p.eqn8.supp: A postiori probability of hyperparameters
In RobinHankin/calibrator: Bayesian Calibration of Complex Computer Codes

Description Usage Arguments Details Author(s) References See Also Examples

Function to determine the a-postiori probability of hyperparameters rho, lambda and psi2, given observations and psi1.

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)

`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

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

Robin K. S. Hankin

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

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)