Modeling Latent Correlation Structures with Application to Agricultural and Environmental Science

In this thesis, we explore the issue of latent correlation structure in spatial and other correlated systems. Firstly, we propose a class of prior distributions on decompos-able graphs, allowing for improved modeling flexibility. While existing methods solely penalize the number of edges, the proposed work empowers practitioners to control clustering, level of separation, and other features of the graph. Emphasis is placed on a particular prior distribution which derives its motivation from the class of product partition models; the properties of this prior relative to existing priors is examined through theory and simulation. We then demonstrate the use of graphical models in the field of agriculture, showing how the proposed prior distri-bution alleviates the inflexibility of previous approaches in properly modeling the interactions between the yield of different crop varieties. Secondly, we describe how spatial dependence can be incorporated into sta-tistical models for crop yield along with the dangers of ignoring it. In particular, approaches that ignore this dependence suffer in their ability to capture (and pre