MonteCarlo {MonteCarlo}

Parallized Monte Carlo Simulation

Description

MonteCarlo runs a Monte Carlo simulation study for a correctly specified function and the desired parameter grids. See details for instructions on the specification of the function.

Usage

MonteCarlo(func, nrep, param_list, ncpus = 1, max_grid = 1000,
  time_n_test = FALSE, save_res = FALSE, raw = TRUE,
  export_also = NULL)

Arguments

func

The function to be evaluated. See details.

nrep

An integer that specifies the desired number of Monte Carlo repetitions.

param_list

A list whose components are named after the parameters of func and each component is a vector containing the desired grid values for that parameter

ncpus

An integer specifying the number of cpus to be used. Default is ncpus=1. For ncpus>1 the simulation is parallized automatically using ncpus cpu units.

max_grid

Integer that specifies for which grid size to throw an error, if grid becomes to large. Default is max_grid=1000.

time_n_test

Boolean that specifies whether the required simulation time should be estimated (useful for large simulations or slow functions). See details. Default is time_n_test=FALSE.

save_res

Boolean that specifies whether the results of time_n_test should be saved to the current directory. Default is save_res=FALSE.

raw

Boolean that specifies whether the output should be averaged over the nrep repetitions. Default is raw=TRUE.

export_also

List specifying additional objects that are supposed to be exported to the cluster. This allows to export data or to bypass the automatic export of functions. Default is export_also=NULL. See details.

Details

The user defined function func handles the generation of data, the application of the method of interest and the evaluation of the result for a single repetition and parameter combination. MonteCarlo handles the generation of loops over the desired parameter grids and the repetition of the Monte Carlo experiment for each of the parameter constellations.

There are two important formal requirements that func has to fulfill.

1. The arguments of func have to be scalar.

2. The value returned by func has to be list of (unnamed) scalars (The list elements can be named).

For the estimation of the required simulation time, a separate simulation is run on a reduced grid that only contains the extreme points for each parameter, e.g. the smallest and the largest sample size. This test simulation is carried out with nrep/10 repetitions and the required simulation time is estimated by a linear interpolation. Since the computational complexity is usually a convex function of the sample size and the dimension of the process, this approach tends to overestimate the time required.

export_also allows to export data to the cluster in case parallized computations on a dataset are desired. It also allows to bypass the automatic export of functions and packages. To manually export a function or dataset or to load a package, pass a list to export_also where the list elements are named "functions", "data" and/or "packages". For example: export_also=list("functions"=c("function_name_1", "function_name_2"), "packages"="package_name", "data"="mtcars".

Value

A list of type MonteCarlo.

Examples

test_func<-function(n,loc,scale){
 sample<-rnorm(n, loc, scale)
 stat<-sqrt(n)*mean(sample)/sd(sample)
 decision<-abs(stat)>1.96
 return(list("decision"=decision))
}

# Example without parallization
n_grid<-c(50,100,250,500)
loc_grid<-seq(0,1,0.2)
scale_grid<-c(1,2)

param_list=list("n"=n_grid, "loc"=loc_grid, "scale"=scale_grid)
erg<-MonteCarlo(func=test_func, nrep=250, param_list=param_list, ncpus=1)
summary(erg)

rows<-c("n")
cols<-c("loc","scale")
MakeTable(output=erg, rows=rows, cols=cols, digits=2)

# Note that parallized computation is not always faster, 
# due to the computational costs of the overhead 
# that is needed to manage multiple CPUs.