p.eqn8.supp {calibrator} | R Documentation |
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.shef.ac.uk/~st1ao/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)
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)