit theorems for Markov chains.
4.5 Further reading.
5. Markov chain Monte Carlo.
5.1 Metropolis-Hastings algorithm.
5.2 Gibbs sampling.
6. Implementing Markov chain Monte Carlo.
6.1 Software for Markov chain Monte Carlo.
6.2 Assessing convergence and run-length.
6.3 Working with BUGS/JAGS from R.
6.4 Tricks of the trade.
6.5 Other examples.
6.6 Further reading.
Part III: Advanced Applications in the Social Sciences.
7. Hierarchical Statistical Models.
7.1 Data and parameters that vary by groups: the case for hierarchical modeling.
7.2 ANOVA as a hierarchical model.
7.3 Hierarchical models for longitudinal data.
7.4 Hierarchical models for non-normal data.
7.5 Multi-level models.
8. Bayesian analysis of choice making.
8.1 Regression models for binary responses.
8.2 Ordered outcomes.
8.3 Multinomial outcomes.
8.4 Multinomial probit.
9. Bayesian approaches to measurement.
9.1 Bayesian inference for latent states.
9.2 Factor analysis.
9.3 Item-response models.
9.4 Dynamic measurement models.
Part IV: Appendices.
Appendix A: Working with vectors and matrices.
Appendix B: Probability review.
B.1 Foundations of probability.
B.2 Probability densities and mass functions.
B.3 Convergence of sequences of random variabales.
Appendix C: Proofs of selected propositions.
C.1 Products of normal densities.
C.2 Conjugate analysis of normal data.
C.3 Asymptotic normality of the posterior density.
Provides an introduction to Bayesian methods, specifically tailored for students of the social sciences.
Contains many real examples from social science research.
Includes software code for implementing the methods in WinBUGS and R.
Includes detailed definitions of key Bayesian ideas, assuming little background knowledge.
Each chapter contains graded exercises to help further the student’s understanding of the methods and applications.
Accompanied by a Website featuring WinBUGS and R code, and data sets.
“This is a comprehensive text on applied Bayesian statistics. Though it is primarily aimed at social scientists with strong computational and statistical backgrounds, its scope should appeal to a wider readership. I recommend it to anybody interested in actually applying Bayesian methods.” (Significance, 1 June 2010)"As in many texts, each chapter ends with a collection of exercises which would make this text suitable for teaching a one-semester course in Bayesian methods with applications in the social sciences . . . with this small caveat, I was impressed with the text and believe it would be a worthy candidate for a first Bayesian courses that gives the student a balanced view of the theory and practice of Bayesian thinking." (The American Statistician, 1 February 2011)
The first text to focus on Bayesian methods specifically for students of social sciences has now been published by Wiley-Blackwell. Bayesian Analysis for the Social Sciences provides an accessible introduction to Bayesian methods, containing many real examples from research in political science, psychology, sociology and economics.
Simon Jackman includes detailed descriptions of key Bayesian concepts, assuming little background knowledge. Each chapter contains graded exercises to help further the student’s understanding of the methods and applications.
Bayesian Analysis for the Social Sciences contains examples of how to implement the methods using WinBUGS and R, an open-source statistical software currently being developed to work in parallel with WinBUGS. There is also a website supporting the text, featuring WinBUGS and R code, data sets, and solutions to exercises.
Bayesian methods are increasingly being used to solve problems in the social sciences. They lend themselves naturally to these areas of research, where data is often qualitative, and based upon subjective expert judgments. The emergence of WinBUGS, a dedicated Bayesian analysis software — has given social scientists, at all levels, the power to solve problems in their work, that would otherwise require a very good understanding of complex Bayesian methodology.
Bayesian Analysis for the Social Sciences is an invaluable tool for graduate and postgraduate students in the social sciences, in such fields as political science, sociology, psychology, communications, education, and economics. It is also of interest to statisticians working on problems in the social sciences.