# sample.four.coef: Sample from the full conditional of the Fourier coefficients. In spate: Spatio-Temporal Modeling of Large Data Using a Spectral SPDE Approach

## Description

Sample from the full conditional of the Fourier coefficients.

## Usage

 1 2 sample.four.coef(w=NULL,wFT=NULL,spec=NULL,Gvec=NULL,tau2=NULL,par=NULL,n,T, NF=n*n,indCos=(1:((n*n-4)/2)*2+3),ns=4,nu=1,dt=1) 

## Arguments

 w Observed data or latent process w (depending on which data model is used) in an T x n*n matrix with columns and rows (points on a grid stacked into a vector) corresponding to time and space, respectively. wFT Vector of length T*n*n containing the real Fourier transform of 'w'. spec Spectrum of the innovations \hat{ε} in a vector of length n*n. If 'spec' is not given, it is constructed based on 'par'. Gvec The propagator matrix G in vector format obtained from 'get.G.vec'. If 'Gvec' is not given, it is constructed based on 'par'. tau2 Measurement error variance tau2. If 'NULL'; tau2=par[9]. par Vector of parameters for the SPDE in the following order: rho_0, sigma^2, zeta, rho_1, gamma, alpha, mu_x, mu_y, tau^2. If 'spec' and 'Gvec' are given, 'par' will not be used. n Number of grid points on each axis. n*n is the total number of spatial points. T Number of points in time. NF Number of Fourier functions used. indCos Vector of integers indicating the position cosine terms in the 1:NF real Fourier functions. The first 'ns' cosine wavenumbers in 'wave' are not included in 'indCos'. ns Number of real Fourier functions that have only a cosine and no sine term. 'ns' is maximal 4. nu Smoothness parameter of the Matern covariance function for the innovations. By default this equals 1 corresponding to the Whittle covariance function. dt Temporal lag between two time points. By default, this equals 1.

## Value

A T x n*n matrix with a sample from the full conditional of latent process α.

Fabio Sigrist

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 ##Specifications for simulated example n <- 50 T <- 4 par <- c(rho0=0.1,sigma2=0.2,zeta=0.5,rho1=0.1,gamma=2,alpha=pi/4,muX=0.2,muY=-0.2,tau2=0.01) spateSim <- spate.sim(par=par,n=n,T=T,seed=4) w <- spateSim\$w ##Sample from full conditional Nmc <- 50 alphaS <- array(0,c(T,n*n,Nmc)) wFT <- real.fft.TS(w,n=n,T=T) for(i in 1:Nmc){ alphaS[,,i] <- sample.four.coef(wFT=wFT,par=par,n=n,T=T,NF=n*n) } ##Mean from full conditional alphaMean <- apply(alphaS,c(1,2),mean) xiMean <- real.fft.TS(alphaMean,n=n,T=T,inv=FALSE) par(mfrow=c(2,4),mar=c(1,1,1,1)) for(t in 1:4) image(1:n,1:n,matrix(w[t,],nrow=n),xlab="",ylab="",col=cols(), main=paste("w(",t,")",sep=""),xaxt='n',yaxt='n') for(t in 1:4) image(1:n,1:n,matrix(xiMean[t,],nrow=n),xlab="",ylab="",col=cols(), main=paste("xiPost(",t,")",sep=""),xaxt='n',yaxt='n') 

spate documentation built on May 29, 2017, 11:37 a.m.