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Abstract:
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This half-day course reviews the basic concepts of Bayesian hierarchical models and focuses on using software to fit multilevel models (including random-effects models). The objectives are to familiarize statistical programmers and practitioners with the essentials of the Bayesian paradigm in the area of conducting hierarchical modeling. The course places significant emphasis on equipping attendees with computational tools through a series of worked-out examples that demonstrate sound practices for fitting Bayesian hierarchical models and conducting inferences.
The first part of the course reviews Bayesian hierarchical modeling, including concepts such as components of a multilevel model, exchangeability, group-specific inferences, choice and impact of prior distributions, and concepts in estimation and prediction.
The second part of the course takes an applied approach, illustrating the Bayesian treatment of a wide range of hierarchical models by using software, with code explained in detail. Topics include linear, generalized linear, and nonlinear random-effects models; nested and non-nested models; latent variable models; models that involve temporal and spatial structures; and meta-analysis applications. Statistical topics discussed include the selection of prior distributions and their implications, sensitivity analysis, prediction, model comparison, and general inferences. The examples are done using SAS (PROC MCMC), with a strong focus on technical details.
Attendees should have a background equivalent to an MS in applied statistics. Previous exposure to Bayesian methods is useful but not required. Familiarity with material at the level of the textbook Probability and Statistics, by DeGroot and Schervish (Addison Wesley), is appropriate.
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