GPfit (version 1.0-0)

GP_deviance: Computes the Deviance of a GP model

Description

Evaluates the deviance (negative 2*log-likelihood), as defined in Ranjan et al. (2011), however the correlation is reparametrized and can be either power exponential or Matern as discussed in corr_matrix.

Usage

GP_deviance(beta, X, Y, nug_thres = 20,
	corr = list(type="exponential",power=1.95))

Arguments

beta

a (d x 1) vector of correlation hyper-parameters, as described in corr_matrix

X

the (n x d) design matrix

Y

the (n x 1) vector of simulator outputs

nug_thres

a parameter used in computing the nugget. See GP_fit.

corr

a list of parameters for the specifing the correlation to be used. See corr_matrix.

Value

the deviance (negative 2*log-likelihood)

References

Ranjan, P., Haynes, R., and Karsten, R. (2011). A Computationally Stable Approach to Gaussian Process Interpolation of Deterministic Computer Simulation Data, Technometrics, 53(4), 366 - 378.

See Also

corr_matrix for computing the correlation matrix; GP_fit for estimating the parameters of the GP model.

Examples

# NOT RUN {
## 1D Example 1
n = 5; d = 1;
computer_simulator <- function(x){
x = 2*x+0.5;
y = sin(10*pi*x)/(2*x) + (x-1)^4;
return(y)
}
set.seed(3);
library(lhs);
x = maximinLHS(n,d);
y = computer_simulator(x);
beta =  rnorm(1);
GP_deviance(beta,x,y);


## 1D Example 2
n = 7; d = 1;
computer_simulator <- function(x) {
y <- log(x+0.1)+sin(5*pi*x);
return(y)
}
set.seed(1);
library(lhs);
x = maximinLHS(n,d);
y = computer_simulator(x);
beta = rnorm(1);
GP_deviance(beta,x,y,corr=list(type="matern",nu=5/2))


## 2D Example: GoldPrice Function
computer_simulator <- function(x) {
x1=4*x[,1] - 2; x2=4*x[,2] - 2;
t1 = 1 + (x1 + x2 + 1)^2*(19 - 14*x1 + 3*x1^2 - 14*x2 + 
6*x1*x2 + 3*x2^2);
t2 = 30 + (2*x1 -3*x2)^2*(18 - 32*x1 + 12*x1^2 + 48*x2 - 
36*x1*x2 + 27*x2^2);
y = t1*t2;
return(y)
}
n = 10; d = 2;
set.seed(1);
library(lhs);
x = maximinLHS(n,d); 
y = computer_simulator(x);
beta = rnorm(2);
GP_deviance(beta,x,y);
# }