Bayesian and Maximum Likelihood Estimation for Gaussian Processes on an Incomplete Lattice
Jonathan R. Stroud, Michael L. Stein and Shaun Lysen
Georgetown University, University of Chicago and Google, Inc.
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
The manuscript is available in PDF format.