  Large spatiotemporal datasets are a challenge for conventional Bayesian
models because of the cubic computational complexity of the algorithms for
obtaining the Cholesky decomposition of the covariance matrix in the
multivariate normal density. Moreover, standard numerical algorithms for
posterior estimation, such as Markov Chain Monte Carlo (MCMC), are intractable
in this context, as they require thousands, if not millions, of costly
likelihood evaluations. To overcome those limitations, we propose IS-MRA
(Importance sampling - Multi-Resolution Approximation), which takes advantage
of the sparse inverse covariance structure produced by the Multi-Resolution
Approximation (MRA) approach. IS-MRA is fully Bayesian and facilitates the
approximation of the hyperparameter marginal posterior distributions. We apply
IS-MRA to large MODIS Level 3 Land Surface Temperature (LST) datasets, sampled
between May 18 and May 31, 2012 in the western part of the state of
Maharashtra, India. We find that IS-MRA can produce realistic prediction
surfaces over regions where concentrated missingness, caused by sizable cloud
cover, is observed. Through a validation analysis and simulation study, we also
find that predictions tend to be very accurate.
