Applied Bayesian Statistics

✍ Scribed by Scott M. Lynch

• Publisher: Sage Publications, Incorporated
• Year: 2022
• Tongue: English
• Leaves: 217
• Category: Library

✦ Synopsis

Bayesian statistical analyses have become increasingly common over the last two decades. The rapid increase in computing power that facilitated their implementation coincided with major changes in the research interests of, and data availability for, social scientists. Specifically, the last two decades have seen an increase in the availability of panel data sets, other hierarchically structured data sets including spatially organized data, along with interests in life course processes and the influence of context on individual behavior and outcomes. The Bayesian approach to statistics is well-suited for these types of data and research questions. Applied Bayesian Statistics is an introduction to these methods that is geared toward social scientists. Author Scott M. Lynch makes the material accessible by emphasizing application more than theory, explaining the math in a step-by-step fashion, and demonstrating the Bayesian approach in analyses of U.S. political trends drawing on data from the General Social Survey.

✦ Table of Contents

Cover
Contents
List of Tables
List of Figures
About the Author
Series Editor's Introduction
Acknowledgments
Chapter 1. Introduction
Data and Topics Explored in Examples
Mathematical Knowledge Required for this Volume
Layout of the Book
Chapter 2. Probability Distributions and Review of Classical Analysis
Probability Distributions
Important Distributions in Bayesian Statistics
Marginal and Conditional Distributions
Review of Maximum Likelihood Analysis
Chapter 3. The Bayesian Approach to Probability and Statistics
Including a Prior Distribution and Summarizing the Posterior
More on Priors
Extending the Beta/Binomial Model to the Dirichlet/Multinomial
Normal Distribution Examples
Chapter 4. Markov Chain Monte Carlo (MCMC) Sampling Methods
Logic of Sampling to Summarize Distributions
A Simple Method for When Direct Simulation Is Impossible
Markov Processes and Chains
Basic Markov Chain Monte Carlo Methods
Slice Sampling
Evaluating MCMC Algorithm Performance
Chapter 5. Implementing the Bayesian Approach in Realistic Applications
The Linear Model
The Dichotomous Probit Model
A Latent Class (Finite Mixture) Model
Comparing Models and Evaluating Model Fit
Chapter 6. Conclusion
Why Take a Bayesian Perspective?
Some Additional Suggested Readings
Appendix
1. R Program for Simple Three-State Model With Uniform Proposal in Chapter 4
2. R Program for Simple Three-State Model With Nonuniform Proposal in Chapter 4
3. Random Walk Metropolis–Hastings Algorithm
4. Function for Computing Original Gelman–Rubin Diagnostic
5. Gibbs Sampler for the Linear Regression Model With Reference Prior
6. Gibbs Sampler for the Probit Regression Model With Uniform Priors
7. Gibbs Sampler for Two-Class Latent Class Model With Priors
8. Posterior Predictive Distribution Simulation (for Linear Model)
References
Index