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Modeling latent correlation structures with application to agricultural and environmental science

University of British Columbia

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 decomposable 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 distribution 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 statistical 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 predict) the underlying phenomena. Prior distributions are developed to accommodate the spatial non-stationarity arising from distinct between-region differences in agricultural policy and practice. As a result, the model developed has improved prediction performance relative to existing models, and allows for straightforward interpretation of climatic effects on the model's output. Lastly, we propose a novel approach to modeling nonstationary spatial fields. The proposed method works by expanding the geographic plane over which these processes evolve into higher dimensional spaces, transforming and clarifying complex patterns in the physical plane. By combining aspects of multi-dimensional scaling, group lasso, and latent variable models, a dimensionally sparse projection is found in which the originally nonstationary field exhibits stationarity. Following a comparison with existing methods in a simulated environment, dimension expansion is studied on a classic test-bed data set historically used to study nonstationary models. Following this, we explore the use of dimension expansion in modeling air pollution in the United Kingdom, a process known to be strongly influenced by rural/urban effects, amongst others, which gives rise to a nonstationary field.

Text

2012-07-30

Attribution 3.0 Unported

http://hdl.handle.net/2429/42834

Statistics

University of British Columbia

UBCV

http://creativecommons.org/licenses/by/3.0/