spectralGP {spectralGP} | R Documentation |
SpectralGP is a collection of functions for creating Gaussian processes in one and two dimensions using the Fourier basis approximation. It provides fast simulation and plotting of process realizations by use of the FFT, allowing simulation and plotting on very dense grids. For inference, it provides tools for use in setting up an MCMC: calculation of coefficient variances, calculation of process density, and coefficient proposals. It uses R environments to store GP objects as references/pointers.
Some major methods include:
gp
Create a Gaussian process object
simulate.gp
Simulate a Gaussian process realization
plot.gp
Plot a Gaussian process
predict.gp
Extract process values at specified domain points
Note that if implementing the Gibbs sampling algorithm of Wikle (2002),
when you use the FFT to calculate t(Psi)z (using Wikle's notation),
you should use the following approach in R:
fft(matrix(z,fun$gridsize[1],fun$gridsize[2]),inv=FALSE)/sqrt(prod(fun$gridsize))
,
where z is a vector of (noisy) process values corresponding to the
process element of the GP (process
).
At some point there may be more information available at http://www.biostat.harvard.edu/~paciorek/code/spectralGP
DISCLAIMER:
This is software for statistical research; I do not guarantee the correctness of any function or program in this package. authors permission.
Many thanks to Chris Wikle who first suggested I use the Fourier basis approximation for Gaussian processes.
For more details, see Paciorek & Ryan (2005). Accounting for space in nonparametric logistic regression: A Bayesian spectral basis model outperforms other methods. In submission. http://www.biostat.harvard.edu/~paciorek/papers.html
See also, Royle, J.A., and C.K. Wikle, (2004). Efficient Statistical Mapping of Avian Count Data. Ecological and Environmental Statistics , to appear. http://www.stat.missouri.edu/~wikle/pub_new.html
Wikle, C.K., (2002). Spatial modeling of count data: A case study in modelling breeding bird survey data on large spatial domains. In Spatial Cluster Modelling, A. Lawson and D. Denison, eds. Chapman and Hall, 199-209. http://www.stat.missouri.edu/~wikle/pub_new.html
gp1=gp(128,matern.specdens,c(1,4)) gp2=gp(c(64,64),matern.specdens,c(1,4)) simulate(gp1) simulate(gp2) plot(gp1) plot(gp2) gridvals=predict(gp1) newlocs=runif(100) offgridvals=predict(gp1,newlocs)