An Empirical Bayesian Approach for Selection of Knot Locations in Reduced Rank Spatial Models Using Penalized Regression

• Activity Number: 379
• Type: Topic Contributed
• Date/Time: Tuesday, August 5, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Rajib Paul*+ and Casey M. Jelsema
• Companies: Western Michigan University and National Institute of Environmental Health Sciences
• Keywords: cloud ; covariance ; LASSO ; MCEM ; regeneration ; split chain

Abstract

Reduced rank approach is very popular in modeling spatial and spatio-temporal covariances for large datasets. The key idea is to model the spatial covariances through basis functions and reduced dimensional latent processes defined over a selected number of knots. The success of these models to characterize the spatial variability adequately depends on the appropriate number and locations of knots. In many applications, this is a two-dimensional spatial design problem. Use of information criteria (such as Akaike Information Criterion (AIC) and Bayes Information Criterion (BIC)) is not feasible as the number of candidate models to compare is quite large. We develop an empirical Bayesian method for automated knot selection. This algorithm proceeds in two steps: (1) Estimation of the covariance of the latent process using Monte Carlo Expectation Maximization (MCEM) algorithm and (2) Selection of knots using Bayesian penalized regression. The performance of our method is assessed through simulated datasets and a real dataset on cloud effective radius obtained from satellite remote sensing.