A Bayesian approach to discrete object detection in astronomical data sets

Abstract

A Bayesian approach is presented for detecting and characterising the signal from discrete objects embedded in a diffuse background. The approach centres around the evaluation of the posterior distribution for the parameters of the discrete objects, given the observed data, and defines the theoretically-optimal procedure for parametrised object detection. Two alternative strategies are investigated: the simultaneous detection of all the discrete objects in the dataset, and the iterative detection of objects. In both cases, the parameter space characterising the object(s) is explored using Markov-Chain Monte-Carlo sampling. For the iterative detection of objects, another approach is to locate the global maximum of the posterior at each iteration using a simulated annealing downhill simplex algorithm. The techniques are applied to a two-dimensional toy problem consisting of Gaussian objects embedded in uncorrelated pixel noise. A cosmological illustration of the iterative approach is also presented, in which the thermal and kinetic Sunyaev-Zel'dovich effects from clusters of galaxies are detected in microwave maps dominated by emission from primordial cosmic microwave background anisotropies.