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

• Activity Number: 85
• Type: Contributed
• Date/Time: Sunday, August 3, 2014 : 4:00 PM to 5:50 AM
• Sponsor: Section on Statistics and the Environment
• Author(s): Wen-Hsi Yang*+ and Christopher K. Wikle and Scott Holan and Brenton Myers and Kenneth A. Sudduth
• Companies: CSIRO Computational Informatics and University of Missouri and University of Missouri and University of Missouri and USDA/ARS
• Keywords: Basis functions ; Diffuse reflectance spectroscopy ; Matrix normal ; Karhunen-Loeve ; Penetrometer ; Soil electrical conductivity

Abstract

Modeling high-dimensional functional responses utilizing multi-dimensional functional covariates is complicated by spatial and/or temporal dependence in the observation 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, as well as 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.