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We develop Bayesian nonparametric models for spatially indexed data of mixed type. Our work is motivated by challenges that occur in environmental epidemiology, where the usual presence of several confounding variables that exhibit complex interactions and high correlations makes it difficult to estimate and understand the effects of risk factors on health outcomes of interest. The modeling approach we adopt assumes that responses and confounding variables are manifestations of continuous latent variables, and uses multivariate Gaussians to jointly model these. Responses and confounding variables are not treated equally as relevant parameters of the distributions of the responses only are modeled in terms of explanatory variables or risk factors. Spatial dependence is introduced by allowing the weights of the nonparametric process priors to be location specific, obtained as probit transformations of Gaussian Markov random fields. Confounding variables and spatial configuration have a similar role in the model, in that they only influence, along with the responses, the allocation probabilities of the areas into the mixture components, thereby allowing for flexible adjustment of the effects of observed confounders, while allowing for the possibility of residual spatial structure, possibly occurring due to unmeasured or undiscovered spatially varying factors. Aspects of the model are illustrated in simulation studies and an application to a real data set.
In some contexts, mixture models can fit certain variables well at the expense of others in ways beyond the analysts control. For example, when the data include some variables with non-trivial amounts of missing values, the mixture model may fit the
In spatial statistics, it is often assumed that the spatial field of interest is stationary and its covariance has a simple parametric form, but these assumptions are not appropriate in many applications. Given replicate observations of a Gaussian sp
In many applications there is interest in estimating the relation between a predictor and an outcome when the relation is known to be monotone or otherwise constrained due to the physical processes involved. We consider one such application--inferrin
Graphical models express conditional independence relationships among variables. Although methods for vector-valued data are well established, functional data graphical models remain underdeveloped. We introduce a notion of conditional independence b
This paper demonstrates the advantages of sharing information about unknown features of covariates across multiple model components in various nonparametric regression problems including multivariate, heteroscedastic, and semi-continuous responses. I