init_grid {blackbox}

Define starting points in parameter space.

Description

This function samples the space of estimated parameters. It also handles other fixed arguments that need to be passed to the function simulating the summary statistics (sample size is likely to be one such argument). The current sampling strategy is crude but achieves three desirable effects: it samples the points uniformly but not independently from each other, avoiding large gaps more than independent ampling would allow; it is not exactly a regular grid; and it can include replicates of some parameter points, required for good inference of a response surface when this inference includes a smoothing step of response values evaluated with some error (as is typical in applications of the Migraine software, for which this function was first conceived).

Usage

init_grid(lower=c(par=0), upper=c(par=1), steps=NULL, nUnique=NULL, 
          nRepl=min(10L,nUnique), maxmin=TRUE, jitterFac=0.5)

Arguments

lower

A vector of lower bounds for the parameters, as well as fixed arguments to be passed to the function simulating the summary statistics. Elements must be named.

upper

A vector of upper bounds for the parameters, as well as fixed parameters. Elements must be named and match those of lower.

steps

Number of steps of the grid, in each dimension of estimated parameters. If NULL, a default value is defined from the other arguments. If a single value is given, it is applied to all dimensions. Otherwise, this must have the same length as lower and upper and named in the same way as the variable parameters in these arguments.

nUnique

Number of distinct values of parameter vectors in output. Default is an heuristic guess for good start from not too many points, computed as floor(50^((v/3)^(1/3))) where v is the number of variable parameters.

nRepl

Number of replicates of distinct values of parameter vectors in output.

maxmin

Boolean. If TRUE, use a greedy max-min strategy (GMM, inspired from Ravi et al. 1994) in the selection of points from a larger set of points generated by an hypercube-sampling step. If FALSE, sample is instead used for this second step. This may be useful as the default method becomes slow when thousands of points are to be sampled. GMM was always used in the second step prior to introduction of this argument.

jitterFac

Controls the amount of jitter of the points around regular grid nodes. The default value 0.5 means that a mode can move by up to half a grid step (independently in each dimension), so that two adjacent nodes moved toward each other can (almost) meet each other.

Value

A data frame. Each row defines a list of arguments of vector of the function simulating the summary statistics.

References

Ravi S.S., Rosenkrantz D.J., Tayi G.K. 1994. Heuristic and special case algorithms for dispersion problems. Operations Research 42, 299-310.

Examples

set.seed(123)
init_grid()
init_grid(lower=c(mu=2.8,s2=0.5,sample.size=20),
          upper=c(mu=5.2,s2=4.5,sample.size=20),
          steps=c(mu=7,s2=9),nUnique=63)