The R package ‘GPHS’ provides the users with various algorithms for MCMC update of the hyperparameters in covariance function in Gaussian process models. It includes the Elliptical Slice Sampling algorithm as discussed in Nishihara, Murray and Adams (2014) and Metropolis-Hastings algorithm and Slice sampling algorithm for the Surrogate data model as discussed in Murray et al. (2010). In addition to these functions, the package also provides the users with a function to invert a matrix using Eigen decomposition, and a function to calculate the density of a multivariate normal distribution.

You can install the most recent version of ‘GPHS’ package from GitHub using the following commands:

# Plain installation
devtools::install_github("niladrik/GPHS")

# For installation with vignette
devtools::install_github("niladrik/GPHS", build_vignettes = TRUE)

For installation with vignette, $\LaTeX$ should be pre-installed in your machine

Here we would give an illustration of the function ESS.

We begin by defining the log likelihood function

library(GPHS)
set.seed(12345)

## defining the log likelihood function
logl = function(y, mu = rep(0, length(y)), sigma = diag(1, length(y))){
  d = mvtnorm::dmvnorm(y, mu, sigma)
  log.val = log(d)
  return(log.val)
}

Then we fix some random starting points for the parameter of interest: x, and we run the ESS update 100 times.

## number of updates
n = 100
## vector of generated x
x_vec = vector("numeric", n + 1)
## starting point
x_vec[1] = 5
## dimension of current state
p = length(x_vec[1])
## ESS update
for(i in 1:n){
  x_vec[i+1] = ESS(x = x_vec[i], mu = rep(0, p), sigma = diag(1, p), log.L = logl, niter = 100)
}

The trace plot of the samples drawn is: The Metropolis-Hastings and the Slice sampling algorithms for Surrogate data model are implemented in SurrogateMH and SurrogateSS respectively. For the illustration of these functions, please refer to the vignette.
This package also contains two other functions:mySolve and dmvnorm_own. The function mySolve helps to find the inverse, determinant and square-root decomposition of (symmetric) matrices that are nearly positive-definite.

A = diag(1:2)
mySolve(A)
#> $inv
#>      [,1] [,2]
#> [1,]    1  0.0
#> [2,]    0  0.5
#> 
#> $det
#> [1] 2
#> 
#> $sqrtDeco
#>      [,1]     [,2]
#> [1,]    1 0.000000
#> [2,]    0 1.414214

The function dmvnorm_own gives the density of a multivariate Normal distribution. For illustration, suppose we want to find the density of (0,0) when it is drawn from $N(0,0.1\times I)$ distribution

dmvnorm_own(y = c(0, 0))
#> [1] 0.1575713

Murray, I., & Adams, R. P. (2010). Slice sampling covariance hyperparameters of latent Gaussian models. Advances in neural information processing systems, 23. https://doi.org/10.48550/arXiv.1006.0868

Murray, I., Adams, R., & MacKay, D. (2010, March). Elliptical slice sampling. In Proceedings of the thirteenth international conference on artificial intelligence and statistics (pp. 541-548). JMLR Workshop and Conference Proceedings. https://doi.org/10.48550/arxiv.1001.0175

Nishihara, R., Murray, I., & Adams, R. P. (2014). Parallel MCMC with generalized elliptical slice sampling. The Journal of Machine Learning Research, 15(1), 2087-2112. https://doi.org/10.48550/arXiv.1210.7477