ABC Shadow algorithm: a tool for statistical analysis of spatial patterns

TL;DR

The paper introduces ABC Shadow, an innovative algorithm for sampling posterior densities in spatial pattern analysis, effectively handling models like Strauss, Candy, and area-interaction point processes.

Contribution

It presents a new ABC algorithm that ensures practical sampling of posterior densities for spatial point process models, improving upon existing methods.

Findings

Successfully applied to Gaussian model posterior

Effectively analyzed Strauss, Candy, and area-interaction patterns

Fulfills key conditions for ABC algorithm practicality

Abstract

This paper presents an original ABC algorithm, "ABC Shadow", that can be applied to sample posterior densities that are continuously differentiable. The proposed method uses the ideas given by the auxiliary variable MH of (M\o ller and Waagepetersen, 2004). The obtained algorithm solves the main condition to be fulfilled by any ABC algorithm, in order to be useful in practice. This condition requires enough samples in the parameter space region, induced by the observed statistics (Blum, 2010). The algorithm is tuned on the posterior of a Gaussian model which is entirely known, and then it is applied for the statistical analysis of several spatial patterns. These patterns are issued or assumed to be outcomes of point processes. The considered models are: Strauss, Candy and area-interaction.