Efficient sampling of fast and slow cosmological parameters

By A. Lewis. 2013

421 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Demography, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/71e0fe26af396907c32bc4b00eb0c90b1e368b01

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Citations in the corpus

Nonminimal dark sector physics and cosmological tensions (2019, methodology): “[247] A.”
The Atacama Cosmology Telescope: DR4 maps and cosmological parameters (2020, positive): “They include CosmoMC [55, 82], CAMB [57], healpy [83], HEALPix [84], the SLATEC33 Fortran subroutine DRC3JJ.”
Improved cosmological constraints from a joint analysis of the SDSS-II and SNLS supernova samples (2014, methodology): “Eight sample chains were drawn using CosmoMC (Lewis & Bridle 2002; Lewis 2013).”
polychord: nested sampling for cosmology (2015, background): “In cosmological applications, likelihoods exhibit a hierarchy of parameters in terms of calculation speed (Lewis 2013).”
Gravitational-wave cosmology across 29 decades in frequency (2015, methodology): “[55] A.”
Alleviating the H0 and σ8 anomalies with a decaying dark matter model (2019, methodology): “We then use the publicly available Markov chain Monte Carlo code CosmoMC [56, 57] to explore our 7-dimensional parameter space with the following assumptions.”
A fresh look at linear cosmological constraints on a decaying Dark Matter component (2016, methodology): “To this end, we make use of a Choleski decomposition which helps in handling the large number of nuisance parameters [32].”
Planck2018 results (2018, methodology): “Our CosmoMC (Lewis 2013) parameter chains are available on the Planck Legacy Archive,10 where for comparison we also provide alternative results with a different set of cosmological priors consistent with those used by the DES collaboration (DES Collaboration 2018b).”
Early Dark Energy can Resolve the Hubble Tension. (2018, methodology): “Moreover, there are many nuisance parameters that we analyze together with the cosmological ones using a Choleski decomposition [51].”
The Atacama Cosmology Telescope: a measurement of the Cosmic Microwave Background power spectra at 98 and 150 GHz (2020, neutral): “They include CosmoMC [82, 100], CAMB [101], healpy [102], HEALPix [103], the SLATEC29 Fortran subroutine DRC3JJ.”
Constraining early dark energy with large-scale structure (2020, methodology): “[74] A.”
Constraint on neutrino masses from SDSS-III/BOSS Lyα forest and other cosmological probes (2014, methodology): “To speed up the MCMC exploration, when we combine Lyα with CMB data, we use a Cholesky decomposition of the proposal density matrix [58], with oversampling factors set to 1 for cosmological parameters, 2 for CMB nuisance parameters and 4 for Lyα parameters.”
Global constraints on absolute neutrino masses and their ordering (2017, methodology): “The cosmological constraints are obtained using the November 2016 version of the publicly available Monte Carlo Markov chain package COSMOMC [93,94], with a convergence diagnostic based on the Gelman and Rubin statistic that implements an efficient sampling of the posterior distribution using the fa”
Planck2015 results (2015, positive): “Our main results are now based on the lensed CMB power spectra computed with the updated January 2015 version of the camb4 Boltzmann code (Lewis et al. 2000), and parameter constraints are based on the January 2015 version of CosmoMC (Lewis & Bridle 2002; Lewis 2013).”