Bayesian and Maximum Likelihood Estimation for Gaussian Processes on an Incomplete Lattice

TL;DR

This paper introduces a novel Bayesian and maximum likelihood estimation method for stationary Gaussian processes on large incomplete lattices, utilizing data augmentation and circulant embedding for exact inference.

Contribution

It presents a new MCMC and Monte Carlo EM approach that improves inference accuracy and efficiency for Gaussian processes with missing data on large lattices.

Findings

Accurate parameter estimation on 512x512 lattices

Outperforms composite likelihood and spectral methods

Effective for satellite sea surface temperature data

Abstract

This paper proposes a new approach for Bayesian and maximum likelihood parameter estimation for stationary Gaussian processes observed on a large lattice with missing values. We propose an MCMC approach for Bayesian inference, and a Monte Carlo EM algorithm for maximum likelihood inference. Our approach uses data augmentation and circulant embedding of the covariance matrix, and provides exact inference for the parameters and the missing data. Using simulated data and an application to satellite sea surface temperatures in the Pacific Ocean, we show that our method provides accurate inference on lattices of sizes up to 512 x 512, and outperforms two popular methods: composite likelihood and spectral approximations.