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Description
We propose a probabilistic galaxy group detection algorithm based on marked point processes with interactions. The pattern of galaxy groups in a catalogue is seen as a random set of interacting objects. The positions and the interactions of these objects are governed by a probability density. The parameters of the probability density are chosen using a priori knowledge. The estimator of the unknown cluster pattern is given by the configuration of objects maximising the proposed probability density. Adopting the Bayesian framework, the proposed probability density is maximised using a simulated annealing (SA) algorithm. At fixed temperature, the SA algorithm is a Monte Carlo sampler of the probability density. Hence, the method provides "for free" additional information such as the probabilities that a point or two points in the observation domain belong to the cluster pattern, respectively. These supplementary tools allow the construction of tests and techniques to validate and to refine the detection result. To test the feasibility of the proposed methodology, we applied it to the well-studied 2MASS Redshift Survey (2MRS) data set. Compared to previously published Friends-of-Friends (FoF) group finders, the proposed Bayesian group finder gives overall similar results. However, for specific applications, like the reconstruction of the local Universe, the details of the grouping algorithms are important.
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