object {approximator}

Optimization of posterior likelihood of hyperparameters

Description

Returns the likelihood of a set of hyperparameters given the data. Functions opt1() and opt.gt.1() find hyperparameters that maximize the relevant likelihood for level 1 and higher levels respectively. Function object() returns the expression given by equation 9 in KOH2000, which is minimized opt1() and opt.gt.1().

Usage

object(level, D, z, basis, subsets, hpa)
opt.1(D, z, basis, subsets, hpa.start, give.answers=FALSE, ...)
opt.gt.1(level, D, z, basis, subsets, hpa.start, give.answers=FALSE, ...)

Arguments

level

level

D

Design matrix for top-level code

z

Data

basis

Basis function

subsets

subsets object

hpa

hyperparameter object

hpa.start

Starting value for hyperparameter object

give.answers

Boolean, with default FALSE meaning to return just the point estimate, and TRUE meaning to return extra information from the call to optim()

...

Extra arguments passed to optim(). A common one would be control=list(trace=100)

Details

This function is the object function used in toy optimizers optimal.hpa().

Author(s)

Robin K. S. Hankin

References

M. C. Kennedy and A. O'Hagan 2000. “Predicting the output from a complex computer code when fast approximations are available” Biometrika, 87(1): pp1-13

See Also

genie

Examples

data(toyapps)
object(level=4, D=D1.toy , z=z.toy,basis=basis.toy,
   subsets=subsets.toy, hpa=hpa.fun.toy(1:19))
object(level=4, D=D1.toy , z=z.toy,basis=basis.toy,
   subsets=subsets.toy, hpa=hpa.fun.toy(3+(1:19)))


# Now a little example of finding optimal hyperpameters in the toy case
# (a bigger example is given on the genie help page)
jj <- list(trace=100,maxit=10)

hpa.toy.level1 <- opt.1(D=D1.toy, z=z.toy, basis=basis.toy,
          subsets=subsets.toy, hpa.start=hpa.toy,control=jj)

hpa.toy.level2 <- opt.gt.1(level=2, D=D1.toy, z=z.toy,
           basis=basis.toy, subsets=subsets.toy,
           hpa.start=hpa.toy.level1, control=jj)

hpa.toy.level3 <- opt.gt.1(level=3, D=D1.toy, z=z.toy,
           basis=basis.toy, subsets=subsets.toy,
           hpa.start=hpa.toy.level2, control=jj) 

hpa.toy.level4 <- opt.gt.1(level=4, D=D1.toy, z=z.toy,
           basis=basis.toy, subsets=subsets.toy,
           hpa.start=hpa.toy.level3, control=jj)