Gaussian Markov Random Field Models for Surveillance Error and Geographic Boundaries

This dissertation addresses two basic problems in epidemiological surveys of insect distributions: the uncertainty in the surveillance process conducted by human inspectors and the modeling of geographic barriers in spatial analysis. In the first work, we propose a Bayesian hierarchical model which models the accuracy of human inspectors. We apply this model to analyze an entomological survey conducted by the Peruvian Ministry of Health in Mariano Melgar, Peru to locate areas of underreporting of insect infestation. We consider how the household assignment of inspectors influences this identifiability problem. We introduce a simulation paradigm where the strength of confounding may be controlled. Through these simulations, we demonstrate how practically implementable assignment recommendations can mitigate the error in infestation estimates created by this confounding. In the second work, we study a method for modeling geographic boundaries. We parameterize the shape of these barriers to vary according to intensity of these effects. We demonstrate the model's properties on simulated data and show the efficiency of Bayesian procedures. We then apply the model to the above data set by modeling streets in Mariano Melgar. We quantify this barrier effect and after performing sensitivity analysis, conclude that streets are a major barrier. Lastly, we discuss some extensions and open possibilities with our approach.