spate - Spatio-Temporal Modeling of Large Data Using a Spectral SPDE
Approach
Functionality for spatio-temporal modeling of large data
sets is provided. A Gaussian process in space and time is
defined through a stochastic partial differential equation
(SPDE). The SPDE is solved in the spectral space, and after
discretizing in time and space, a linear Gaussian state space
model is obtained. When doing inference, the main computational
difficulty consists in evaluating the likelihood and in
sampling from the full conditional of the spectral
coefficients, or equivalently, the latent space-time process.
In comparison to the traditional approach of using a
spatio-temporal covariance function, the spectral SPDE approach
is computationally advantageous. See Sigrist, Kuensch, and
Stahel (2015) <doi:10.1111/rssb.12061> for more information on
the methodology. This package aims at providing tools for two
different modeling approaches. First, the SPDE based
spatio-temporal model can be used as a component in a
customized hierarchical Bayesian model (HBM). The functions of
the package then provide parameterizations of the process part
of the model as well as computationally efficient algorithms
needed for doing inference with the HBM. Alternatively, the
adaptive MCMC algorithm implemented in the package can be used
as an algorithm for doing inference without any additional
modeling. The MCMC algorithm supports data that follow a
Gaussian or a censored distribution with point mass at zero.
Covariates can be included in the model through a regression
term.
