Markov chain Monte Carlo in practice
Markov chain Monte Carlo (MCMC) is an essential set of tools for estimating features of
probability distributions commonly encountered in modern applications. For MCMC …
probability distributions commonly encountered in modern applications. For MCMC …
[HTML][HTML] Convergence Diagnostics for Entity Resolution
S Aleshin-Guendel, RC Steorts - Annual Review of Statistics …, 2024 - annualreviews.org
Entity resolution is the process of merging and removing duplicate records from multiple
data sources, often in the absence of unique identifiers. Bayesian models for entity …
data sources, often in the absence of unique identifiers. Bayesian models for entity …
Explicit convergence bounds for Metropolis Markov chains: isoperimetry, spectral gaps and profiles
We derive the first explicit bounds for the spectral gap of a random walk Metropolis algorithm
on R d for any value of the proposal variance, which when scaled appropriately recovers the …
on R d for any value of the proposal variance, which when scaled appropriately recovers the …
Wasserstein-based methods for convergence complexity analysis of MCMC with applications
Over the last 25 years, techniques based on drift and minorization (d&m) have been
mainstays in the convergence analysis of MCMC algorithms. However, results presented …
mainstays in the convergence analysis of MCMC algorithms. However, results presented …
HMC and underdamped Langevin united in the unadjusted convex smooth case
N Gouraud, PL Bris, A Majka, P Monmarché - arXiv preprint arXiv …, 2022 - arxiv.org
We consider a family of unadjusted generalized HMC samplers, which includes standard
position HMC samplers and discretizations of the underdamped Langevin process. A …
position HMC samplers and discretizations of the underdamped Langevin process. A …
Convergence of position-dependent MALA with application to conditional simulation in GLMMs
V Roy, L Zhang - Journal of Computational and Graphical Statistics, 2023 - Taylor & Francis
We establish conditions under which Metropolis-Hastings (MH) algorithms with a position-
dependent proposal covariance matrix will or will not have the geometric rate of …
dependent proposal covariance matrix will or will not have the geometric rate of …
Convergence rates of Metropolis–Hastings algorithms
Given a target probability density known up to a normalizing constant, the Metropolis–
Hastings algorithm simulates realizations from a Markov chain which are eventual …
Hastings algorithm simulates realizations from a Markov chain which are eventual …
Explicit bounds for spectral theory of geometrically ergodic Markov kernels and applications
L Hervé, J Ledoux - Bernoulli, 2024 - projecteuclid.org
In this paper, we deal with a Markov chain on a measurable state space (X, X) which has a
transition kernel P admitting an aperiodic small-set S and satisfying the standard geometric …
transition kernel P admitting an aperiodic small-set S and satisfying the standard geometric …
Convergence and concentration properties of constant step-size SGD through Markov chains
I Merad, S Gaïffas - arXiv preprint arXiv:2306.11497, 2023 - arxiv.org
We consider the optimization of a smooth and strongly convex objective using constant step-
size stochastic gradient descent (SGD) and study its properties through the prism of Markov …
size stochastic gradient descent (SGD) and study its properties through the prism of Markov …
Exact convergence analysis of the independent Metropolis-Hastings algorithms
G Wang - Bernoulli, 2022 - projecteuclid.org
A well-known difficult problem regarding Metropolis-Hastings algorithms is to get sharp
bounds on their convergence rates. Moreover, a fundamental but often overlooked problem …
bounds on their convergence rates. Moreover, a fundamental but often overlooked problem …