Markov Chain Monte Carlo: Can We Trust the Third Significant Figure?

Abstract

Current reporting of results based on Markov chain Monte Carlo computations could be improved. In particular, a measure of the accuracy of the resulting estimates is rarely reported. Thus we have little ability to objectively assess the quality of the reported estimates. We address this issue in that we discuss why Monte Carlo standard errors are important, how they can be easily calculated in Markov chain Monte Carlo and how they can be used to decide when to stop the simulation. We compare their use to a popular alternative in the context of two examples.

Published in at http://dx.doi.org/10.1214/08-STS257 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (4)

• Simulated Tempering: A New Monte Carlo Scheme
• General state space Markov chains and MCMC algorithms
• Sufficient burn-in for Gibbs samplers for a hierarchical random effects model
• Practical drift conditions for subgeometric rates of convergence

Cited by in corpus (31)

• Batch means and spectral variance estimators in Markov chain Monte Carlo
• A new multivariate measurement error model with zero-inflated dietary data, and its application to dietary assessment
• Accelerating MCMC with active subspaces
• Calibrating an ice sheet model using high-dimensional binary spatial data
• Restricted Spatial Regression Methods: Implications for Inference
• Component-Wise Markov Chain Monte Carlo: Uniform and Geometric Ergodicity under Mixing and Composition
• Sampling Errors in Nested Sampling Parameter Estimation
• Markov Chain Monte Carlo Estimation of Quantiles
• Detectability of the subdominant mode in a binary black hole ringdown
• Statistical Test of Distance--Duality Relation with Type Ia Supernovae and Baryon Acoustic Oscillations
• On The XUV Luminosity Evolution of TRAPPIST-1
• The Informed Sampler: A Discriminative Approach to Bayesian Inference in Generative Computer Vision Models
• Fast and flexible inference for joint models of multivariate longitudinal and survival data using Integrated Nested Laplace Approximations
• Convergence analysis of the Gibbs sampler for Bayesian general linear mixed models with improper priors
• DeepQMC: an open-source software suite for variational optimization of deep-learning molecular wave functions
• Exact sampling for intractable probability distributions via a Bernoulli factory
• Spatial Factor Modeling: A Bayesian Matrix-Normal Approach for Misaligned Data
• Improving the Convergence Properties of the Data Augmentation Algorithm with an Application to Bayesian Mixture Modeling
• Bayesian graph convolutional neural networks via tempered MCMC
• Gaussian-Charge Polarizable Interaction Potential for Carbon Dioxide
• Some models are useful, but how do we know which ones? Towards a unified Bayesian model taxonomy
• Approximating Probability Densities by Iterated Laplace Approximations
• Characterising poroelastic materials in the ultrasonic range - A Bayesian approach
• Comment: Gibbs Sampling, Exponential Families, and Orthogonal Polynomials
• Separating internal and externally-forced contributions to global temperature variability using a Bayesian stochastic energy balance framework
• Simultaneously modelling far-infrared dust emission and its relation to CO emission in star forming galaxies
• Using a Bayesian-Inference Approach to Calibrating Models for Simulation in Robotics
• Convergence analysis of block Gibbs samplers for Bayesian linear mixed models with $p>N$
• Estimating the material parameters of an inhomogeneous poroelastic plate from ultrasonic measurements in water
• Joint Estimation of Robin Coefficient and Domain Boundary for the Poisson Problem
• Efficient Fully Bayesian Approach to Brain Activity Mapping with Complex-Valued fMRI Data