Related papers: Theoretical guarantees for lifted samplers
The ability to generate samples of the random effects from their conditional distributions is fundamental for inference in mixed effects models. Random walk Metropolis is widely used to conduct such sampling, but such a method can converge…
I show how Markov chain sampling with the Metropolis-Hastings algorithm can be modified so as to take bigger steps when the distribution being sampled from has the characteristic that its density can be quickly recomputed for a new point if…
Gibbs sampling is a Markov Chain Monte Carlo (MCMC) method often used in Bayesian learning. MCMC methods can be difficult to deploy on parallel and distributed systems due to their inherently sequential nature. We study asynchronous Gibbs…
Piecewise-deterministic Markov process (PDMP) samplers constitute a state-of-the-art Markov chain Monte Carlo paradigm in Bayesian computation, with examples including the zig-zag and bouncy particle sampler (bps). Recent work on the…
In engineering examples, one often encounters the need to sample from unnormalized distributions with complex shapes that may also be implicitly defined through a physical or numerical simulation model, making it computationally expensive…
We discuss modern ideas in Monte Carlo algorithms in the simplified setting of the one-dimensional anharmonic oscillator. After reviewing the connection between molecular dynamics and Monte Carlo, we introduce to the Metropolis and the…
Statisticians often use Monte Carlo methods to approximate probability distributions, primarily with Markov chain Monte Carlo and importance sampling. Sequential Monte Carlo samplers are a class of algorithms that combine both techniques to…
The most common way to sample from a probability distribution is to use Monte-Carlo methods. For distributions on a continuous state space, one can find diffusions with the target distribution as equilibrium measure, so that the state of…
Bayesian shrinkage methods have generated a lot of recent interest as tools for high-dimensional regression and model selection. These methods naturally facilitate tractable uncertainty quantification and incorporation of prior information.…
Motivated by Bayesian inference with highly informative data we analyze the performance of random walk-like Metropolis-Hastings algorithms for approximate sampling of increasingly concentrating target distributions. We focus on Gaussian…
Likelihood-free methods, such as approximate Bayesian computation, are powerful tools for practical inference problems with intractable likelihood functions. Markov chain Monte Carlo and sequential Monte Carlo variants of approximate…
The purpose of this paper is to introduce a new Markov chain Monte Carlo method and exhibit its efficiency by simulation and high-dimensional asymptotic theory. Key fact is that our algorithm has a reversible proposal transition kernel,…
This paper develops a Bayesian computational platform at the interface between posterior sampling and optimization in models whose marginal likelihoods are difficult to evaluate. Inspired by adversarial optimization, namely Generative…
Probability measures supported on submanifolds can be sampled by adding an extra momentum variable to the state of the system, and discretizing the associated Hamiltonian dynamics with some stochastic perturbation in the extra variable. In…
We introduce an ensemble Markov chain Monte Carlo approach to sampling from a probability density with known likelihood. This method upgrades an underlying Markov chain by allowing an ensemble of such chains to interact via a process in…
It is commonly admitted that non-reversible Markov chain Monte Carlo (MCMC) algorithms usually yield more accurate MCMC estimators than their reversible counterparts. In this note, we show that in addition to their variance reduction…
An Automated Sliced Gibbs framework is proposed for fully automated Markov chain Monte Carlo sampling from arbitrary finite dimensional probability kernels. The method targets unnormalized, non-smooth, heavy tailed, and highly multimodal…
Component-wise MCMC algorithms, including Gibbs and conditional Metropolis-Hastings samplers, are commonly used for sampling from multivariate probability distributions. A long-standing question regarding Gibbs algorithms is whether a…
As the number of samples and dimensionality of optimization problems related to statistics an machine learning explode, block coordinate descent algorithms have gained popularity since they reduce the original problem to several smaller…
In this paper we study the ergodicity properties of some adaptive Markov chain Monte Carlo algorithms (MCMC) that have been recently proposed in the literature. We prove that under a set of verifiable conditions, ergodic averages calculated…