BACCO (version 1.0-50)

Ez.eqn9.supp: Expectation as per equation 10 of KOH2001

Description

Expectation as per equation 10 of KOH2001 (not the supplement)

Usage

Ez.eqn9.supp(x, theta, d, D1, D2, H1, H2,  phi)
Ez.eqn9.supp.vector(x, theta, d, D1, D2, H1, H2, phi)

Arguments

x

point at which expectation is needed

theta

parameters

d

observations and code outputs

D1

code run points

D2

observation points

H1

regression function for D1

H2

regression function for D2

phi

hyperparameters

Details

The user should always use Ez.eqn9.supp(), which is a wrapper for Ez.eqn9.supp.vector(). The forms differ in their treatment of $\theta$. In the former, $\theta$ must be a vector; in the latter, $\theta$ may be a matrix, in which case Ez.eqn9.supp.vector() is applied to the rows.

Note that Ez.eqn9.supp.vector() is vectorized in x but not $\theta$ (if given a multi-row object, apply(theta,1,...) is used to evaluate the function for each row supplied).

Function Ez.eqn9.supp() will take multiple-row arguments for x and theta. The output will be a matrix, with rows corresponding to the rows of x and columns corresponding to the rows of theta. See the third example below. Note that function Ez.eqn9.supp() determines whether there are multiple values of $\theta$ by is.vector(theta). If this returns TRUE, it is assumed that $\theta$ is a single point in multidimensional parameter space; if FALSE, it is assumed to be a matrix whose rows correspond to points in parameter space.

So if $\theta$ is one dimensional, calling Ez.eqn9.supp() with a vector-valued $\theta$ will fail because the function will assume that $\theta$ is a single, multidimensional, point. To get round this, use as.matrix(theta), which is not a vector; the rows are the (1D) parameter values.

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)

See Also

tee

Examples

data(toys)
Ez.eqn9.supp(x=x.toy,  theta=theta.toy,  d=d.toy, D1=D1.toy,  D2=D2.toy, H1=H1.toy,H2=H2.toy, phi=phi.toy)
Ez.eqn9.supp(x=D2.toy, theta=t.vec.toy,  d=d.toy, D1=D1.toy, D2=D2.toy, H1=H1.toy,H2=H2.toy, phi=phi.toy)
Ez.eqn9.supp(x=x.vec,  theta=t.vec.toy,  d=d.toy, D1=D1.toy, D2=D2.toy, H1=H1.toy,H2=H2.toy, phi=phi.toy)