bceMCMC_mvrnorm: This is an MCMC function with a multivariate normal proposal...

In galotalp/gpMCMC: Generate MCMC or FBI samples from the posterior distribution of Gaussian Process hyper-parameters

Description

#### MCMC 3, multivariate normal distributed steps, each step is one p-dimensional vector from a multivariate normal distribution

Usage

bceMCMC_mvrnorm(nmcmc, burn, thin, x, y, reg, step, priortheta)

Arguments

nmcmc	Number of mcmc samples to generate, before burning and thinning
burn	number of samples to burn
thin	keep only one of every 'thin' samples
x	predictors
y	response
reg	currently only option is "constant"
step	$(step^2)/p$ is multiplied by the identity matrix, which is then used as the covariance for a multivariate normal proposal density in the Metropolis Algorithm
priortheta	only currently only option is "Exp", "Higs" and "none" will also be implemented

Value

returns a list containing mcmc.ma (samples) and accept (acceptance rates)

Examples

nsamp <- 100
burn <- 200
thin <- 10

n <- 10
x1 <- seq(-5,10,length.out = n)
x2 <- seq(0,15,length.out = n)
x <- expand.grid(x1,x2)
x <- as.matrix(x)
d2 <- c(0.01,0.2,0,0) #here we set the theta parameters to be 0.01 and 0.2.
# These are the modes of the distribution that we will sample from using MCMC
cor.par <- data.frame(matrix(data = d2,nrow = dim(x)[2],ncol = 2))
names(cor.par) <- c("Theta.y","Alpha.y")

R <- cor.matrix(x,cor.par) # obtain covariance matrix
L <- chol(R)
z <- as.matrix(rnorm(n^2))
y <- L%*%z

gp <- bceMCMC_mvrnorm(1000,10,10,x,y,reg = "constant",step =1, priortheta = "Exp")
mean(gp$mcmc.ma[,2]) #these means should be similar to the theta parameters set above
mean(gp$mcmc.ma[,1])

galotalp/gpMCMC documentation built on May 16, 2019, 5:36 p.m.