I am modeling using a Gillespie algorithm, which stochastically simulates a biological process. Since I want to complicate the structure of my model, I do not know whether the resulting distribution of counts of one of the species follows a poissonian distribution. I have experimental data for the distribution of counts and now I want to use some kind of optimization method to get at the rates of my reactions happening (inside the Gillespie model). Normally, you would use the log likelihood to optimize the parameters of a model, but now I do not know the underlying pdf.

I thought that the resulting count distribution from my model actually resembles the pdf and I could use that to optimize the parameters. However, I do not know how to calculate the log likelihood when comparing two (count) distributions.