Proportion data falling in the continuum (0, 1) are very common in practice. It can also happen that an inflated number of zeros (or ones) occur with proportion data. There are extensive studies of zero-inflated data in the literature. Almost all of them, however, focus on zero-inflated count data. Furthermore,...
Graphical models use Markov properties to establish associations among dependent variables. To estimate spatial correlation and other parameters in graphical models, the conditional independences and joint probability distribution of the graph need to be specified. We can rely on Gaussian multivariate models to derive the joint distribution when all the...
In this thesis we focus on a graphical model for multivariate spatially
correlated data--isomorphic chain graphs (ICG; Gitelman and Herlihy, 2007).
We feel ICG allow flexibility for modeling spatial correlation and are intuitively
appealing because each model has an associated graph that visually represents a
complex multivariate system. We examine...
We describe spatio-temporal random processes using linear mixed models and discuss estimation, inference, and prediction under this formulation. We show how many commonly used covariances are special cases of this more general framework and pay special attention to the separable and product-sum covariances. The linear mixed model formulation facilitates straightforward...
For spatial data visualization, we approach two problems and provide solutions: heat map resolution selection, and heat map confidence interval presentation. Analysts often present spatial data in gridded heat maps, at some chosen resolution. However, many data types vary in density across the domain. We develop variable-resolution heat maps to...
Many of Earth’s terrestrial large carnivore species are threatened with extinction. As a result, some of the ecological effects associated with these species may be lost. With the goal of furthering large carnivore conservation research, I conduct three global scale analyses involving these species. First, I explore prey depletion as...
A copula is the representation of a multivariate distribution. Copulas are used to model multivariate data in many fields. Recent developments include copula models for spatial data and for discrete marginals. We will present a new methodological approach for modeling discrete spatial processes and for predicting the process at unobserved...
In this thesis we develop a theoretical framework for the identification of situations where the equal frequency (EF) or equal variance (EV) subclassification may produce lower bias and/or variance of the estimator. We conduct simulation studies to examine the EF and EV approaches under different types of model misspecification. We...