p.page4 {calibrator}

A postiori probability of hyperparameters

Description

Function to determine a postiori probability of hyperparameters \rho, \lambda and \psi_2, given observations and \psi_1.

Usage

p.page4(D1, D2, H1, H2, V, y, z, E.theta, Edash.theta, extractor, include.prior=FALSE,
lognormally.distributed=FALSE, return.log=FALSE, phi)

Arguments

D1

Matrix of code run points

D2

Matrix of observation points

H1

Basis function (vectorized)

H2

Regression function for D2

V

Covariance matrix; default value of NULL results in the function evaluating it (but this takes a long time, so supply V if known)

y

Vector of code outputs

z

Vector of observation values

E.theta

Expectation over theta

Edash.theta

Expectation over theta WRT E'

extractor

Function to extract independent variables and parameters from D1

include.prior

Boolean, with TRUE meaning to include the prior PDF for \theta and default value of FALSE meaning to return the likelihood multiplied by an undetermined constant

lognormally.distributed

Boolean with TRUE meaning to assume lognormality. See prob.psi1 for details

return.log

Boolean, with default FALSE meaning to return the probability, and TRUE meaning to return the (natural) logarithm of the probability (which is useful when considering very small probabilities)

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)

p.page4(D1=D1.toy, D2=D2.toy, H1=H1.toy, H2=H2.toy, V=NULL, y=y.toy,
z=z.toy,E.theta=E.theta.toy, Edash.theta=Edash.theta.toy, extractor=extractor.toy, phi=phi.toy)

## Now compare the above value with p.page4() calculated with phi
## differing only in psi2:

phi.toy.new <- phi.change(phi.fun=phi.fun.toy, old.phi = phi.toy, psi2=c(8,8,8))

p.page4(D1=D1.toy, D2=D2.toy, H1=H1.toy, H2=H2.toy, V=V.toy, y=y.toy, z=z.toy,
E.theta=E.theta.toy, Edash.theta=Edash.theta.toy,
extractor=extractor.toy, phi=phi.toy.new)
## different!