# Get marginal likelihood for gaussian distribution with mean and
# covariance matrix being distributed from a Normal inverse Wishart
# distribution with parameters given by S
pred <- function(z, S){
mu0 <- S[["mu"]]
kappa0 <- S[["kappa"]]
nu0 <- S[["nu"]]
lambda0 <- S[["lambda"]]
p <- length(mu0)
S <- lambda0*(kappa0+1)/kappa0/(nu0-p+1)
nu <- nu0-p+1
out <- ((1+t(z-mu0)%*%solve(S)%*%(z-mu0)/nu)^(-(nu+p)/2)
*exp(lgamma((nu+p)/2))/exp(lgamma((nu)/2))
*(det(nu*p*S))^(-0.5)
)
return(out)
}
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