‘Powellsnakes’, a fast Bayesian approach to discrete object detection in multi-frequency astronomical data sets

Abstract

In this work we introduce a fast Bayesian algorithm designed for detecting compact objects immersed in a diffuse background. A general methodology is presented in terms of formal correctness and optimal use of all the available information in a consistent unified framework, where no distinction is made between point sources (unresolved objects), SZ clusters, single or multi-channel detection. An emphasis is placed on the necessity of a multi-frequency, multi-model detection algorithm in order to achieve optimality. We have chosen to use the Bayes/Laplace probability theory as it grants a fully consistent extension of formal deductive logic to a more general inferential system with optimal inclusion of all ancillary information [Jaynes, 2004]. Nonetheless, probability theory only informs us about the plausibility, a ‘degree-of-belief ’, of a proposition given the data, the model that describes it and all ancillary (prior) information. However, detection or classification is mostly about making educated choices and a wrong decision always carries a cost/loss. Only resorting to ‘Decision Theory’, supported by probability theory, one can take the best decisions in terms of maximum yield at minimal cost. Despite the rigorous and formal approach employed, practical efficiency and applicability have always been kept as primary design goals. We have attempted to select and employ the relevant tools to explore a likelihood form and its manifold symmetries to achieve the very high computational performance required not only by our ‘decision machine’ but mostly to tackle large realistic contemporary cosmological data sets. As an illustration, we successfully applied the methodology to ESA’s (European Space Agency) Planck satellite data [Planck Collaboration et al., 2011d]. This data set is large, complex and typical of the contemporary precision observational cosmology state-of-the-art. Two catalogue products are already released: (i) A point sources catalogue [Planck Collaboration et al., 2011e], (ii) A catalogue of galaxy clusters [Planck Collaboration et al., 2011f]. Many other contributions, in science products, as an estimation device, have recently been issued [Planck et al., 2012; Planck Collaboration et al., 2011g,i, 2012a,b,c]. This new method is called ‘PowellSnakes’ (PwS).