## code to accompany the MVN (bivariate) example from
## lecture 11 of PSTAT 215A, Bayesian Inference, UCSB
##
## Robert B. Gramacy

## load necessary libraries
library(mvtnorm)

mu <- c(50,50)
S2 <- rbind(c(64, 0), c(0,144))
S1 <- S2 + rbind(c(0, -48), c(-48, 0))
S3 <- S2 + rbind(c(0, 48), c(48, 0))

## make the posterior image plot
library(akima)
N <- 200
y.grid <- seq(28, 72, length=N)
g <- expand.grid(y.grid, y.grid)
names(g) <- c("y1", "y2")

## negatively correlated
p1 <- matrix(dmvnorm(g, mu, S1), nrow=N)
image(y.grid, y.grid, p1)

## un-correlated
p2 <- matrix(dmvnorm(g, mu, S2), nrow=N)
image(y.grid, y.grid, p2)

## positively correlated
p3 <- matrix(dmvnorm(g, mu, S3), nrow=N)
image(y.grid, y.grid, p3)