I hold a joint appointment in the Departments of Plant Pathology and Statistics. My research deals both with the development of theoretical statistics and with the use of statistical tools to address complex problems in the agricultural, environmental and biological sciences. A particular focus is on the detection and description of patterns of plant and human diseases across large geographical regions.
In epidemiological studies it is often of interest to know whether the occurrence of a given disease is clustered, and if so, where the clusters occur. For example we may wish to know whether cases of childhood leukemia appear in clusters within Wisconsin, and if so, where those clusters occur. If they occur near nuclear power plants, for example, or in highly polluted urban centers, then this would lead to hypotheses of cause for the cases of leukemia. The difficulty in making these assessments are manifold. For example, cases often appear to be clustered in cities, but that would be expected simply because more people are living together in cities anyway. (The underlying population is clustered to begin with.) Thus we need to determine whether the clustering is above and beyond that of the population. Second, the prevalence rates of some diseases under study are low, and thus clusters are not easily found. We use a variety of Bayesian and non-Bayesian methods, coupled with Markov chain Monte Carlo techniques, to address these problems.
Another broad area of interest involves studying the association between variables measured across regions. When categorical data are spatially correlated, for example, the usual chi-squared tests of independence can be invalid. One approach we take is to use a multinomial autologistic model coupled with a Markov chain Monte Carlo approach for deriving Bayesian inferences from the data. In other work in this general area, we seek to find models that can be used to relate data obtained through remote sensing. In a sense, this consists of “regressing” one image on another. Our approach involves, again, both non-Bayesian and Bayesian approaches, combined with a variety of additional statistical tools.
More broadly, I collaborate with numerous scientists on a diverse array of problems, including survey design for assessing human nutrition, determining indicators of dairy herd health, modeling patterns of wolf re-establishment in northern Wisconsin, and describing soil formation processes in Africa, to name a few.