Lynch Introduction to Applied Bayesian Statistics and Estimation for Social Scientists

1. Auflage 2007
ISBN: 978-0-387-71265-9
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 359 Seiten

Reihe: Statistics for Social and Behavioral Sciences

"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.

Autoren/Hrsg.

Lynch, Scott M.

Inhaltsverzeichnis

1;Preface;7
1.1;Acknowledgements;11
2;Contents;13
3;List of Figures;18
4;List of Tables;25
5;1 Introduction;27
5.1;1.1 Outline;29
5.2;1.2 A note on programming;31
5.3;1.3 Symbols used throughout the book;32
6;2 Probability Theory and Classical Statistics;34
6.1;2.1 Rules of probability;34
6.2;2.2 Probability distributions in general;37
6.3;2.3 Some important distributions in social science;50
6.4;2.4 Classical statistics in social science;58
6.5;2.5 Maximum likelihood estimation;60
6.6;2.6 Conclusions;69
6.7;2.7 Exercises;69
7;3 Basics of Bayesian Statistics;71
7.1;3.1 Bayes’ Theorem for point probabilities;71
7.2;3.2 Bayes’ Theorem applied to probability distributions;74
7.3;3.3 Bayes’ Theorem with distributions: A voting example;77
7.4;3.4 A normal prior–normal likelihood example with s2 known;86
7.5;3.5 Some useful prior distributions;92
7.6;3.6 Criticism against Bayesian statistics;94
7.7;3.7 Conclusions;97
7.8;3.8 Exercises;98
8;4 Modern Model Estimation Part 1: Gibbs Sampling;100
8.1;4.1 What Bayesians want and why;100
8.2;4.2 The logic of sampling from posterior densities;101
8.3;4.3 Two basic sampling methods;103
8.4;4.4 Introduction to MCMC sampling;111
8.5;4.5 Conclusions;126
8.6;4.6 Exercises;128
9;5 Modern Model Estimation Part 2: Metroplis– Hastings Sampling;129
9.1;5.1 A generic MH algorithm;130
9.2;5.2 Example: MH sampling when conditional densities are difficult to derive;137
9.3;5.3 Example: MH sampling for a conditional density with an unknown form;140
9.4;5.4 Extending the bivariate normal example: The full multiparameter model;143
9.5;5.5 Conclusions;150
9.6;5.6 Exercises;151
10;6 Evaluating Markov Chain Monte Carlo ( MCMC) Algorithms and Model Fit;153
10.1;6.1 Why evaluate MCMC algorithm performance?;154
10.2;6.2 Some common problems and solutions;154
10.3;6.3 Recognizing poor performance;157
10.4;6.4 Evaluating model fit;175
10.5;6.5 Formal comparison and combining models;181
10.6;6.6 Conclusions;185
10.7;6.7 Exercises;185
11;7 The Linear Regression Model;187
11.1;7.1 Development of the linear regression model;187
11.2;7.2 Sampling from the posterior distribution for the model parameters;190
11.3;7.3 Example: Are people in the South "nicer” than others?;196
11.4;7.4 Incorporating missing data;204
11.5;7.5 Conclusions;213
11.6;7.6 Exercises;214
12;8 Generalized Linear Models;215
12.1;8.1 The dichotomous probit model;217
12.2;8.2 The ordinal probit model;239
12.3;8.3 Conclusions;250
12.4;8.4 Exercises;251
13;9 Introduction to Hierarchical Models;253
13.1;9.1 Hierarchical models in general;254
13.2;9.2 Hierarchical linear regression models;262
13.3;9.3 A note on fixed versus random effects models and other terminology;286
13.4;9.4 Conclusions;290
13.5;9.5 Exercises;291
14;10 Introduction to Multivariate Regression Models;292
14.1;10.1 Multivariate linear regression;292
14.2;10.2 Multivariate probit models;298
14.3;10.3 A multivariate probit model for generating distributions of multistate life tables;324
14.4;10.4 Conclusions;336
14.5;10.5 Exercises;338
15;11 Conclusion;339
16;A Background Mathematics;343
16.1;A.1 Summary of calculus;343
16.2;A.2 Summary of matrix algebra;350
16.3;A.3 Exercises;355
17;B The Central Limit Theorem, Confidence Intervals, and Hypothesis Tests;357
17.1;B.1 A simulation study;357
17.2;B.2 Classical inference;358
18;References;365
19;Index;372