log_posterior: log.posterior for gaussian process for x,y, and f, at the...

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

Description

log.posterior for gaussian process for x,y, and f, at the given correlation hyperparameters specified in cor.par

Usage

log_posterior(x, y, f, cor.par, prior)

Arguments

x	covariate matrix/vector x
y	response vector y
f	regression model, must be a matrix. If constant, should be a vector (as.matrix) of 1s of length n, where n is the number of data points in x
cor.par	matrix of theta and alpha parameters for power-exponential model, includes two columns, the first for theta parameters and the second for alpha parameters. For Guassian correlation structure, alpha parameters can be initialized as 0.
prior	prior for log-posterior, options are "Exp" for exponential prior and "Hig" for Higdon's prior

Value

returns the log-posterior

Examples

n <- 5
x1 <- seq(-5,10,length.out = n)
x2 <- seq(0,15,length.out = n)

data1 <- expand.grid(x1,x2)
x <- data1
# create hyperparameter matrix of thetas and alphas, alphas set to 0 indicated guassian correlation
d2 <- c(0.01,0.2,0,0)
cor.par <- data.frame(matrix(data = d2,nrow = dim(x)[2],ncol = 2))
names(cor.par) <- c("Theta.y","Alpha.y")


R <- cor.matrix(data1,cor.par) # obtain covariance matrix
L <- chol(R)
z <- as.vector(rnorm(n^2))
y <- t(L)%*%z

logpost <- log_posterior(data1,y,as.matrix(rep(1,n^2)),cor.par,prior = "Exp")

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