For a Monte Carlo simulation involving photon counting detectors, I am running into the problem of creating random numbers that have a given expectation and a given correlation matrix. Due to the statistics of the detector (double counting), the diagonal elements can be larger than 1 so that the statistics is not exactly Poisson. The off-diagonals of the correlation are positive.
Has anyone come across a similar problem?
I would put in two steps
1) generating Poisson distributed sets(vectors) of random numbers e.g. using some classical way https://wiki.q-researchsoftware.com/wiki/How_to_Generate_Random_Numbers:_Poisson_Distribution
2) Amending generated vectors (let's call them A, B) by adding other vector multiplied by required covariance matrix
A := A + cov(A,B)* ( B - average(B))
B := B + cov(B,A)* ( A - average(A))
Thank you Nicolai!
This indeed seems to work decently if A and B have the same expectation and if I replace cov(A,B) with 0.5*correlation(A,B).
But I would need a more general algorithm that works for arbitrary A and B, even multidimentionsonal random vectors...
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