W {calibrator} R Documentation

## 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)

betahat.fun.koh
data(toys)