Variational Bayes approach for classification of points in superpositions of point processes

We investigate the problem of classifying superpositions of spatial point processes. In particular, we are interested in realizations formed as a superposition of a regular point process and a Poisson point process. The aim is to decide which of the two processes each point belongs to. Recently, a Markov chain Monte Carlo (MCMC) approach was suggested by Redenbach et al. (2015), which however, is computationally heavy. In this paper, we will introduce a method based on variational Bayes approximation and compare its performance to the performance of a slightly refined version of the MCMC approach.