Description Usage Arguments Details Author(s) References Examples
Determines the mean of beta, given parameters theta,
hyperparameters phi, and the vector of code outputs and observations
d. It is named so as to avoid conflict with
function betahat.fun
of package emulator.
1 2 | betahat.fun.koh(D1, D2, H1, H2, theta, d, phi)
betahat.fun.koh.vector(D1, D2, H1, H2, theta, d, phi)
|
D1 |
Matrix whose rows are observation points and parameter values at which the code has been run |
D2 |
Matrix whose rows are the observation points |
H1 |
Regression function for D1 |
H2 |
Regression function for D2 |
theta |
Parameters |
d |
Vector of code outputs and observations |
phi |
Hyperparameters |
This function is defined between equations 2 and 3 of the
supplement. It is used in functions Ez.eqn9.supp()
and
p.eqn8.supp()
.
The user should always use betahat.fun.koh()
, which is a
wrapper for betahat.fun.koh.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
betahat.fun.koh.vector()
is applied to the rows.
In betahat.fun.koh()
, the rownames are assigned by a kludgy
call to H.fun()
, which itself uses a kludge to determine
colnames.
The function returns
betahat(theta)=W(theta) H(theta)^T inv(Vd(theta)) d.
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)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 | data(toys)
betahat.fun.koh(theta=theta.toy, d=d.toy, D1=D1.toy, D2=D2.toy,
H1=H1.toy, H2=H2.toy, phi=phi.toy)
betahat.fun.koh.vector(theta=theta.toy, d=d.toy, D1=D1.toy,
D2=D2.toy, H1=H1.toy, H2=H2.toy, phi=phi.toy)
## should be identical
jj.theta <- rbind(theta.toy,theta.toy+1,theta.toy+2,theta.toy*0)
betahat.fun.koh(theta=jj.theta, d=d.toy, D1=D1.toy, D2=D2.toy,
H1=H1.toy, H2=H2.toy, phi=phi.toy)
## Now try with true hyperparameters:
phi.true <- phi.true.toy(phi=phi.toy)
## And magically create the REAL parameters:
theta.REAL <- create.new.toy.datasets(export=TRUE)$REAL.PARAMS
jj.theta <- rbind(jj.theta, theta.REAL)
## Generate some data:
jj <- create.new.toy.datasets(D1.toy , D2.toy)
d.toy <- jj$d.toy
## And finally, observe that the estimated values for beta are pretty
## close to the real values (which omniscient beings can extract using
## reality() and computer.model()):
betahat.fun.koh(theta=jj.theta, d=d.toy, D1=D1.toy, D2=D2.toy,
H1=H1.toy, H2=H2.toy, phi=phi.true)
## [
## that is, compare the last column of the above with
## c(computer.model(ex=T)$REAL.COEFFS, reality(ex=T)$REAL.BETA2)
## ]
|
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