fit.gpr {bdpopt}R Documentation

Fit A Gaussian Process Regression Function

Description

Fit a GPR regression function to the estimated expected utility values obtained through simulation via JAGS by calling eval.on.grid. This is a generic function for S3 objects.

Usage

fit.gpr(model, start, gr = TRUE, method = "L-BFGS-B",
lower = 0, upper = Inf, control = list())

Arguments

model

A model object obtained as the return value from eval.on.grid.

start

Start value passed on to optim when performing the marginal likelihood optimisation to find appropriate values for the hyperparameters for the GPR regression function.

gr

Set to TRUE if gradient information should be passed to optim. If false, optim uses a finite difference approximation of the gradient when performing the optimisation of the hyperparameters.

method

The optimisation method to be used by optim. One of "Nelder-Mead", "BFGS", "CG", "L-BFGS-B", "SANN" or "Brent".

lower

A numeric, atomic vector containing the lower limits for the hyperparameters. The first entry is for the standard deviation parameter and the remaining entries are for the length parameters. If supplied, all elements must be >= 0.

upper

A numeric, atomic vector containing the upper limits for the hyperparameters. The first entry is for the standard deviation parameter and the remaining entries are for the length parameters.

control

A list of control parameters passed on to optim.

Details

The fitting operation consists of maximising the marginal likelihood of the hyperparameters for a GPR model based on a squared-exponential covariance model. This is done by minimising a function proportional to the negative marginal likelihood. The number of hyperparameters for this model equals 1 + the number of decision variables of the decision model. The first hyperparameter is a standard deviation and the rest consists of a length parameter for each decision dimension.

The optimisation strategy depends on the value of method. If "L-BFGS-B" is used, then the arguments lower and upper are passed on as specified to optim as the lower and upper limits for the optimisation of the hyperparameters. If any other value is provided for method, then optim will be used to minimise a function defined to be equal to the objective function when the hyperparameter argument x satisfies x >= lower, x <= upper and equal to Inf otherwise. The actual lower and upper limits passed to optim in this latter case are -Inf and Inf, respectively.

Value

A new simulation model object constructed from the object given as the first argument and the GPR regression results. The updated components in the new object are model$regression.fun and model$gpr.hyper.params. See sim.model for a description of these components.

Author(s)

Sebastian Jobjörnsson jobjorns@chalmers.se

See Also

fit.loess


[Package bdpopt version 1.0-1 Index]