I'm fitting a complex cognitive model to data. Because the model does not
have closed-form solution for the likelihood, computationally intensive
simulation is required to generate the model predictions for fitting. My
fitting routine involves two steps: (1) a brute force search of the
plausible parameter space to find a good starting point for (2) finetuning
with Optim. I have been able to parallelize the second step but I am having
trouble with the first.
Here is what I did: I precomputed kernel density functions from 100,000
parameter combinations, resulting in three files: (1) ParmList, a list of
the 100,000 parameter combinations, (2) RangeVar, the range inputs into the
kernel density function, UnivariateKDE(), and (3) DensityVar, the density
inputs also for the kernel density function,UnivariateKDE(). I would like
to use a distributed array to compute the loglikelihood of various sets of
data across the 100,000 paramter combinations. I'm having trouble using
map with a function that loops over the kernel densities. I'm also having
trouble getting the data to the function. The basic code I have is
provided below. Any help would be greatly appreciated.
addprocs(16)
#RangeVar and DensityVar are precomputed inputs for the kernel density
function
#UnivariateKDE
#100,000 by 4 array
RangeVar = readcsv("RangeVar.csv")
#2048 by 100,000 array
DensityVar = readcsv("DesnsityVar.csv")
#List of parameters corresponding to each kernel density function
#100,000 by 4 array
ParmList = readcsv("ParmList.csv")
#Convert to Distributed Array
RangeVarD = distribute(RangeVar)
#Convert to Distributed Array
DensityVarD = distribute(DensityVar)
#Example data
data = [.34 .27 .32 .35 .34 .33]
@everywhere function LogLikelihood(DensityVar,DensityRange,data)
#Loop over the parameter combinations, grabbing the appropriate inputes to
reconstruct the kernel density functions
for i = 1:size(RangeVar,1)
range = FloatRange(RangeVar[i,1],RangeVar[i,2],RangeVar[i,3],RangeVar[i,4])
Dens = DensityVar[:,i]
#Reconstruct the Kernal density function corresponding to the ith parameter
set
f = UnivariateKDE(range,Dens)
#Estimate the likelihood of the data given the parameters using
the kernel density function
L = pdf(f,data)
#Compute the summed log likelihood
KDLL[i] = sum(log(L))
end
return KDLL
end
