cov.p5.supp {calibrator}R Documentation

Covariance function for posterior distribution of z

Description

Covariance function for posterior distribution of z(.) conditional on estimated hyperparameters and calibration parameters theta.

Usage

Cov.eqn9.supp(x, xdash=NULL, theta, d, D1, D2, H1, H2, phi)
cov.p5.supp  (x, xdash=NULL, theta, d, D1, D2, H1, H2, phi)

Arguments

x first point, or (Cov.eqn9.supp()) a matrix whose rows are the points of interest
xdash The second point, or (Cov.eqn9.supp()) a matrix whose rows are the points of interest. The default of NULL means to use xdash=x.
theta Parameters; supply a vector to Cov.eqn9.supp() and a matrix whose rows are the points in parameter space to cov.p5.supp()
d Observed values
D1 Code run design matrix
D2 Observation points of real process
H1 Basis function for D1
H2 Basis function for D2
phi Hyperparameters

Details

Evaluates the covariance function: the last formula on page 5 of the supplement. The two functions documented here are vectorized differently.

Function Cov.eqn9.supp() takes matrices for arguments x and xdash and a single vector for theta. Evaluation is thus taken at a single, fixed value of theta. The function returns a matrix whose rows correspond to rows of x and whose columns correspond to rows of xdash.

Function cov.p5.supp() takes a vector for arguments x and xdash and a matrix for argument theta whose rows are the points in parameter space. A vector V, with elements corresponding to the rows of argument theta is returned: V[i] = cov(z(x),z(x')|theta[i]).

Value

Returns a matrix of covariances

Note

May return the transpose of the desired object

Author(s)

Robin K. S. Hankin

References

M. C. Kennedy and A. O'Hagan 2001. “Bayesian calibration of computer models”. Journal of the Royal Statistical Society B, 63(3) pp425-464

M. C. Kennedy and A. O'Hagan 2001. “Supplementary details on Bayesian calibration of computer models”, Internal report, University of Sheffield. Available at http://www.shef.ac.uk/~st1ao/ps/calsup.ps

R. K. S. Hankin 2005. “Introducing BACCO, an R bundle for Bayesian analysis of computer code output”, Journal of Statistical Software, 14(16)

Examples

data(toys)
x <- rbind(x.toy,x.toy+1,x.toy,x.toy,x.toy)
rownames(x) <- letters[1:5]
xdash <- rbind(x*2,x.toy)
rownames(xdash) <- LETTERS[1:6]

Cov.eqn9.supp(x=x,xdash=xdash,theta=theta.toy,d=d.toy,D1=D1.toy,D2=D2.toy,H1=H1.toy,H2=H2.toy,phi=phi.toy)

phi.true <- phi.true.toy(phi=phi.toy)
Cov.eqn9.supp(x=x,xdash=xdash,theta=theta.toy,d=d.toy,D1=D1.toy,D2=D2.toy,H1=H1.toy,H2=H2.toy,phi=phi.true)

# Now try a sequence of thetas:
cov.p5.supp(x=x.toy,theta=t.vec.toy,d=d.toy,D1=D1.toy,D2=D2.toy,H1=H1.toy,H2=H2.toy,phi=phi.toy)


[Package calibrator version 1.0-50 Index]