Modern Bayesian Sampling Methods for Cosmological Inference: A Comparative Study

Understand

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.