## Applied Bayesian Data Analysis

A 2-Day Seminar Taught by Jeff Gill, Ph.D.

To see a sample of the course materials, click here.

Bayesian methods have revolutionized statistics over the last quarter of a century. This is not an exaggeration. The appeal of Bayesian statistics is its intuitive basis in making direct probability statements for all assertions, and the ability to blend disparate types of data into the same model. Bayesian models take existing knowledge and update it as new data becomes available. This principle works across all scientific disciplines. The cost of this added inferential power is more reliance on computing. Fortunately, there are powerful software packages for Bayesian statistics that are free and easy to use (with some training).

This introductory course covers the theoretical and applied foundations of basic Bayesian statistical analysis with an emphasis on computational tools for Bayesian hierarchical models. We will discuss model checking, model assessment, and model comparison. The course will cover Bayesian stochastic simulation (Markov Chain Monte Carlo) in depth. We will fit linear and nonlinear specifications with multiple levels, longitudinal features, and non-normal distributional assumptions. Lectures will include theoretical discussions of modeling and estimation as well as practical guidance for fitting Bayesian multilevel models with software. Applications will be drawn from the social and biomedical sciences.

This is an applied course, but it covers the statistical theory necessary for understanding the methods, and therefore includes discussion of required mathematical statistics for Bayesian inference. There will be hands-on activities throughout the two days so that participants will leave knowing actually how to apply Bayesian methods to their own data.

### Who should attend?

This seminar is designed for quantitative researchers in business, government, and academia who would like exposure to Bayesian methods and the suite of tools to estimate Bayesian regression-style models. Participants should have a good foundation in basic statistics including linear and nonlinear regression and statistical inference, experience with statistical computing including some exposure to R, and experience with data manipulation. A basic understanding of calculus principles (principles not mechanics) and matrix algebra will be helpful.

### COMPUTING

This seminar uses the free software R and JAGS. To participate in the hands-on exercises with the instructor-supplied data, participants need to bring a laptop computer with R and JAGS. In addition, the following R packages should be pre-installed with the install.packages() command: “rjags”,”R2jags”,”arm”,”coda”,”superdiag”,”R2WinBUGS”.

For those not familiar with R, please review materials on the software here prior to the course.

### Location, Format and materials

The class will meet from 9 am to 5 pm each day with a 1-hour lunch break at Temple University Center City, 1515 Market Street, Philadelphia, PA 19103.

Participants receive a bound manual containing detailed lecture notes (with equations and graphics), examples of computer printout, and many other useful features. This book frees participants from the distracting task of note taking.

### Registration and Lodging

The fee of $995.00 includes all course materials. The early registration fee of $895.00 is available until October 3.

**Refund Policy**

If you cancel your registration at least two weeks before the course is scheduled to begin, you are entitled to a full refund (minus a processing fee of $50).

**Lodging Reservation Instructions**

A block of guest rooms has been reserved at the Club Quarters Hotel, 1628 Chestnut Street, Philadelphia, PA at a special rate of $154. In order to make reservations, call 203-905-2100 during business hours and identify yourself by using group code** STAT11 **or click here. For guaranteed rate and availability, you must reserve your room no later than **Monday****,** **October**** 2**.

### Seminar outline

INTRODUCTION:

– Typology of Statistics

– Critical Differences Between Bayesians and Non-Bayesians

– Some Problems with Traditional Statistical Thinking in the Social Sciences

– The History of Bayesian Statistics–Milestones

– Two Primary Principles of Bayesian Inference

– Simple Mechanics

– Views On Priors Determine Types of Bayesians

– Example: the Beta-Binomial

– Bayesian Tobit Model for Death Penalty Support

– Important Application: Did Vinnie Johnson Have a Hot Hand?

– Using Bayes Factors

BAYESIAN NORMAL MODELS

– Standard Bayesian Conventions

– Reporting Posterior Results

– Credible Intervals and Sets

– Highest Posterior Density Intervals and Sets

– Bayesian Updating: Overview

– Application of Bayesian Updating: A Meta-Estimate of Deaths in Stalin’s

Gulags

– Bayesian Normal Models

– Variance Estimation with Public Health Data

– Bayesian Normal Models, Uninformative Priors

– Bayesian Normal Models, IQ Example

SOME MODELS

– Simple Linear Bayesian Specification

– Prior Sensitivity

– Graphing

– ANES Data from 2012

– Logit Model for Survey Responses in Scotland, Explanatory Variables

– Percent Predicted Correctly

– Poisson Model of Military Coups

MULTILEVEL MODELS

– Advantages of Multilevel Models

– Features of Multilevel Models

– Modern Notation

– Linear Model Illustration

– Vocabulary Overview

– Comparison with Variable Contrasts

– Pooling

– Partial Pooling Estimates with No Explanatory Variables

– Presenting Results from Multilevel Models

– Illustration of Bayesian Inference

– A Bayesian Take On Hierarchical Models

– A Nonlinear Multilevel Approach

– Panel Data as Group Membership

– Varying-Intercept, Varying-Slope Logit Multilevel Model

– Bayesian Multinomial Specifications for Employment Status

– Nonlinear Random Effects Example for Indomethacin Trials

– Nested Classification Factors

MARKOV CHAIN MONTE CARLO

– Bureaucratic Politics Example

– Ordered Logit Model

– What is a Markov Chain?

– Marginal Distributions

– Markov Chain Properties

– The Gibbs Sampler

– Bayesian Tobit Model for Death Penalty Support

– The Metropolis-Hastings Algorithm

– Simple Metropolis-Hastings Example

– A Not-Simple Metropolis-Hastings Example

– The Hit-and-Run Algorithm

USING THE BUGS LANGUAGE

– BUGS Software for MCMC

– Specifying Models with \bugs

– Simple but Real Logit Example

– Thermonuclear Testing Example

– Back to the 1988 Election Example

– Blood Pressure Example

– Ordered Logit Example

– Left Censoring Example In JAGS

– An Example of Right Censoring in JAGS

– A Hierarchical Model of Lobbying Influence in the US States

– MCMC Convergence

– A Normal-Hierarchical Model of Cold War Military Personnel

– Correlation and Autocorrelation

– Geweke Time-Series Diagnostic

– Gelman and Rubin’s Multiple Sequence Diagnostic

– Heidelberger and Welch Diagnostic

MORE MODELS

– The Weibull Model

– Continuous Time, Factor Covariate Interpretation

– Multilevel Survival Model

– AML Survival Example

– Two General Approaches to Model Checking

– Four General Approaches to Assessing Model Quality

– More On Posterior Predictive Checks

– Likelihood Function Robustness

– Model, Abortion Attitudes in Britain

– Outcome Comparison: Observed Versus Simulated

– Posterior Predictive Distribution

– Bayes Factor

### Suggested readings

Gill, Jeff. “The Insignificance of Null Hypothesis Significance Testing.” Political Research Quarterly, vol. 52, no. 3, 1999, pp.647–674, JSTOR. Click here.

Gill, Jeff and Christopher Witko. “Bayesian Analytical Methods: A Methodological Prescription for Public Administration.” Journal of Public Administration Research and Theory, vol. 23, no. 2, 2013, pp. 457-494. Click here.

Leamer, Edward E. “Let’s Take the Con Out of Econometrics.” The American Economic Review, vol. 73, no. 1, 1983, pp. 31–43, JSTOR. Click here.

King, Gary. 1986. “How Not to Lie With Statistics: Avoiding Common Mistakes in Quantitative Political Science.” American Journal of Political Science, 30: pp. 666–687. Click here.

Gill, Jeff and Andrew J. Womack. “The Multilevel Model Framework.” In The SAGE Handbook of Multilevel Modeling. Scott, Marc A, Jeffrey S Simonoff and Brian D Marx (eds). London: SAGE Publications Ltd, 2013. Pp. 3-20. SAGE Research Methods. Click here.