W {calibrator}

covariance matrix for beta

Description

Covariance matrix of beta given theta, phi, d

Usage

W(D1, D2, H1, H2, theta, det=FALSE, phi)

Arguments

D1

Matrix whose rows are code run points

D2

Matrix whose rows are observation points

H1

regression function

H2

regression function

theta

parameters

det

Boolean, with default FALSE meaning to return the covariance matrix, and TRUE meaning to return its determinant.

phi

Hyperparameters

Details

This function is defined between equations 2 and 3 of the supplement. It is used in functions betahat.fun.koh(), p.eqn8.supp(), and p.joint().

Returns

{\mathbf W} (\theta)= \left( {\mathbf H}(\theta)^T {\mathbf V}_d(\theta)^{-1} {\mathbf H}(\theta) \right)^{-1}

If only the determinant is required, setting argument det to TRUE is faster than using det(W(..., det=FALSE)), as the former avoids an unnecessary use of solve().

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.tonyohagan.co.uk/academic/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)

See Also

betahat.fun.koh

Examples

data(toys)
W(D1=D1.toy, D2=D2.toy, H1=H1.toy, H2=H2.toy,  theta=theta.toy, phi=phi.toy)