stage1 {calibrator} | R Documentation |
Perform O'Hagan's three stage optimization on the toy dataset. Function
stage1()
and stage2()
find the optimal values for
the hyperparameters and stage3()
finds the optimal values for
the three parameters.
stage1(D1, y, H1, maxit, trace=100, method="Nelder-Mead", directory = ".", do.filewrite=FALSE, do.print=TRUE, phi.fun, lognormally.distributed=FALSE, include.prior=TRUE, phi) stage2(D1, D2, H1, H2, y, z, maxit, trace=100, method = "Nelder-Mead", directory = ".", do.filewrite=FALSE, do.print=TRUE, extractor, phi.fun, E.theta, Edash.theta, isotropic=FALSE, lognormally.distributed = FALSE, include.prior = TRUE, use.standin = FALSE, rho.eq.1 = TRUE, phi) stage3(D1, D2, H1, H2, d, maxit, trace=100, method="Nelder-Mead", directory = ".", do.filewrite=FALSE, do.print=TRUE, include.prior = TRUE, lognormally.distributed=FALSE, theta.start=NULL, phi)
maxit |
Maximum number of iterations as passed to optim() |
trace |
Amount of information displayed, as passed to optim() |
D1 |
Matrix whose rows are points at which code output is known |
D2 |
Matrix whose rows are points at which observations were made |
H1,H2 |
Regressor basis functions for D1 and D2 |
y |
Code outputs. Toy example is y.toy |
z |
Observations. Toy example is z.toy |
d |
Data vector consisting of the code runs and observations |
extractor |
extractor function for D1 |
E.theta,Edash.theta |
Expectation WRT theta, and dashed theta.
Toy examples are E.theta.toy() and Edash.theta.toy() |
phi.fun |
Function to create hyperparameters; passed (in
stage1() and stage2() ) to phi.change() . Toy
version is phi.fun.toy() |
method |
Method argument passed to optim() ; qv |
include.prior |
Boolean variable with default TRUE meaning
to include the prior distribution in the optimization process and
FALSE meaning to use an uniformative prior (effectively
uniform support). This variable is passed to p.eqn4.supp()
for stage1() , p.page4() for stage2() , and
p.eqn8.supp() for stage3() |
lognormally.distributed |
Boolean with TRUE meaning to use
a lognormal distn. See prob.theta for details |
do.filewrite |
Boolean, with TRUE meaning to
save a load able file stage[123].<date> , containing the interim value of phi
and the corresponding optimand to directory at each evalution
of the optimizer. If FALSE , don't write the files |
directory |
The directory to write files to; only matters if
do.filewrite is TRUE |
isotropic |
In function stage2() , Boolean with default
FALSE meaning to carry out a full optimization, and
TRUE meaning to restrict the scope to isotroic roughness
matrices. See details section below |
do.print |
Boolean, with default TRUE meaning to print
interim values of phi at each evaluation |
use.standin |
In stage2() , a Boolean argument, with
default FALSE meaning to use the real value for matrix
V.temp , and TRUE meaning to use a standing that is the
same size but contains fictitious values. The only time to set
use.standin to TRUE is when debugging as it runs
several orders of magnitude faster |
rho.eq.1 |
Boolean, with default TRUE meaning to hold the
value of rho constant at one (1) |
theta.start |
In stage3() , the starting point of the
optimization with default NULL meaning to use the maximum
likelihood point of the apriori distribution (ie phi$theta.apriori$mean ) |
phi |
Hyperparameters. Used as initial values for the hyperparameters in the optimization routines |
The three functions documented here carry out the multi-stage
optimization detailed in KOH2001 (actually, KOH2001 only defined stage
1 and stage 2, which estimated the hyperparameters. What is here
called “stage3()
” estimates the true value of
theta given the hyperparameters).
stage1()
carries out stage 1 of KOH2001 which is used to
estimate psi1 using optimization.
In function stage2()
, setting argument isotropic
to
TRUE
will force phi$omegastar_x
to be a function of a
length one scalar. The value of phi$omegastar_x
used will
depend on pdm.maker.psi2()
(an internal function appearing in
hpa.fun.toy()
). In stage2()
, several kludges are made.
The initial conditions are provided by argument phi
. The
relevant part of this is phi$psi2
.
Function stage2()
estimates psi2 and
rho and lambda, using
optimization. Note that psi2 includes
sigma2squared in addition to omegastar_X
(in
the toy case, psi2 has three elements: the first two are
the diagonal of omegastar_x
and the third is
sigma2squared but this information is
encoded in phi.fun.toy()
, which changes from application to
application).
Function stage3()
attempts to find the maximum likelihood
estimate of theta, given hyperparameters and
observations, using optimization
Robin K. S. Hankin
data(toys) stage1(D1=D1.toy,y=y.toy,H1=H1.toy, maxit=5, phi.fun=phi.fun.toy, phi=phi.toy) ##now try with a slightly bigger dataset: ##Examples below take a few minutes to run: set.seed(0) data(toys) jj <- create.new.toy.datasets(D1.toy , D2.toy) y.toy <- jj$y.toy z.toy <- jj$z.toy d.toy <- jj$d.toy phi.toy.stage1 <- stage1(D1=D1.toy, y=y.toy, H1=H1.toy, maxit=10, phi.fun=phi.fun.toy, phi=phi.toy) phi.toy.stage2 <- stage2(D1=D1.toy, D2=D2.toy, H1=H1.toy, H2=H2.toy, y=y.toy, z=z.toy, extractor=extractor.toy, phi.fun=phi.fun.toy, E.theta=E.theta.toy, Edash.theta=Edash.theta.toy, maxit=3, phi=phi.toy.stage1) stage3(D1=D1.toy, D2=D2.toy, H1=H1.toy, H2=H2.toy, d=d.toy, maxit=3, phi=phi.toy.stage2) # Now try with the true values of the hyperparameters: phi.true <- phi.true.toy(phi=phi.toy) stage3(D1=D1.toy, D2=D2.toy, H1=H1.toy, H2=H2.toy, d=d.toy, maxit=3, phi=phi.true)