Nothing
gaussian.MVCARar2MCMC <- function(Y, offset, X.standardised, W, rho, alpha, fix.rho.S, fix.rho.T, K, N, NK, J, N.all, p, miss.locator, n.miss, burnin, n.sample, thin, prior.mean.beta, prior.var.beta, prior.nu2, prior.Sigma.df, prior.Sigma.scale, verbose, chain)
{
#Rcpp::sourceCpp("src/CARBayesST.cpp")
#source("R/common.functions.R")
#library(spdep)
#library(truncnorm)
#library(MCMCpack)
#
#
############################################
#### Set up the key elements before sampling
############################################
#### Generate the initial parameter values
beta <- array(NA, c(p, J))
nu2 <- rep(NA, J)
for(i in 1:J)
{
mod.glm <- lm(Y[ ,i]~X.standardised-1, offset=offset[ ,i])
beta.mean <- mod.glm$coefficients
beta.sd <- sqrt(diag(summary(mod.glm)$cov.unscaled)) * summary(mod.glm)$sigma
beta[ ,i] <- rnorm(n=p, mean=beta.mean, sd=beta.sd)
nu2[i] <- runif(1, var(mod.glm$residuals)*0.5, var(mod.glm$residuals))
}
res.temp <- Y - X.standardised %*% beta - offset
res.sd <- sd(res.temp, na.rm=TRUE)/5
phi.vec <- rnorm(n=N.all, mean=0, sd=res.sd)
phi <- matrix(phi.vec, ncol=J, byrow=TRUE)
Sigma <- cov(phi)
Sigma.inv <- solve(Sigma)
Sigma.a <- rep(1, J)
regression <- X.standardised %*% beta
fitted <- regression + phi + offset
Y.DA <- Y
#### Matrices to store samples
n.keep <- floor((n.sample - burnin)/thin)
samples.beta <- array(NA, c(n.keep, J*p))
samples.nu2 <- array(NA, c(n.keep, J))
samples.phi <- array(NA, c(n.keep, N.all))
samples.Sigma <- array(NA, c(n.keep, J, J))
samples.Sigma.a <- array(NA, c(n.keep, J))
if(!fix.rho.S) samples.rho <- array(NA, c(n.keep, 1))
if(!fix.rho.T) samples.alpha <- array(NA, c(n.keep, 2))
samples.loglike <- array(NA, c(n.keep, N.all))
samples.fitted <- array(NA, c(n.keep, N.all))
if(n.miss>0) samples.Y <- array(NA, c(n.keep, n.miss))
#### Metropolis quantities
accept <- rep(0,4)
proposal.sd.phi <- 0.1
proposal.sd.rho <- 0.02
Sigma.post.df <- prior.Sigma.df + J - 1 + K * N
Sigma.a.post.shape <- (prior.Sigma.df + J) / 2
nu2.posterior.shape <- prior.nu2[1] + 0.5 * K * N
#### CAR quantities
W.quants <- common.Wcheckformat.leroux(W)
W <- W.quants$W
W.triplet <- W.quants$W.triplet
n.triplet <- W.quants$n.triplet
W.triplet.sum <- W.quants$W.triplet.sum
n.neighbours <- W.quants$n.neighbours
W.begfin <- W.quants$W.begfin
Wstar <- diag(apply(W,1,sum)) - W
Q <- rho * Wstar + diag(rep(1-rho,K))
#### Create the determinant
if(!fix.rho.S)
{
Wstar.eigen <- eigen(Wstar)
Wstar.val <- Wstar.eigen$values
det.Q <- sum(log((rho * Wstar.val + (1-rho))))
}else
{}
#### Check for islands
W.list<- mat2listw(W, style = "B")
W.nb <- W.list$neighbours
W.islands <- n.comp.nb(W.nb)
islands <- W.islands$comp.id
n.islands <- max(W.islands$nc)
if(rho==1 & alpha[1]==2 & alpha[2]==-1)
{
Sigma.post.df <- prior.Sigma.df + ((N-2) * (K-n.islands)) + J - 1
}else if(rho==1)
{
Sigma.post.df <- prior.Sigma.df + (N * (K-n.islands)) + J - 1
}else if(alpha[1]==2 & alpha[2]==-1)
{
Sigma.post.df <- prior.Sigma.df + ((N-2) * K) + J - 1
}else
{}
#### Beta update quantities
data.precision <- t(X.standardised) %*% X.standardised
if(length(prior.var.beta)==1)
{
prior.precision.beta <- 1 / prior.var.beta
}else
{
prior.precision.beta <- solve(diag(prior.var.beta))
}
#### Start timer
if(verbose)
{
cat("\nMarkov chain", chain, "- generating", n.keep, "post burnin and thinned samples.\n", sep = " ")
progressBar <- txtProgressBar(style = 3)
percentage.points<-round((1:100/100)*n.sample)
}else
{
percentage.points<-round((1:100/100)*n.sample)
}
##############################
#### Generate the MCMC samples
##############################
#### Create the MCMC samples
for(j in 1:n.sample)
{
####################################
## Sample from Y - data augmentation
####################################
if(n.miss>0)
{
Y.DA[miss.locator] <- rnorm(n=n.miss, mean=fitted[miss.locator], sd=sqrt(nu2[miss.locator[ ,2]]))
}else
{}
##################
## Sample from nu2
##################
fitted.current <- regression + phi + offset
nu2.posterior.scale <- prior.nu2[2] + 0.5 * apply((Y.DA - fitted.current)^2, 2, sum)
nu2 <- 1 / rgamma(J, nu2.posterior.shape, scale=(1/nu2.posterior.scale))
###################
## Sample from beta
###################
for(r in 1:J)
{
fc.precision <- prior.precision.beta + data.precision / nu2[r]
fc.var <- solve(fc.precision)
fc.temp1 <- t(((Y.DA[, r] - phi[ , r] - offset[ , r]) %*% X.standardised) / nu2[r]) + prior.precision.beta %*% prior.mean.beta
fc.mean <- fc.var %*% fc.temp1
chol.var <- t(chol(fc.var))
beta[ ,r] <- fc.mean + chol.var %*% rnorm(p)
}
regression <- X.standardised %*% beta
##################
## Sample from phi
##################
#### Create the offset elements
den.offset <- rho * W.triplet.sum + 1 - rho
phi.offset <- Y.DA - regression - offset
#### Create the random draws to create the proposal distribution
Chol.Sigma <- t(chol(proposal.sd.phi*Sigma))
z.mat <- matrix(rnorm(n=N.all, mean=0, sd=1), nrow=J, ncol=NK)
innovations <- t(Chol.Sigma %*% z.mat)
#### Update the elements of phi
temp1 <- gaussianmvar2carupdateRW(W.triplet, W.begfin, W.triplet.sum, K, N, J, phi, alpha[1], alpha[2], rho, Sigma.inv, nu2, innovations, phi.offset, den.offset)
phi <- temp1[[1]]
for(r in 1:J)
{
phi[ ,r] <- phi[ ,r] - mean(phi[ ,r])
}
accept[1] <- accept[1] + temp1[[2]]
accept[2] <- accept[2] + NK
####################
## Sample from Sigma
####################
Sigma.post.scale <- 2 * prior.Sigma.df * diag(1 / Sigma.a) + t(phi[1:K, ]) %*% Q %*% phi[1:K, ] + t(phi[(K+1):(2*K), ]) %*% Q %*% phi[(K+1):(2*K), ]
for(t in 3:N)
{
phit <- phi[((t-1)*K+1):(t*K), ]
phitminus1 <- phi[((t-2)*K+1):((t-1)*K), ]
phitminus2 <- phi[((t-3)*K+1):((t-2)*K), ]
temp1 <- phit - alpha[1] * phitminus1 - alpha[2] * phitminus2
Sigma.post.scale <- Sigma.post.scale + t(temp1) %*% Q %*% temp1
}
Sigma <- riwish(Sigma.post.df, Sigma.post.scale)
Sigma.inv <- solve(Sigma)
######################
## Sample from Sigma.a
######################
Sigma.a.posterior.scale <- prior.Sigma.df * diag(Sigma.inv) + 1 / prior.Sigma.scale^2
Sigma.a <- 1 / rgamma(J, Sigma.a.post.shape, scale=(1/Sigma.a.posterior.scale))
######################
#### Sample from alpha
######################
if(!fix.rho.T)
{
temp <- MVSTrhoTAR2compute(W.triplet, W.triplet.sum, n.triplet, den.offset, K, N, J, phi, rho, Sigma.inv)
alpha.precision <- matrix(c(temp[[1]], temp[[2]], temp[[2]], temp[[3]]), nrow=2, ncol=2)
alpha.var <- solve(alpha.precision)
alpha.mean <- rep(NA, 2)
alpha.mean[2] <- (temp[[1]] * temp[[5]] - temp[[2]] * temp[[4]]) / (temp[[1]] * temp[[3]] - temp[[2]]^2)
alpha.mean[1] <- (temp[[5]] - temp[[3]] * alpha.mean[2]) / temp[[2]]
alpha <- mvrnorm(n=1, mu=alpha.mean, Sigma=alpha.var)
}else
{}
##################
## Sample from rho
##################
if(!fix.rho.S)
{
## Propose a new value
proposal.rho <- rtruncnorm(n=1, a=0, b=1, mean=rho, sd=proposal.sd.rho)
proposal.Q <- proposal.rho * Wstar + diag(rep(1-proposal.rho), K)
proposal.det.Q <- sum(log((proposal.rho * Wstar.val + (1-proposal.rho))))
proposal.den.offset <- proposal.rho * W.triplet.sum + 1 - proposal.rho
## Compute the quadratic forms based on current and proposed values of rho
temp1.QF <- MVSTrhoSAR2compute(W.triplet, W.triplet.sum, n.triplet, den.offset, K, N, J, phi, rho, alpha[1], alpha[2], Sigma.inv)
temp2.QF <- MVSTrhoSAR2compute(W.triplet, W.triplet.sum, n.triplet, proposal.den.offset, K, N, J, phi, proposal.rho, alpha[1], alpha[2], Sigma.inv)
## Compute the acceptance rate
logprob.current <- 0.5 * J * N * det.Q - 0.5 * temp1.QF
logprob.proposal <- 0.5 * J * N * proposal.det.Q - 0.5 * temp2.QF
hastings <- log(dtruncnorm(x=rho, a=0, b=1, mean=proposal.rho, sd=proposal.sd.rho)) - log(dtruncnorm(x=proposal.rho, a=0, b=1, mean=rho, sd=proposal.sd.rho))
prob <- exp(logprob.proposal - logprob.current + hastings)
if(prob > runif(1))
{
rho <- proposal.rho
det.Q <- proposal.det.Q
Q <- proposal.Q
accept[3] <- accept[3] + 1
}else
{}
accept[4] <- accept[4] + 1
}else
{}
#########################
## Calculate the deviance
#########################
fitted <- regression + phi + offset
loglike <- dnorm(x=as.numeric(t(Y)), mean=as.numeric(t(fitted)), sd=rep(sqrt(nu2), K*N), log=TRUE)
###################
## Save the results
###################
if(j > burnin & (j-burnin)%%thin==0)
{
ele <- (j - burnin) / thin
samples.beta[ele, ] <- as.numeric(beta)
samples.nu2[ele, ] <- nu2
samples.phi[ele, ] <- as.numeric(t(phi))
samples.Sigma[ele, , ] <- Sigma
samples.Sigma.a[ele, ] <- Sigma.a
if(!fix.rho.S) samples.rho[ele, ] <- rho
if(!fix.rho.T) samples.alpha[ele, ] <- alpha
samples.loglike[ele, ] <- loglike
samples.fitted[ele, ] <- as.numeric(t(fitted))
if(n.miss>0) samples.Y[ele, ] <- Y.DA[miss.locator]
}else
{}
########################################
## Self tune the acceptance probabilties
########################################
if(ceiling(j/100)==floor(j/100) & j < burnin)
{
#### Update the proposal sds
proposal.sd.phi <- common.accceptrates1(accept[1:2], proposal.sd.phi, 40, 50)
if(!fix.rho.S)
{
proposal.sd.rho <- common.accceptrates2(accept[3:4], proposal.sd.rho, 40, 50, 0.5)
}
accept <- c(0,0,0,0)
}else
{}
################################
## print progress to the console
################################
if(j %in% percentage.points & verbose)
{
setTxtProgressBar(progressBar, j/n.sample)
}
}
############################################
#### Return the results to the main function
############################################
#### Compile the results
if(n.miss==0) samples.Y <- NA
if(fix.rho.S) samples.rho <- NA
if(fix.rho.T) samples.alpha <- NA
chain.results <- list(samples.beta=samples.beta, samples.phi=samples.phi, samples.nu2=samples.nu2, samples.Sigma=samples.Sigma, samples.Sigma.a=samples.Sigma.a, samples.rho=samples.rho, samples.alpha=samples.alpha, samples.loglike=samples.loglike, samples.fitted=samples.fitted,
samples.Y=samples.Y, accept=accept)
#### Return the results
return(chain.results)
}
Any scripts or data that you put into this service are public.
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.