Efficient Cosmological Parameter Estimation with Hamiltonian Monte Carlo

Abstract

Traditional Markov Chain Monte Carlo methods suffer from low acceptance rate, slow mixing and low efficiency in high dimensions. Hamiltonian Monte Carlo resolves this issue by avoiding the random walk. Hamiltonian Monte Carlo (HMC) is a Markov chain Monte Carlo (MCMC) technique built upon the basic principle of Hamiltonian mechanics. Hamiltonian dynamics allows the chain to move along trajectories of constant energy, taking large jumps in the parameter space with relatively inexpensive computations. This new technique improves the acceptance rate by a factor of 4 and boosts up the efficiency by at least a factor of D in a D-dimensional parameter space. Therefor shorter chains will be needed for a reliable parameter estimation comparing to a traditional MCMC chain yielding the same performance. Besides that, the HMC is well suited for sampling from non-Gaussian and curved distributions which are very hard to sample from using the traditional MCMC methods. The method is very simple to code and can be easily plugged into standard parameter estimation codes such as CosmoMC. In this paper we demonstrate how the HMC can be efficiently used in cosmological parameter estimation.

References in corpus (12)

• Cosmological parameters from SDSS and WMAP
• Cosmological parameters from CMB and other data: a Monte-Carlo approach
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Parameter Estimation Methodology
• Improving the Efficiency of Markov Chain Monte Carlo for Analyzing the Orbits of Extrasolar Planets
• Fast and reliable MCMC for cosmological parameter estimation
• II: Bayesian Methods for Cosmological Parameter Estimation from Cosmic Microwave Background Measurements
• LISA Data Analysis using MCMC methods
• Fast cosmological parameter estimation using neural networks
• Analyze This! A Cosmological Constraint Package for CMBEASY
• MCMC Exploration of Supermassive Black Hole Binary Inspirals
• Fast Cosmological Parameter Estimation from Microwave Background Temperature and Polarization Power Spectra
• Speeding Up Cosmological Boltzmann Codes

Cited by in corpus (36)

• Markov Chain Monte Carlo Methods for Bayesian Data Analysis in Astronomy
• COSMOPOWER: emulating cosmological power spectra for accelerated Bayesian inference from next-generation surveys
• ELUCID - Exploring the Local Universe with reConstructed Initial Density field I: Hamiltonian Markov Chain Monte Carlo Method with Particle Mesh Dynamics
• Fast Hamiltonian sampling for large scale structure inference
• SED fitting with Markov Chain Monte Carlo: Methodology and Application to z=3.1 Lyman Alpha Emitting Galaxies
• Estimation of cosmological parameters using adaptive importance sampling
• Estimation of Primordial Spectrum with post-WMAP 3 year data
• Fast optimal CMB power spectrum estimation with Hamiltonian sampling
• CONNECT: A neural network based framework for emulating cosmological observables and cosmological parameter inference
• Statistical methods for cosmological parameter selection and estimation
• Planck priors for dark energy surveys
• Bayesian inference of CMB gravitational lensing
• CosmoPower-JAX: high-dimensional Bayesian inference with differentiable cosmological emulators
• Two Component Model of Dark Energy
• Bayesian estimation of our local motion from the Planck-2018 CMB temperature map
• candl: Cosmic Microwave Background Analysis with a Differentiable Likelihood
• Riemannian Manifold Hamiltonian Monte Carlo
• syren-halofit: A fast, interpretable, high-precision formula for the $\Lambda$CDM nonlinear matter power spectrum
• Cosmology with the largest galaxy cluster surveys: Going beyond Fisher matrix forecasts
• Almanac: Weak Lensing power spectra and map inference on the masked sphere
• A Hamiltonian Monte Carlo method for Bayesian Inference of Supermassive Black Hole Binaries
• Joint Bayesian analysis of large angular scale CMB temperature anomalies
• Bayesian inference for binary neutron star inspirals using a Hamiltonian Monte Carlo Algorithm
• Non-Gaussian forecasts of weak lensing with and without priors
• Probing local non-Gaussianities within a Bayesian framework
• Bayesian inference on the sphere beyond statistical isotropy
• Almanac: MCMC-based signal extraction of power spectra and maps on the sphere
• Grid-based exploration of cosmological parameter space with Snake
• Mapping the Cosmological Confidence Ball Surface
• User-specified random sampling of quantum channels and its applications
• Gaussbock: Fast parallel-iterative cosmological parameter estimation with Bayesian nonparametrics
• Improved Gibbs samplers for Cosmic Microwave Background power spectrum estimation
• SIToolBox : A package for Bayesian estimation of the isotropy violation in the CMB sky
• Bayesian inference methodology to characterize the dust emissivity at far-infrared and submillimeter frequencies
• Theoretical and observational aspects of cosmological inflation
• Bayesian inference in single-line spectroscopic binaries with a visual orbit