Hierarchical Modeling with Spatial Data

Authored by: Christopher K. Wikle

Handbook of Spatial Statistics

Print publication date:  March  2010
Online publication date:  March  2010

Print ISBN: 9781420072877
eBook ISBN: 9781420072884
Adobe ISBN:

10.1201/9781420072884-c7

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Abstract

In spatial statistics, one often must develop statistical models in the presence of complicated processes, multiple sources of data, uncertainty in parameterizations, and various degrees of scientific knowledge. One can approach such complex problems from either a joint or conditional viewpoint. Although it may be intuitive to consider processes from a joint perspective, such an approach can present serious challenges to statistical modeling. For example, it can be very difficult to specify joint multivariate dependence structures for related spatial datasets. It maybe much easier to factor such joint distributions into a series of conditional models. For example, it is simpler (and a reasonable scientific assumption) to consider a near-surface ozone process conditional upon the near-surface ambient air temperature (especially in the summer), rather than consider the ozone and temperature processes jointly. Indeed, it is often possible to simplify modeling specifications, account for uncertainties, and use scientific knowledge in a series of conditional models, coherently linked together by simple probability rules. This is the essence of hierarchical modeling.

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