Nothing
location_sig <- function(X,y,priors,BTE = c(3000,100000,1), verb =1, eps = sqrt(.Machine$double.eps)){
nDigits <- function(x){
truncX <- floor(abs(x))
if(truncX != 0){
floor(log10(truncX)) + 1
} else {
1
}
}
## Tests
K <- ncol(y[[1]])
## Sample Locations
N <- nrow(y[[1]])
## Components
M <- length(y)
burn <- BTE[1]
iters <-BTE[2]
thin <- BTE[3]
x.unit <- X
X.unit <- bdiag(replicate(M,x.unit,simplify = FALSE))
X.unit <- as.matrix(X.unit)
X.shuffle <- matrix(1:(N*M), ncol = N, nrow = M, byrow = TRUE)
X.shuffle <- as.vector(X.shuffle)
X.unit <- X.unit[X.shuffle,]
X <- do.call("rbind", replicate(K, X.unit, simplify=FALSE))
no.betas <- ncol(X)/M
y.reorg <- list()
cov.names <- list()
for(i in 1:N){
y.reorg[[i]] <- matrix(NA,ncol = K, nrow = M)
cov.names[[i]] <- matrix(NA, ncol = M, nrow = M)
for(j in 1:M){
y.reorg[[i]][j,] <- y[[j]][i,]
cov.names[[i]][j,] <- paste(paste(names(y)[rep(j, times = M)],i,sep = "")
,paste(names(y)[1:M],i,sep = ""), sep = ":")
}
}
X.N <- list()
Sig <- list()
Sig.rows <- length(diag(M)[upper.tri(diag(M),diag = TRUE)])
for(i in 1:N){
X.N[[i]] <- X.unit[((i-1)*M+1):(i*M),]
Sig[[i]] <- matrix(NA, nrow = Sig.rows, ncol = iters)
Sig[[i]][,1] <- diag(M)[upper.tri(diag(M),diag = TRUE)]
}
ybar <- lapply(y.reorg,rowMeans)
ybar <- do.call(rbind, ybar)
ybar <- as.vector(t(ybar))
Y <- do.call(rbind,y.reorg)
Y <- as.vector(Y)
beta <- matrix(NA, nrow = no.betas*M, ncol = iters)
bhat <- as.vector(solve(t(X) %*% X) %*% t(X) %*% Y)
bhat[which(bhat < 0)] <- 0
if(priors == "Jeffreys"){
mu0 <- rep(0, length(bhat))
dgts <- sapply(bhat,nDigits)
V0i <- diag(length(dgts))*0
nu0 <- 0
S.prior <- replicate(N, matrix(0, nrow = M, ncol = M), simplify = FALSE)
if(verb != 0){message("Jeffreys Priors Used\n")}
}else if(is.list(priors)){
nu0 <- priors$Sig$nu0
mu0 <- priors$beta$mu0
V0i <- solve(priors$beta$V0)
S.prior <- priors$Sig$S
if(verb != 0){message("User Specified Priors Used\n")}
}else{
S.prior <- lapply(y.reorg,function(X){diag((apply(X,1,sd))^2) + diag(nrow(X))*eps})
nu0 <- M
mu0 <- bhat
dgts <- sapply(bhat,nDigits)
V0i <- diag(1/(10^(dgts+6)))
if(verb != 0){message("Default Priors Used\n")}
}
for(i in 1:N){
S.prior[[i]][S.prior[[i]] == eps] <- 1/nu0
}
bhat[which(bhat == 0)] <- eps
beta[,1] <- bhat
V0imu0 <- V0i %*% mu0
beta.temp <- rep(NA, times = no.betas*N)
Wi.temp <- list()
if(verb != 0){
message("Sampling from posterior distributions")
pb <- txtProgressBar(min = 0, max = iters/100, initial = 0, style = 3)
step <- 0
}
for(t in 2:iters){
if(verb != 0 & (t/100) %% 1 == 0){
step <- step + 1
setTxtProgressBar(pb,value = step)
}
b.use <- as.vector(beta[,t-1])
for(i in 1:N){
xB <- as.vector(X.N[[i]] %*% b.use)
psi <- matrix(0, ncol = M, nrow = M)
for(k in 1:K){
psi <- (y.reorg[[i]][,k] - xB) %*% t(y.reorg[[i]][,k] - xB) + psi
}
psi <- psi + S.prior[[i]]*(nu0)
W <- rinvwishart(K + nu0, psi)
Sig[[i]][,t] <- W[upper.tri(W, diag = TRUE)]
Wi.temp[[i]] <- solve(W)
}
Oi <- as.matrix(bdiag(Wi.temp))
XtOiX <- t(X.unit) %*% Oi %*% X.unit * K
precis <- XtOiX + V0i
cov.use <- solve(precis)
bhat <- cov.use %*% (V0imu0 + t(X.unit)%*%Oi %*% ybar * K)
beta[,t] <- as.vector(rtmvnorm(n = 1, mean = bhat[,1], sigma = cov.use, lower = rep(0, length = no.betas*M)))
}
if(verb != 0){close(pb)}
Sig <- lapply(Sig,function(X, b){X[,-(1:b)]}, b = burn)
Sig <- lapply(Sig, function(X,t){X[,seq(from = 1, to = ncol(X), by = t)]}, t = thin)
beta <- beta[,-(1:burn)]
beta <- beta[,seq(from = 1, to = ncol(beta), by = thin)]
beta.return <- list()
for(i in 1:M){
beta.return[[i]] <- beta[((i - 1)*no.betas +1):(i*no.betas),]
}
names(beta.return) <- names(y)
return(list(beta = beta.return,
Sig = Sig,
priors= list(beta = list(mu0 = mu0, V0 = diag(1/diag(V0i))), Sig = list(nu0 = nu0, S = S.prior)), cov.structure = "location", y.cov = cov.names))
}
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