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 may be 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.
