# Ez.eqn9.supp

0th

Percentile

##### Expectation as per equation 10 of KOH2001

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

Keywords
array
##### 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.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)

tee

##### Aliases
• Ez.eqn9.supp
• Ez.eqn9.supp.vector
##### Examples
# NOT RUN {
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)

# }

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

### Community examples

Looks like there are no examples yet.