Approximated inference for marked Gibbs point process

Abstract: Parameter estimation for point processes is achieved via solving optimisation problems built using general strategies. Three well established strategies are enumerated. The first consists of considering contrast fuctions based on summary statistics. The second one uses the pseudo-likelihood. And the third approximates the likelihood function via Monte Carlo procedures. Each of these techniques has known advantages and drawbacks (Moler and Waagepetersen 2004, van Lieshout 2001, 2019).

Sampling point process posterior densities is an inference approach deeply intertwinned wih the previous one, since it allows simultaneous parameter estimation and statistical tests based on observations. The auxiliary variable method (Moller et al.,2006) gives the mathematical solution to this problem, while pointing out the difficulties of its practical implementation due to poor mixing. The exchange algorithm proposed by (Murray et al. 2006), (Caimo and Friel, 2011) proposes a solution for the poor mixing induced by the auxiliary variable method. As its predecessor it requires exact simulation for the sampling of the auxiliary variable. This is not really a drawback, but it may explode the computational time for models exhibiting strong interactions (van Lieshout and Stoica, 2006).

This talk presents the approximate ABC Shadow and SSA methods as complementary inference methods to the ones based on posterior density sampling. These methods do not require exact simulation, while providing the necessary theoretical control. The derived algorithms are applied on data from several application domains such as astronomy, geosciences and network sciences (Stoica et al.,17), (Stoica et al.,21), (Hurtado et al.,21), (Laporte et al.,22).

machine learningprobabilitystatistics theory

Audience: researchers in the discipline

Gothenburg statistics seminar

Series comments: Gothenburg statistics seminar is open to the interested public, everybody is welcome. It usually takes place in MVL14 (http://maps.chalmers.se/#05137ad7-4d34-45e2-9d14-7f970517e2b60, see specific talk). Speakers are asked to prepare material for 35 minutes excluding questions from the audience.