Modern Bayesian Sampling Methods for Cosmological Inference: A Comparative Study

Abstract

We present a comprehensive comparison of different Markov Chain Monte Carlo (MCMC) sampling methods, evaluating their performance on both standard test problems and cosmological parameter estimation. Our analysis includes traditional Metropolis-Hastings MCMC, Hamiltonian Monte Carlo (HMC), slice sampling, nested sampling as implemented in dynesty, and PolyChord. We examine samplers through multiple metrics including runtime, memory usage, effective sample size, and parameter accuracy, testing their scaling with dimension and response to different probability distributions. While all samplers perform well with simple Gaussian distributions, we find that HMC and nested sampling show advantages for more complex distributions typical of cosmological problems. Traditional MCMC and slice sampling become less efficient in higher dimensions, while nested methods maintain accuracy but at higher computational cost. In cosmological applications using BAO data, we observe similar patterns, with particular challenges arising from parameter degeneracies and poorly constrained parameters.

16 pages, Final published version,

References in corpus (16)

• emcee: The MCMC Hammer
• Cosmological parameters from CMB and other data: a Monte-Carlo approach
• MultiNest: an efficient and robust Bayesian inference tool for cosmology and particle physics
• dynesty: A Dynamic Nested Sampling Package for Estimating Bayesian Posteriors and Evidences
• Bayes in the sky: Bayesian inference and model selection in cosmology
• PolyChord: nested sampling for cosmology
• PolyChord: next-generation nested sampling
• Fast likelihood-free cosmology with neural density estimators and active learning
• Likelihood-free inference with neural compression of DES SV weak lensing map statistics
• Nested Sampling Methods
• Neural Sampling Machine with Stochastic Synapse allows Brain-like Learning and Inference
• Analytic Methods for Cosmological Likelihoods
• Late-Time constraints on Interacting Dark Energy: Analysis independent of $H_0$, $r_d$ and $M_B$
• Constraining the dark energy models using Baryon Acoustic Oscillations: An approach independent of $H_0\cdot r_d$
• Utilizing Gaussian mixture models in all-sky searches for short-duration gravitational wave bursts
• On the effect of the degeneracy between w_0 and w_a

Cited by in corpus (1)

• The CosmoVerse White Paper: Addressing observational tensions in cosmology with systematics and fundamental physics