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A fast Bayesian approach to discrete object detection in astronomical data sets – PowellSnakes I

Carvalho, Pedro and Rocha, Graça and Hobson, M. P. (2009) A fast Bayesian approach to discrete object detection in astronomical data sets – PowellSnakes I. Monthly Notices of the Royal Astronomical Society, 393 (3). pp. 681-702. ISSN 0035-8711. http://resolver.caltech.edu/CaltechAUTHORS:20090416-161058812

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Abstract

A new fast Bayesian approach is introduced for the detection of discrete objects immersed in a diffuse background. This new method, called PowellSnakes, speeds up traditional Bayesian techniques by (i) replacing the standard form of the likelihood for the parameters characterizing the discrete objects by an alternative exact form that is much quicker to evaluate; (ii) using a simultaneous multiple minimization code based on Powell's direction set algorithm to locate rapidly the local maxima in the posterior and (iii) deciding whether each located posterior peak corresponds to a real object by performing a Bayesian model selection using an approximate evidence value based on a local Gaussian approximation to the peak. The construction of this Gaussian approximation also provides the covariance matrix of the uncertainties in the derived parameter values for the object in question. This new approach provides a speed up in performance by a factor of '100' as compared to existing Bayesian source extraction methods that use Monte Carlo Markov chain to explore the parameter space, such as that presented by Hobson & McLachlan. The method can be implemented in either real or Fourier space. In the case of objects embedded in a homogeneous random field, working in Fourier space provides a further speed up that takes advantage of the fact that the correlation matrix of the background is circulant. We illustrate the capabilities of the method by applying to some simplified toy models. Furthermore, PowellSnakes has the advantage of consistently defining the threshold for acceptance/rejection based on priors which cannot be said of the frequentist methods. We present here the first implementation of this technique (version I). Further improvements to this implementation are currently under investigation and will be published shortly. The application of the method to realistic simulated Planck observations will be presented in a forthcoming publication.


Item Type:Article
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URLURL TypeDescription
http://dx.doi.org/10.1111/j.1365-2966.2008.14016.xDOIUNSPECIFIED
http://www3.interscience.wiley.com/journal/121674409/abstractPublisherUNSPECIFIED
Additional Information:© 2009 Royal Astronomical Society. Accepted 2008 September 26; received 2008 August 2; in original form 2008 February 25; published Online: 31 Jan 2009. PC thanks the Cavendish Astrophysics Group of the University of Cambridge for support and hospitality during the progression of this work. GR acknowledges support from the US Planck Project, which is funded by the NASA Science Mission Directorate. GR would like to acknowledge useful discussions with Krzystof Górsky and Charles Lawrence.
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U. S. Planck ProjectUNSPECIFIED
Subject Keywords:methods: data analysis; cosmic microwave background; cosmology: observations
Issue or Number:3
Record Number:CaltechAUTHORS:20090416-161058812
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20090416-161058812
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:14005
Collection:CaltechAUTHORS
Deposited By: Jason Perez
Deposited On:22 Apr 2009 16:54
Last Modified:08 Jul 2019 21:01

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