Invited Session V Abstracts

Invited Session V: Non-Gaussian Spatial Processes

Saturday, October 6, 2:30 p.m. – 4:30 p.m.

Session Chair: Bo Li

 

Bayesian Probit Regression Models for Multicategory Spatial Data

Catherine Calder

 Albert and Chib (1993)'s latent variable representation of the Bayesian probit regression model for categorical outcomes is widely recognized to facilitate model fitting.  This representation has also been used in various settings to incorporate residual dependence into regression models with discrete outcomes.  In this talk, we further extend this latent variable strategy to specify models for multicategory spatially-dependent outcomes.  In particular, we discuss parameter identifiability in the latent mean model specification and introduce covariance structures for describing the cross spatial/category residual dependence.  We also consider data augmentation MCMC strategies for improving the efficiency of model fitting algorithms.  Finally, we illustrate the proposed modeling framework through an analysis of land-cover/land-use observations taken over mainland Southeast Asia.  This is joint work with Candace Berrett.

 

 On Properties of Hierarchical Poisson Models for Spatial Count Data

Victor De Oliveira

 Spatial count data occur often in many of the earth sciences, but unlike spatial continuous data few models are available in the literature for their analysis. Currently, the most commonly used class of models seems to be that of spatial generalized linear mixed model, which is difficult to fit. Perhaps due to the latter, most of the recent literature has concentrated on computational methods to fit this class of models, and some of its basic model properties are not well understood. In this talk I explore some properties and limitations of this class of models, and illustrate the findings with simulated and real datasets.

 

Multilevel Latent Gaussian Spatial Process Model for Mixed Discrete and Continuous Multivariate Response Data

Jennifer A. Hoeting and Erin M. Schliep

 We propose a Bayesian model for mixed ordinal and continuous multivariate data to evaluate a latent spatial Gaussian process. Our proposed model can be used in many contexts where mixed continuous and discrete multivariate responses are observed in an effort to quantify an unobservable continuous measurement. In our example, the latent measurement is wetland condition. While the predicted values of the latent wetland condition, or health, variable at each location produced by the model do not hold any intrinsic value, the relative magnitudes of the wetland condition values are of interest. In addition, by including point-referenced covariates in the model, we are able to make predictions at new locations for both the latent random variable and the multivariate response. Lastly, the model produces ranks of the multivariate responses in relation to the unobserved latent random field. This is an important result as it allows us to determine which variables of the multivariate response are relevant in understanding the latent variable. This offers an alternative to traditional indexes based on best professional judgment that are frequently used in ecology. We apply our model to create a profile of wetland condition in the North Platte and Rio Grande River Basins in Colorado based on a variety of measurements made in the field. The model facilitates a comparison of wetland condition at multiple locations and ranks the importance of in-field measurements of wetland condition.

 

 Analysis of Areal Data: Should a Model with (Spatial) Dependence be Considered?

Petrutza Caragea

 The application of Markov random fields to problems involving spatial data on lattice systems (as often desirable in the environmental and ecological sciences, agriculture, and other areas of biology) requires decisions regarding a number of important aspects of model structure. Existing exploratory techniques appropriate for spatial data do not provide direct guidance to an investigator about these decisions. We introduce a diagnostic quantity useful in situations for which one is contemplating the application of a Markov random field model based on conditional one parameter exponential family distributions. This exploratory diagnostic is shown to be a meaningful statistic that can inform decisions involved in modeling spatial structure with statistical dependence terms. We illustrate its use in guiding modeling decisions with simulated examples and demonstrate that these properties have use in applications.