DEPARTMENT OF BIOSTATISTICS AND BIOINFORMATICS SEMINAR
Hierarchical Models: A Paradigm Shift in the Statistical Analysis of Large, Complex Datasets
Presented By
Abstract:
Hierarchical models have become the primary stochastic specification for modeling complex processes. The range of application for such specifications is enormous, reflecting a paradigm shift in the way that statisticians engage in interdisciplinary science. As part of this shift, there is increasing attention paid to bigger picture science, to looking at complex processes with an integrative perspective, to bringing a range of knowledge to this effort. Increasingly, we find researchers working with observational data, less with designed experiments, recognizing that the latter can help inform about the former but the gathering of such experiments provides only one source of data for learning about the complex process. Other information sources, empirical, theoretical, physical, etc. will also be included in the synthesis.
In the most generic form these models are prescribed as
f(data|process, parameters)f(process|parameters)f(parameters)
revealing the hierarchical nature of the specification as well as the fact that explicit modeling of the process is included. The simple form of this specification belies its breadth. The process component can include multiple levels. It can be dynamic, it can be spatial. Inference is usually conducted within the Bayesian framework, turning the inference to the posterior distribution, f(process, parameters|data), providing full inference as well as uncertainty.
I will present a brief review of the scope of settings in which hierarchical models arise. In the development I will show that, in most cases, the hierarchical structure is built with latent variables, e.g., random effects, missing data, indicators, and more general forms. We will see that these latent variables introduce unobservable process features which will be of interest. By way of illustration, I will present the mixture model setting, the context of structured dependence (e.g., spatial and temporal) for random effects, a look at dynamic models, and relatively recent ideas in data fusion.
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