beta2hat.fun {calibrator}

estimator for beta2

Description

estimates beta2 as per the equation of page 4 of the supplement. Used by p.page4()

Usage

beta2hat.fun(D1, D2, H1, H2, V, z, etahat.d2, extractor, E.theta,
Edash.theta, phi)

Arguments

D1

Matrix of code run points

D2

Matrix of observation points

H1

regression basis functions

H2

regression basis functions

V

overall covariance matrix

z

vector of observations

etahat.d2

expectation as per etahat.vector

extractor

extractor function

E.theta

Expectation

Edash.theta

Expectation wrt thetadash

phi

hyperparameters

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)

See Also

W2

Examples

data(toys)

etahat.d2 <- etahat(D1=D1.toy, D2=D2.toy, H1=H1.toy, y=y.toy,
E.theta=E.theta.toy, extractor=extractor.toy, phi=phi.toy)

beta2hat.fun(D1=D1.toy, D2=D2.toy, H1=H1.toy, H2=H2.toy, V=NULL,
z=z.toy, etahat.d2=etahat.d2, extractor=extractor.toy,
E.theta=E.theta.toy, Edash.theta=Edash.theta.toy, phi=phi.toy)

jj <- create.new.toy.datasets(D1.toy , D2.toy)
phi.true <- phi.true.toy(phi=phi.toy)
y.toy <- jj$y.toy
z.toy <- jj$z.toy
d.toy <- jj$d.toy

etahat.d2 <- etahat(D1=D1.toy, D2=D2.toy, H1=H1.toy, y=y.toy,
E.theta=E.theta.toy, extractor=extractor.toy, phi=phi.toy)

beta2hat <- beta2hat.fun(D1=D1.toy, D2=D2.toy, H1=H1.toy, H2=H2.toy, V=NULL,
z=z.toy, etahat.d2=etahat.d2, extractor=extractor.toy,
E.theta=E.theta.toy, Edash.theta=Edash.theta.toy,
phi=phi.toy)

print(beta2hat)

plot(z.toy , H2.toy(D2.toy) %*% beta2hat)