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. 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.

AuthorFabio Sigrist, Hans R. Kuensch, Werner A. Stahel
Date of publication2016-08-29 19:29:37
MaintainerFabio Sigrist <>

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Man pages

cols: Function that returns the color scale for 'image()'.

ffbs: Forward Filtering Backward Sampling algorithm.

ffbs.spectral: Forward Filtering Backward Sampling algorithm in the spectral...

get.propagator: Propagator matrix G.

get.propagator.vec: Propagator matrix G in vector form.

get.real.dft.mat: Matrix applying the two-dimensional real Fourier transform. Histogram of posterior distributions. Auxilary function for the real Fourier transform.

innov.spec: Spectrum of the innovation term epsilon.

lin.pred: Linear predictor.

loglike: Log-likelihood of the hyperparameters. Maps non-gridded data to a grid.

matern.spec: Spectrum of the Matern covariance function.

mcmc.summary: Summary function for MCMC output.

Palpha: Prior for direction of anisotropy in diffusion parameter...

Pgamma: Prior for amount of anisotropy in diffusion parameter gamma.

Plambda: Prior for transformation parameter of the Tobit model.

plot.spateMCMC: Plot fitted spateMCMC objects.

plot.spateSim: Plotting function for 'spateSim' objects.

Pmux: Prior for y-component of drift.

Pmuy: Prior for y-component of drift.

Prho0: Prior for range parameter rho0 of innovation epsilon.

Prho1: Prior for range parameter rho1 of diffusion.

print.spateMCMC: Print function for spateMCMC objects.

print.spateSim: Print function for 'spateSim' objects.

propagate.spectral: Function that propagates a state (spectral coefficients).

Psigma2: Prior for for variance parameter sigma2 of innovation...

Ptau2: Prior for nugget effect parameter tau2.

Pzeta: Prior for damping parameter zeta.

real.fft: Fast calculation of the two-dimensional real Fourier...

real.fft.TS: Fast calculation of the two-dimensional real Fourier...

sample.four.coef: Sample from the full conditional of the Fourier coefficients.

spate.init: Constructor for 'spateFT' object which are used for the...

spate.mcmc: MCMC algorithm for fitting the model.

spateMCMC: 'spateMCMC' object output obtained from 'spate.mcmc'.

spateMLE: Maximum likelihood estimate for SPDE model with Gaussian...

spate-package: Spatio-temporal modeling of large data with the spectral SPDE...

spate.plot: Plot a spatio-temporal field.

spate.predict: Obtain samples from predictive distribution in space and...

spate.sim: Simulate from the SPDE.

summary.spateSim: Summary function for 'spateSim' objects.

tobit.lambda.log.full.cond: Full conditional for transformation parameter lambda.

trace.plot: Trace plots for MCMC output analysis. Converts a matrix stacked vector. Converts a stacked vector into matrix.

vnorm: Eucledian norm of a vector

wave.numbers: Wave numbers.


cols Man page
ffbs Man page
ffbs.spectral Man page
get.propagator Man page
get.propagator.vec Man page
get.real.dft.mat Man page Man page
innov.spec Man page
lin.pred Man page
loglike Man page Man page
matern.spec Man page
mcmc.summary Man page
Palpha Man page
Pgamma Man page
Plambda Man page
plot.spateMCMC Man page
plot.spateSim Man page
Pmux Man page
Pmuy Man page
post.dist.hist Man page
Prho0 Man page
Prho1 Man page
print.spateMCMC Man page
print.spateSim Man page
propagate.spectral Man page
Psigma2 Man page
Ptau2 Man page
Pzeta Man page
real.fft Man page
real.fft.TS Man page
sample.four.coef Man page
spate Man page
spate.init Man page
spate.mcmc Man page
spateMCMC Man page
spateMLE Man page
spate-package Man page
spate.plot Man page
spate.predict Man page
spate.sim Man page
summary.spateSim Man page
tobit.lambda.log.full.cond Man page
trace.plot Man page Man page Man page
vnorm Man page
wave.numbers Man page


spate/man/Pmuy.Rd spate/man/Pmux.Rd spate/man/Palpha.Rd spate/man/mcmc.summary.Rd spate/man/matern.spec.Rd spate/man/propagate.spectral.Rd spate/man/Prho0.Rd spate/man/innov.spec.Rd spate/man/spateMLE.Rd spate/man/Prho1.Rd spate/man/real.fft.TS.Rd spate/man/Pzeta.Rd spate/man/get.real.dft.mat.Rd spate/man/loglike.Rd spate/man/tobit.lambda.log.full.cond.Rd spate/man/real.fft.Rd spate/man/ spate/man/cols.Rd spate/man/Psigma2.Rd spate/man/Ptau2.Rd spate/man/spate.predict.Rd spate/man/summary.spateSim.Rd spate/man/ spate/man/sample.four.coef.Rd spate/man/plot.spateSim.Rd spate/man/trace.plot.Rd spate/man/lin.pred.Rd spate/man/plot.spateMCMC.Rd spate/man/ spate/man/spate.mcmc.Rd spate/man/spate.sim.Rd spate/man/ spate/man/vnorm.Rd spate/man/spateMCMC.Rd spate/man/ffbs.Rd spate/man/Pgamma.Rd spate/man/spate.init.Rd spate/man/get.propagator.vec.Rd spate/man/spate-package.Rd spate/man/print.spateMCMC.Rd spate/man/wave.numbers.Rd spate/man/Plambda.Rd spate/man/ spate/man/get.propagator.Rd spate/man/spate.plot.Rd spate/man/ffbs.spectral.Rd spate/man/print.spateSim.Rd

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