calibrator (version 1.2-8)

EK.eqn10.supp: Posterior mean of K

Description

Estimates the posterior mean of K as per equation 10 of KOH2001S, section 4.2

Usage

EK.eqn10.supp(X.dist, D1, D2, H1, H2, d, hbar.fun,
   lower.theta, upper.theta, extractor, give.info=FALSE,
   include.prior=FALSE, phi, ...)

Arguments

X.dist

Probability distribution of X, in the form of a two-element list. The first element is the mean (which should have name “mean”), and the second element is the variance matrix, which should be a positive definite matrix of the correct size, and have name “var”

D1

Matrix whose rows are the code run points

D2

Matrix whose rows are field observation points

H1

Regression function for D1

H2

Regression function for D2

d

Vector of code outputs and field observations

include.prior

Boolean; passed to function p.eqn8.supp() (qv)

hbar.fun

Function that gives expectation (with respect to X) of h1(x,theta) and h2(x) as per section 4.2

lower.theta

Lower integration limit for theta (NB: a vector)

upper.theta

Lower integration limit for theta (NB: a vector)

extractor

Extractor function; see extractor.toy() for an example

give.info

Boolean, with default FALSE meaning to return just the answer and TRUE to return the answer along with all output from both integrations as performed by adaptIntegrate()

phi

Hyperparameters

...

Extra arguments passed to the integration function. If multidimensional (ie length(theta)>1), then the arguments are passed to adaptIntegrate(); if one dimensional, they are passed to integrate()

Value

Returns a scalar

Details

This function evaluates a numerical approximation to equation 10 of section 4.2 of the supplement.

Equation 10 integrates over the prior distribution of theta. If theta is a vector, multidimensional integration is necessary.

In the case of multidimensional integration, function adaptIntegrate() is used.

In the case of one dimensional integration---theta being a scalar---function integrate() of the stats package is used.

Note that equation 10 is conditional on the observed data and the hyperparameters

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)

Examples

# NOT RUN {
1+1
# }
# NOT RUN {
# Not run because it takes R CMD check too long

data(toys)
EK.eqn10.supp(X.dist=X.dist.toy, D1=D1.toy, D2=D2.toy,
          H1=H1.toy, H2=H2.toy, d=d.toy,
          hbar.fun=hbar.fun.toy, lower.theta=c(-3,-3,-3),
          upper.theta=c(3,3,3),extractor=extractor.toy,
          phi=phi.toy)
# }