Circulant Embedding of Approximate Covariances for Inference from Gaussian Data on Large Lattices

• Activity Number: 150
• Type: Invited
• Date/Time: Monday, August 10, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Montserrat Fuentes* and Joseph Guinness
• Companies: North Carolina State University and North Carolina State University

Abstract

The mobility and environmental impacts of arsenic is regulated by its reactions with soils. We describe an experiment that maps the composition of elements on an individual soil sand grain using X-ray fluorescence microprobe analyses. To understand the behavior of arsenic in soils, it is important to disentangle the complex multivariate relationships among the elements in the sample. This problem motivates our work to define conditional correlation in spatial lattice models and give general conditions under which two components are conditionally uncorrelated given the rest. We describe how to enforce that two components are conditionally uncorrelated given a third in parametric models, which provides a basis for likelihood ratio tests for conditional correlation between arsenic and chromium given iron. We show how to apply our results to big datasets introducing periodic covariance approximations designed for embedding covariance matrices for lattice-located observations inside of nested block circulant covariance matrices.