Efficient sampling of fast and slow cosmological parameters

TL;DR

The paper introduces a decorrelation method for fast and slow parameters in cosmological data analysis, significantly reducing computational costs and improving sampling efficiency, especially with many nuisance parameters.

Contribution

A novel decorrelation technique for fast and slow parameters that enhances sampling efficiency in cosmological parameter estimation.

Findings

Achieved a speed-up factor of five in Planck data analysis.

Demonstrated effectiveness with dozens of nuisance parameters.

Applicable to complex, highly correlated parameter spaces.

Abstract

Physical parameters are often constrained from the data likelihoods using sampling methods. Changing some parameters can be much more computationally expensive (`slow') than changing other parameters (`fast parameters'). I describe a method for decorrelating fast and slow parameters so that parameter sampling in the full space becomes almost as efficient as sampling in the slow subspace when the covariance is well known and the distributions are simple. This gives a large reduction in computational cost when there are many fast parameters. The method can also be combined with a fast 'dragging' method proposed by Neal (2005) that can be more robust and efficient when parameters cannot be fully decorrelated a priori or have more complicated dependencies. I illustrate these methods for the case of cosmological parameter estimation using data likelihoods from the Planck satellite observations with dozens of fast nuisance parameters, and demonstrate a speed up by a factor of five or more. In more complicated cases, especially where the fast subspace is very fast but complex or highly correlated, the fast-slow sampling methods can in principle give arbitrarily large performance gains. The new samplers are implemented in the latest version of the publicly available CosmoMC code.