Simulating Multivariate Nonhomogeneous Poisson Processes Using Projections

Established techniques for generating an instance of a multivariate NonHomogeneous Poisson Process (NHPP) such as thinning can become highly inefficient as the dimensionality of the process is increased, particularly if the defining intensity (or rate) function has a pronounced peak. To overcome this inefficiency, we propose an alternative approach where one first generates a projection of the NHPP onto a lower-dimensional space, and then extends the generated points to points in the original space by generating from appropriate conditional distributions. One version of this algorithm replaces a high-dimensional problem with a series of one-dimensional problems. Several examples are presented.