p.eqn8.supp {calibrator} R Documentation

## A postiori probability of hyperparameters

### Description

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

### Usage

p.eqn8.supp(theta, D1, D2, H1, H2, d, include.prior=FALSE,
lognormally.distributed=FALSE, return.log=FALSE, phi)
p.eqn8.supp.vector(theta, D1, D2, H1, H2, d, include.prior=FALSE,
lognormally.distributed=FALSE, return.log=FALSE, phi)


### Arguments

 theta Parameters D1 Matrix of code run points D2 Matrix of observation points H1 Regression function for D1 H2 Regression function for D2 d Vector of code output values and observations include.prior Boolean, with TRUE meaning to include the prior PDF for \theta and default FALSE meaning return the likelihood, multiplied by an undetermined constant lognormally.distributed Boolean, with TRUE meaning to assume prior is lognormal (see prob.theta() for more info) return.log Boolean, with default FALSE meaning to return the probability; TRUE means to return the (natural) logarithm of the answer phi Hyperparameters

### Details

The user should always use p.eqn8.supp(), which is a wrapper for p.eqn8.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 p.eqn8.supp.vector() is applied to the rows

### 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)

W2,stage1

### Examples

data(toys)
p.eqn8.supp(theta=theta.toy, D1=D1.toy, D2=D2.toy, H1=H1.toy, H2=H2.toy,
d=d.toy, phi=phi.toy)

## Now try using the true hyperparameters, and data directly drawn from
## the appropriate multivariate distn:

phi.true <- phi.true.toy(phi=phi.toy)
jj <- create.new.toy.datasets(D1.toy , D2.toy)
d.toy <- jj\$d.toy
p.eqn8.supp(theta=theta.toy, D1=D1.toy, D2=D2.toy, H1=H1.toy,
H2=H2.toy, d=d.toy, phi=phi.true)

## Now try p.eqn8.supp() with a vector of possible thetas:
p.eqn8.supp(theta=sample.theta(n=11,phi=phi.true), D1=D1.toy,
D2=D2.toy, H1=H1.toy, H2=H2.toy,  d=d.toy, phi=phi.true)



[Package calibrator version 1.2-8 Index]