Stationarity and Convergence of the Metropolis-Hastings Algorithm: Insights into Theoretical Aspects

  title={Stationarity and Convergence of the Metropolis-Hastings Algorithm: Insights into Theoretical Aspects},
  author={Stacy D. Hill and James C. Spall},
  journal={IEEE Control Systems},
  • S. HillJ. Spall
  • Published 17 January 2019
  • Computer Science
  • IEEE Control Systems
Markov chain Monte Carlo (MCMC) is a versatile sampling approach that is useful in a wide range of estimation and simulation applications. Fundamentally, MCMC is a powerful general means of generating random samples from probability distributions from which it is otherwise difficult to draw samples. The MCMC method is named for its reliance on the construction of a Markovian (dependent) sequence of random variables. Under modest conditions, the sequence has a limiting probability distribution… 

Objective Bayesian meta-analysis based on generalized multivariate random effects model

Objective Bayesian inference procedures are derived for the parameters of the multivariate random effects model generalized to elliptically contoured distributions. The posterior for the overall mean

My title

This protocol can be seen as an alternative to black-box data assimilation methods, that forces the modeler to lay bare the assumptions of the model, to think about the inferential process, and to spot potential identification problems.

On learning agent-based models from data

This protocol can be seen as an alternative to black-box data assimilation methods, that forces the modeler to lay bare the assumptions of the model, to think about the inferential process, and to spot potential identification problems.

State estimation for the electro-hydraulic actuator based on particle filter with an improved resampling technique

  • Runxia GuoZ. WeiYeo Wei
  • Engineering
    Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability
  • 2019
The novel resampling method based on support vector regression-particle filters can keep the diversity of particles as well as relieve the degeneracy phenomenon and eventually make the estimated state more realistic.

The volatility of stock market returns: Application of Monte Carlo simulation

Stock exchange is the "mirror" of the economy and helps industry (and commerce) to accelerate the development of the country. The prices on the stock exchanges increase or decrease over the

MADFU: An Improved Malicious Application Detection Method Based on Features Uncertainty

A malicious application detection model based on features uncertainty (MADFU) is proposed, which uses logistic regression function to describe the input (permissions) and output (labels) relationship and the Markov chain Monte Carlo algorithm to solve features’ uncertainty.

Analysis of Online Learning Time in Flipped classroom Based on MCMC

The MCMC algorithm is used to analyze the online learning time of the flipped classroom, and analyzes the student learning time in the form of probability.

Benchmarking Quantum Simulators

  • A. Shaw
  • Physics, Computer Science
  • 2021
Time-averaged mixed-state equivalence (TAME) is used to benchmark quantum simulators with classical computing resources. The classical computation is feasible even if direct computation of the

Metropolis Monte Carlo sampling: convergence, localization transition and optimality

Among random sampling methods, Markov Chain Monte Carlo algorithms are foremost. Using a combination of analytical and numerical approaches, we study their convergence properties towards the steady

Sensitivity of non-conditional climatic variables to climate-change deep uncertainty using Markov Chain Monte Carlo simulation

There is substantial evidence suggesting climate change is having an adverse impact on the world’s water resources. One must remember, however, that climate change is beset by uncertainty. It is



Estimation via Markov chain Monte Carlo

  • J. Spall
  • Computer Science, Mathematics
    Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301)
  • 2002
A survey of popular implementations of Markov chain Monte Carlo, focusing especially on the two most popular specific implementations of MCMC: Metropolis-Hastings and Gibbs sampling.

Geometric convergence and central limit theorems for multidimensional Hastings and Metropolis algorithms

We develop results on geometric ergodicity of Markov chains and apply these and other recent results in Markov chain theory to multidimensional Hastings and Metropolis algorithms. For those based on

Markov Chains and Stochastic Stability

This second edition reflects the same discipline and style that marked out the original and helped it to become a classic: proofs are rigorous and concise, the range of applications is broad and knowledgeable, and key ideas are accessible to practitioners with limited mathematical background.

A Monte Carlo Approach to Nonnormal and Nonlinear State-Space Modeling

Abstract A solution to multivariate state-space modeling, forecasting, and smoothing is discussed. We allow for the possibilities of nonnormal errors and nonlinear functionals in the state equation,

Simulation and the Monte Carlo Method, 3rd ed.

  • Dootika Vats
  • Economics
    Journal of the American Statistical Association
  • 2019
weighted sum of the claims, which is related to discounting the future cash flows. The latter is related to real life applications when interest rate is accounted in the ruin model. Chapter 9

Modes of convergence of Markov chain transition probabilities

Explaining the Gibbs Sampler

A simple explanation of how and why the Gibbs sampler works is given and analytically establish its properties in a simple case and insight is provided for more complicated cases.


The Markov chain simulation method has been successfully used in many problems, including some that arise in Bayesian statistics. We give a self-contained proof of the convergence of this method in

A Markov Chain Monte Carlo Approach to Nonlinear Parametric System Identification

A Markov chain Monte Carlo (MCMC) approach is proposed that estimates the feasible parameter set, the minimum volume outer-bounding ellipsoid and the minimum variance estimate.