Tapered Covariance: Bayesian Estimation and Asymptotics

Abstract

The method of maximum tapered likelihood has been proposed as a way to quickly estimate covariance parameters for stationary Gaussian random fields. We show that under a useful asymptotic regime, maximum tapered likelihood estimators are consistent and asymptotically normal for covariance models in common use. We then formalize the notion of tapered quasi-Bayesian estimators and show that they too are consistent and asymptotically normal. We also present asymptotic confidence intervals for both types of estimators and show via simulation that they accurately reflect sampling variability, even at modest sample sizes. Proofs, an example, and detailed derivations are provided in the supplementary materials, available online.

Key Words:

• Bayesian inference
• Consistency
• Covariance estimation
• Gaussian process
• Tapering