spate: Spatio-Temporal Modeling of Large Data Using a Spectral SPDE Approach

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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.

Author
Fabio Sigrist, Hans R. Kuensch, Werner A. Stahel
Date of publication
2016-08-29 19:29:37
Maintainer
Fabio Sigrist <sigrist@stat.math.ethz.ch>
License
GPL-2
Version
1.5

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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.
hist.post.dist
Histogram of posterior distributions.
index.complex.to.real.dft
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.
map.obs.to.grid
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.
TSmat.to.vect
Converts a matrix stacked vector.
vect.to.TSmat
Converts a stacked vector into matrix.
vnorm
Eucledian norm of a vector
wave.numbers
Wave numbers.

Files in this package

spate
spate/inst
spate/inst/CITATION
spate/inst/doc
spate/inst/doc/spate_tutorial.Rnw
spate/inst/doc/spate_tutorial.pdf
spate/inst/doc/spate_tutorial.R
spate/configure.ac
spate/src
spate/src/Makevars.in
spate/src/ffbs.spectral.c
spate/src/Makevars.win
spate/NAMESPACE
spate/data
spate/data/spateMLE.RData
spate/data/spateMCMC.RData
spate/R
spate/R/spateFcts.R
spate/vignettes
spate/vignettes/spate_tutorial-FourierBasis2.pdf
spate/vignettes/spate_tutorial.Rnw
spate/vignettes/spate_tutorial-Propagator.pdf
spate/MD5
spate/build
spate/build/vignette.rds
spate/DESCRIPTION
spate/configure
spate/man
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/TSmat.to.vect.Rd
spate/man/cols.Rd
spate/man/Psigma2.Rd
spate/man/Ptau2.Rd
spate/man/spate.predict.Rd
spate/man/summary.spateSim.Rd
spate/man/hist.post.dist.Rd
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/map.obs.to.grid.Rd
spate/man/spate.mcmc.Rd
spate/man/spate.sim.Rd
spate/man/vect.to.TSmat.Rd
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/index.complex.to.real.dft.Rd
spate/man/get.propagator.Rd
spate/man/spate.plot.Rd
spate/man/ffbs.spectral.Rd
spate/man/print.spateSim.Rd
spate/configure.win
spate/cleanup
spate/tools
spate/tools/aclocal.m4