Bayesian and Maximum Likelihood Estimation for Gaussian Processes on an Incomplete Lattice
Event Description:
This research 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.