Bayesian Analysis of Spatially-Dependent Functional Responses with Spatially-Dependent Multi-Dimensional Functional Predictors

Abstract

Modeling high-dimensional functional responses utilizing multi-dimensional functional covariates is complicated by spatial and/or temporal dependence in the observations in addition to high-dimensional predictors. To utilize such rich sources of information we develop multi-dimensional spatial functional models that employ low-rank basis function expansions to facilitate model implementation. These models are developed within a hierarchical Bayesian framework that accounts for several sources of uncertainty, including the error that arises from truncating the infinite dimensional basis function expansions, error in the observations, and uncertainty in the parameters. We illustrate the predictive ability of such a model through a simulation study and an application that considers spatial models of soil electrical conductivity depth profiles using spatially dependent near-infrared spectral images of electrical conductivity covariates.