Fast and reliable Markov chain Monte Carlo technique for cosmological parameter estimation |
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| Authors: | Joanna Dunkley Martin Bucher Pedro G Ferreira Kavilan Moodley Constantinos Skordis |
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| Institution: | Astrophysics, University of Oxford, Denys Wilkinson Building, 1 Keble Road, Oxford OX1 3RH;Laboratoire de Physique théorique, UniversitéParis-Sud, 91405 Orsay, France;DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA;African Institute for Mathematical Sciences (AIMS), 6–8 Melrose Road, Muizenberg 7945, South Africa;Astrophysics &Cosmology Research Unit and School of Mathematical Sciences, University of KwaZulu-Natal, Durban, 4041, South Africa |
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| Abstract: | Markov chain Monte Carlo (MCMC) techniques are now widely used for cosmological parameter estimation. Chains are generated to sample the posterior probability distribution obtained following the Bayesian approach. An important issue is how to optimize the efficiency of such sampling and how to diagnose whether a finite-length chain has adequately sampled the underlying posterior probability distribution. We show how the power spectrum of a single such finite chain may be used as a convergence diagnostic by means of a fitting function, and discuss strategies for optimizing the distribution for the proposed steps. The methods developed are applied to current cosmic microwave background and large-scale structure data interpreted using both a pure adiabatic cosmological model and a mixed adiabatic/isocurvature cosmological model including possible correlations between modes. For the latter application, because of the increased dimensionality and the presence of degeneracies, the need for tuning MCMC methods for maximum efficiency becomes particularly acute. |
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| Keywords: | methods: data analysis methods: statistical cosmic microwave background |
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