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This course provides coverage of intermediate and advanced topics arising in the formulation, fitting, and checking of hierarchical or multilevel models from the Bayesian point of view. Hierarchical models (HMs) arise frequently in four main kinds of applications:
* HMs are common in fields such as health and education, in which data -- both outcomes and predictors -- are often gathered in a nested or hierarchical fashion: for example, patients within hospitals, or students within classrooms within schools. HMs are thus also ideally suited to the wide range of applications in government and business in which single- or multi-stage cluster samples are routinely drawn, and offer a unified approach to the analysis of random-effects (variance-components) and mixed models.
* A different kind of nested data arises in meta-analysis in, e.g., medicine and the social sciences. In this setting the goal is combining information from a number of studies of essentially the same phenomenon, to produce more accurate inferences and predictions than those available from any single study. Here the data structure is subjects within studies, and as in the clustered case above there will generally be predictors available at both the subject and study levels.
* When individuals -- in medicine, for instance -- are sampled cross-sectionally but then studied longitudinally, with outcomes observed at multiple time points for each person, a hierarchical data structure of the type studied in repeated-measures or growth curve analyses arises, with the readings at different time points nested within person.
* Hierarchical modeling also provides a natural way to treat issues of model selection and model uncertainty with all types of data, not just cluster samples or repeated measures outcomes. For example, in regression, if the data appear to exhibit residual variation that changes with the predictors, you can expand the model that assumes constant variation, by embedding it hierarchically in a family of models that span a variety of assumptions about residual variation. In this way, instead of having to choose one of these models and risk making the wrong choice, you can work with several models at once, weighting them in proportion to their plausibility given the data.
The Bayesian approach is particularly effective in fitting hierarchical models, because other model-based methods -- principally involving maximum likelihood -- often do not capture all relevant sources of uncertainty, leading to over-confident decisions and scientific conclusions.
In this course the basic principles of Bayesian hierarchical modeling are reviewed, with emphasis on practical rather than theoretical issues, and intermediate- and advanced-level ideas are illustrated with real data drawn from case studies involving complicated applications of HMs in cluster sampling and mixture modeling. The course is intended for applied statisticians with an interest in learning more about intermediate and advanced topics in hierarchical modeling in general, and the Bayesian analysis of such models in particular. An understanding of probability and
statistics at the level typically required for a Master's degree in statistics provides sufficient mathematical background.
This course is intended to be a follow-on from an introductory treatment of Bayesian hierarchical modeling, so I will assume that participants have background in Bayesian methods and hierarchical modeling at the level of
the first six chapters of the textbook by Gelman et al. (Bayesian Data Analysis, second edition, 2003) or equivalent.
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= Applied Session,
= Theme Session,
= Presenter