[astro-ph/0405462] Fast and reliable MCMC for cosmological parameter estimation

Authors:  Joanna Dunkley, Martin Bucher, Pedro G. Ferreira, Kavilan Moodley, Constantinos Skordis
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 CMB and LSS 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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Antony Lewis
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[astro-ph/0405462] Fast and reliable MCMC for cosmological p

Post by Antony Lewis » September 24 2004

The result for scaling the proposal density with dimension given in the paper appears to be generally useful and correct. Two comments:

1. There are some potential problems using the autocorrelation function to assess chain efficiency: it is quite possible for the autocorrelation to be small but the separation between effectively independence samples to be large. Jo has confirmed that similar problems can happen with the spectral estimator.

2. Results are restricted to using N-D Gaussians as the proposal density. In high-N (N>2) this is probably rather un-robust, and it may be better to use a lower dimensional proposal.

I've written up these comments in detail in the cosmomc notes

http://cosmologist.info/notes/cosmomc.ps.gz

Similar comments apply to [arxiv]astro-ph/0310723[/arxiv]

Michael Doran
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[astro-ph/0405462] Fast and reliable MCMC for cosmological p

Post by Michael Doran » November 22 2004

The scaling is indeed useful (and easy to implement). Funny enough, the adaptive
stepsize I used in AnlalyzeThis! provided roughly the same acceptance rate.
But as the adaptive stepping in AnalyzeThis! stops after "sensing" the distribution (i.e. some extended burn-in), the formula is still useful for the step-proposal after "burn-in".

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