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Preface; CONTENTS; Contents; List of Figures; List of Tables; 1 Introduction; 1.1 Outline; 1.2 A note on programming; 1.3 Symbols used throughout the book; 2 Probability Theory and Classical Statistics; 2.1 Rules of probability; 2.2 Probability distributions in general; 2.3 Some important distributions in social science; 2.4 Classical statistics in social science; 2.5 Maximum likelihood estimation; 2.6 Conclusions; 2.7 Exercises; 3 Basics of Bayesian Statistics; 3.1 Bayes' Theorem for point probabilities; 3.2 Bayes' Theorem applied to probability distributions
3.3 Bayes' Theorem with distributions: A voting example3.4 A normal prior-normal likelihood example with σ 2 known; 3.5 Some useful prior distributions; 3.6 Criticism against Bayesian statistics; 3.7 Conclusions; 3.8 Exercises; 4 Modern Model Estimation Part 1: Gibbs Sampling; 4.1 What Bayesians want and why; 4.2 The logic of sampling from posterior densities; 4.3 Two basic sampling methods; 4.4 Introduction to MCMC sampling; 4.5 Conclusions; 4.6 Exercises; 5 Modern Model Estimation Part 2: Metroplis-HastingsSampling; 5.1 A generic MH algorithm
5.2 Example: MH sampling when conditional densities are difficult to derive5.3 Example: MH sampling for a conditional density with an unknown form; 5.4 Extending the bivariate normal example: The full multiparameter model; 5.5 Conclusions; 5.6 Exercises; 6 Evaluating Markov Chain Monte Carlo Algorithms andModel Fit; 6.1 Why evaluate MCMC algorithm performance?; 6.2 Some common problems and solutions; 6.3 Recognizing poor performance; 6.4 Evaluating model fit; 6.5 Formal comparison and combining models; 6.6 Conclusions; 6.7 Exercises; 7 The Linear Regression Model
7.1 Development of the linear regression model7.2 Sampling from the posterior distribution for the modelparameters; 7.3 Example: Are people in the South "nicer" than others?; 7.4 Incorporating missing data; 7.5 Conclusions; 7.6 Exercises; 8 Generalized Linear Models; 8.1 The dichotomous probit model; 8.2 The ordinal probit model; 8.3 Conclusions; 8.4 Exercises; 9 Introduction to Hierarchical Models; 9.1 Hierarchical models in general; 9.2 Hierarchical linear regression models; 9.3 A note on fixed versus random effects models and otherterminology; 9.4 Conclusions; 9.5 Exercises
10 Introduction to Multivariate Regression Models10.1 Multivariate linear regression; 10.2 Multivariate probit models; 10.3 A multivariate probit model for generating distributions of multistate life tables; 10.4 Conclusions; 10.5 Exercises; 11 Conclusion; A Background Mathematics; A.1 Summary of calculus; A.2 Summary of matrix algebra; A.3 Exercises; B The Central Limit Theorem, Confidence Intervals, andHypothesis Tests; B.1 A simulation study; B.2 Classical inference; References; Index
Anmerkung:
Includes bibliographical references (p. [345]-351) and index
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 Markov Chain Monte Carlo Algorithms and Model Fit -- The Linear Regression Model -- Generalized Linear Models -- to Hierarchical Models -- to Multivariate Regression Models -- Conclusion.
Introduction to Applied Bayesian Statistics and Estimation for Social Scientists covers the complete process of 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. The first part of the book 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 MCMC algorithms, monitoring their performance, and improving them is provided before turning to the larger examples involving real social science models and data. Scott M. Lynch is an associate professor in the Department of Sociology and Office of Population Research at Princeton University. His substantive research interests are in changes in racial and socioeconomic inequalities in health and mortality across age and time. His methodological interests are in the use of Bayesian stastistics in sociology and demography generally and in multistate life table methodology specifically
Introduction to Applied Bayesian Statistics and Estimation for Social Scientists / Scott M. Lynch. New York, NY : Springer Science+Business Media, LLC, 2007
