Introduction to Bayesian Analysis and Bayesian Model Averaging in Stata

Session Submission Type: Short Course Half Day

Session Description

This short course will be divided into two sections. In the first section, I will give an introduction to the general Bayesian approach for regression analysis. In the second section, I will focus on the Bayesian model-averaging approach for regression analysis. We will be combining theoretical aspects with empirical applications using Stata.

Section 1 Introduction to Bayesian analysis using Stata

In recent years, researchers across disciplines have become increasingly interested in Bayesian analysis. This is not surprising, because researchers often have some prior knowledge about parameters of interest, and this can be incorporated when using Bayesian estimation. This approach also provides a more natural interpretation of the results in terms of probabilities for hypotheses of interest and predictions. Another attractive characteristic of Bayesian regression is that it offers a common theoretical framework for a wide variety of models. In the first part of this short course, I will provide an overview of the main concepts associated with regression analysis using the Bayesian approach, and I will use empirical applications to illustrate the way different elements associated with Bayesian estimation can be implemented in
Stata.

I will be covering the following aspects in this first section:

- A brief introduction to Stata
- A brief overview of Bayesian analysis
- Why and when to use Bayesian analysis
- Intuitive description of Markov chain Monte Carlo
- Empirical applications using the -bayes:- prefix with Stata estimation commands
- Linear regression
- Probit model
- Random effects Poisson model

Section 2 Introduction to Bayesian model averaging (BMA) using Stata

Most empirical applications consider a fixed unknown underlying data-generating model (DGM) that researchers try to find, based on a particular theoretical framework that is combined with the data associated with the variables involved in the selected model specification. Bayesian model averaging provides an approach, where instead of focusing the estimation on the search for that unique unknown model, researchers can incorporate the uncertainty about the DGM to obtain probabilities associated with relevant predictors, measurements about complementary or substitutable predictors across different model candidates, and also predictions that incorporate uncertainty about the model and the parameters. This approach is particularly appealing because the results can be intuitively interpreted and are useful to help the researcher in determining the more important predictors for the outcome variable. In this section, I will work with an empirical application to illustrate the way we can implement the Bayesian model-averaging approach using the Stata bma commands.

I will be covering the following aspects:

- Brief introduction to model averaging
- Brief description of Bayesian model averaging
- Empirical application (Linear regression)
- Posterior model probabilities
- Posterior inclusion probabilities
- Jointness (complement and substitute regressors)
- Sensitivity
- Predictions

Sub Unit

• Pre-Conference Short Courses

Chair

• Gustavo Sanchez StataCorp, LLC

Presenter

• Gustavo Sanchez StataCorp, LLC