Question

Can you please explain what the "thinning" process of the nonhomogenous Poisson Process is.

If given realizations of a random variable from (0,1), how can you use them for the "thinning" process?

Answer 1

Here I would like to explain thinning process,

If the thinning operation is statistically independent, then the resulting point process formed from the retained points is also a poisson point process, regardless if it is spatially independent or dependent thinning. The resulting intensity of this new poisson point process has a simple expression.

simulating this thinning operation is rather straightforward. given a realization of a point process, for each point a uniform random variable on the interval simply generate or simulate, and if this random variable is less than , remove the point.