Nothing
gaussian.CARlinearMCMC <- function(Y, offset, X.standardised, W, rho, lambda, fix.rho.int, fix.rho.slo, K, N, N.all, p, which.miss, n.miss, burnin, n.sample, thin, prior.mean.beta, prior.var.beta, prior.mean.alpha, prior.var.alpha, prior.tau2, prior.nu2, verbose, chain)
{
#Rcpp::sourceCpp("src/CARBayesST.cpp")
#source("R/common.functions.R")
#library(spdep)
#library(truncnorm)
#
#
############################################
#### Set up the key elements before sampling
############################################
#### Generate the initial parameter values
time <-(1:N - mean(1:N))/N
time.all <- kronecker(time, rep(1,K))
mod.glm <- glm(Y~X.standardised-1 + time.all, offset=offset)
beta.mean <- mod.glm$coefficients
beta.sd <- sqrt(diag(summary(mod.glm)$cov.scaled))
temp <- rnorm(n=length(beta.mean), mean=beta.mean, sd=beta.sd)
beta <- temp[1:p]
alpha <- temp[(p+1)]
res.temp <- Y - as.numeric(X.standardised %*% beta) - time.all * alpha - offset
res.sd <- sd(res.temp, na.rm=TRUE)/5
phi <- rnorm(n=K, mean=0, sd = res.sd)
delta <- rnorm(n=K, mean=0, sd = res.sd)
tau2.phi <- var(phi)/10
tau2.delta <- var(delta)/10
nu2 <- runif(1, 0, res.sd)
#### Specify matrix quantities
Y.DA <- Y
offset.mat <- matrix(offset, nrow=K, ncol=N, byrow=FALSE)
regression.mat <- matrix(X.standardised %*% beta, nrow=K, ncol=N, byrow=FALSE)
phi.mat <- matrix(rep(phi, N), byrow=F, nrow=K)
time.mat <- matrix(rep(time, K), byrow=TRUE, nrow=K)
delta.time.mat <- apply(time.mat, 2, "*", delta)
alpha.offset1 <- sum(time.mat^2)
fitted <- as.numeric(offset.mat + regression.mat + phi.mat + delta.time.mat + alpha * time.mat)
#### Matrices to store samples
n.keep <- floor((n.sample - burnin)/thin)
samples.beta <- array(NA, c(n.keep, p))
samples.alpha <- array(NA, c(n.keep, 1))
samples.phi <- array(NA, c(n.keep, K))
samples.delta <- array(NA, c(n.keep, K))
if(!fix.rho.int) samples.rho <- array(NA, c(n.keep, 1))
if(!fix.rho.slo) samples.lambda <- array(NA, c(n.keep, 1))
samples.nu2 <- array(NA, c(n.keep, 1))
samples.tau2 <- array(NA, c(n.keep, 2))
colnames(samples.tau2) <- c("tau2.int", "tau2.slo")
samples.fitted <- array(NA, c(n.keep, N.all))
samples.loglike <- array(NA, c(n.keep, N.all))
if(n.miss>0) samples.Y <- array(NA, c(n.keep, n.miss))
#### Specify the Metropolis quantities
accept <- rep(0,4)
proposal.sd.rho <- 0.02
proposal.sd.lambda <- 0.02
nu2.shape <- prior.nu2[1] + N*K/2
tau2.phi.shape <- prior.tau2[1] + K/2
tau2.delta.shape <- prior.tau2[1] + K/2
#### CAR quantities
W.quants <- common.Wcheckformat.leroux(W)
W <- W.quants$W
W.triplet <- W.quants$W.triplet
W.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
#### Create the determinant
if(!fix.rho.int | !fix.rho.slo)
{
Wstar <- diag(apply(W,1,sum)) - W
Wstar.eigen <- eigen(Wstar)
Wstar.val <- Wstar.eigen$values
}else
{}
if(!fix.rho.int) det.Q.rho <- 0.5 * sum(log((rho * Wstar.val + (1-rho))))
if(!fix.rho.slo) det.Q.lambda <- 0.5 * sum(log((lambda * Wstar.val + (1-lambda))))
#### Check for islands
W.list<- mat2listw(W, style = "B")
W.nb <- W.list$neighbours
W.islands <- n.comp.nb(W.nb)
islands <- W.islands$comp.id
n.islands <- max(W.islands$nc)
if(rho==1) tau2.phi.shape <- prior.tau2[1] + 0.5 * (K-n.islands)
if(lambda==1) tau2.delta.shape <- prior.tau2[1] + 0.5 * (K-n.islands)
#### Beta update quantities
data.precision.beta <- 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[which.miss==0] <- rnorm(n=n.miss, mean=fitted[which.miss==0], sd=sqrt(nu2))
}else
{}
Y.DA.mat <- matrix(Y.DA, nrow=K, ncol=N, byrow=FALSE)
##################
## Sample from nu2
##################
nu2.offset <- as.numeric(Y.DA.mat - offset.mat - regression.mat - phi.mat - delta.time.mat - alpha * time.mat)
nu2.scale <- prior.nu2[2] + sum(nu2.offset^2)/2
nu2 <- 1 / rgamma(1, nu2.shape, scale=(1/nu2.scale))
####################
## Sample from beta
####################
fc.precision <- prior.precision.beta + data.precision.beta / nu2
fc.var <- solve(fc.precision)
beta.offset <- as.numeric(Y.DA.mat - offset.mat - phi.mat - delta.time.mat - alpha * time.mat)
beta.offset2 <- t(X.standardised) %*% beta.offset / nu2 + prior.precision.beta %*% prior.mean.beta
fc.mean <- fc.var %*% beta.offset2
chol.var <- t(chol(fc.var))
beta <- fc.mean + chol.var %*% rnorm(p)
regression.mat <- matrix(X.standardised %*% beta, nrow=K, ncol=N, byrow=FALSE)
####################
## Sample from alpha
####################
fc.var <- 1 / (1 / prior.var.alpha + alpha.offset1 / nu2)
alpha.offset <- (Y.DA.mat - offset.mat - regression.mat - phi.mat - delta.time.mat) * time.mat
alpha.offset2 <- sum(alpha.offset, na.rm=TRUE) / nu2
fc.mean <- fc.var * (alpha.offset2 + prior.mean.alpha / prior.var.alpha)
alpha <- rnorm(n=1, mean=fc.mean, sd=sqrt(fc.var))
####################
## Sample from phi
####################
phi.offset <- Y.DA.mat - offset.mat - regression.mat - delta.time.mat - alpha * time.mat
phi.offset2 <- apply(phi.offset,1, sum, na.rm=TRUE)
temp1 <- gaussiancarupdate(W.triplet, W.begfin, W.triplet.sum, K, phi, tau2.phi, nu2, phi.offset2, rho, N)
phi <- temp1
if(rho<1)
{
phi <- phi - mean(phi)
}else
{
phi[which(islands==1)] <- phi[which(islands==1)] - mean(phi[which(islands==1)])
}
phi.mat <- matrix(rep(phi, N), byrow=F, nrow=K)
####################
## Sample from delta
####################
delta.offset <- (Y.DA.mat - offset.mat - regression.mat - phi.mat - alpha * time.mat) * time.mat
delta.offset2 <- apply(delta.offset,1, sum, na.rm=TRUE)
temp2 <- gaussiancarupdate(W.triplet, W.begfin, W.triplet.sum, K, delta, tau2.delta, nu2, delta.offset2, lambda, sum(time^2))
delta <- temp2
if(lambda <1)
{
delta <- delta - mean(delta)
}else
{
delta[which(islands==1)] <- delta[which(islands==1)] - mean(delta[which(islands==1)])
}
delta.time.mat <- apply(time.mat, 2, "*", delta)
#######################
## Sample from tau2.phi
#######################
temp2.phi <- quadform(W.triplet, W.triplet.sum, W.n.triplet, K, phi, phi, rho)
tau2.phi.scale <- temp2.phi + prior.tau2[2]
tau2.phi <- 1 / rgamma(1, tau2.phi.shape, scale=(1/tau2.phi.scale))
#########################
## Sample from tau2.delta
#########################
temp2.delta <- quadform(W.triplet, W.triplet.sum, W.n.triplet, K, delta, delta, lambda)
tau2.delta.scale <- temp2.delta + prior.tau2[2]
tau2.delta <- 1 / rgamma(1, tau2.delta.shape, scale=(1/tau2.delta.scale))
##################
## Sample from rho
##################
if(!fix.rho.int)
{
proposal.rho <- rtruncnorm(n=1, a=0, b=1, mean=rho, sd=proposal.sd.rho)
temp3 <- quadform(W.triplet, W.triplet.sum, W.n.triplet, K, phi, phi, proposal.rho)
det.Q.proposal <- 0.5 * sum(log((proposal.rho * Wstar.val + (1-proposal.rho))))
logprob.current <- det.Q.rho - temp2.phi / tau2.phi
logprob.proposal <- det.Q.proposal - temp3 / tau2.phi
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)
#### Accept or reject the proposal
if(prob > runif(1))
{
rho <- proposal.rho
det.Q.rho <- det.Q.proposal
accept[1] <- accept[1] + 1
}else
{}
accept[2] <- accept[2] + 1
}else
{}
#####################
## Sample from lambda
#####################
if(!fix.rho.slo)
{
proposal.lambda <- rtruncnorm(n=1, a=0, b=1, mean=lambda, sd=proposal.sd.lambda)
temp3 <- quadform(W.triplet, W.triplet.sum, W.n.triplet, K, delta, delta, proposal.lambda)
det.Q.proposal <- 0.5 * sum(log((proposal.lambda * Wstar.val + (1-proposal.lambda))))
logprob.current <- det.Q.lambda - temp2.delta / tau2.delta
logprob.proposal <- det.Q.proposal - temp3 / tau2.delta
hastings <- log(dtruncnorm(x=lambda, a=0, b=1, mean=proposal.lambda, sd=proposal.sd.lambda)) - log(dtruncnorm(x=proposal.lambda, a=0, b=1, mean=lambda, sd=proposal.sd.lambda))
prob <- exp(logprob.proposal - logprob.current + hastings)
#### Accept or reject the proposal
if(prob > runif(1))
{
lambda <- proposal.lambda
det.Q.lambda <- det.Q.proposal
accept[3] <- accept[3] + 1
}else
{}
accept[4] <- accept[4] + 1
}else
{}
#########################
## Calculate the deviance
#########################
fitted <- as.numeric(offset.mat + regression.mat + phi.mat + delta.time.mat + alpha * time.mat)
loglike <- dnorm(Y, mean = fitted, sd = rep(sqrt(nu2),N.all), log=TRUE)
###################
## Save the results
###################
if(j > burnin & (j-burnin)%%thin==0)
{
ele <- (j - burnin) / thin
samples.beta[ele, ] <- beta
samples.phi[ele, ] <- phi
samples.delta[ele, ] <- delta
samples.alpha[ele, ] <- alpha
if(!fix.rho.int) samples.rho[ele, ] <- rho
if(!fix.rho.slo) samples.lambda[ele, ] <- lambda
samples.nu2[ele, ] <- nu2
samples.tau2[ele, ] <- c(tau2.phi, tau2.delta)
samples.fitted[ele, ] <- fitted
samples.loglike[ele, ] <- loglike
if(n.miss>0) samples.Y[ele, ] <- Y.DA[which.miss==0]
}else
{}
########################################
## Self tune the acceptance probabilties
########################################
if(ceiling(j/100)==floor(j/100) & j < burnin)
{
if(!fix.rho.int) proposal.sd.rho <- common.accceptrates2(accept[1:2], proposal.sd.rho, 40, 50, 0.5)
if(!fix.rho.slo) proposal.sd.lambda <- common.accceptrates2(accept[3:4], proposal.sd.lambda, 40, 50, 0.5)
accept <- rep(0,4)
}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.int) samples.rho <- NA
if(fix.rho.slo) samples.lambda <- NA
chain.results <- list(samples.beta=samples.beta, samples.alpha=samples.alpha, samples.phi=samples.phi, samples.delta=samples.delta, samples.tau2=samples.tau2, samples.nu2=samples.nu2, samples.rho=samples.rho, samples.lambda=samples.lambda, samples.loglike=samples.loglike, samples.fitted=samples.fitted,
samples.Y=samples.Y, accept=accept)
#### Return the results
return(chain.results)
}
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