# W

##### covariance matrix for beta

Covariance matrix of beta given theta, phi, d

- Keywords
- array

##### 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()`

.

##### 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

##### Examples

```
# NOT RUN {
data(toys)
W(D1=D1.toy, D2=D2.toy, H1=H1.toy, H2=H2.toy, theta=theta.toy, phi=phi.toy)
# }
```

*Documentation reproduced from package calibrator, version 1.2-8, License: GPL-2*