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To sample from a given target distribution, Markov chain Monte Carlo (MCMC) sampling relies on constructing an ergodic Markov chain with the target distribution as its invariant measure. For any MCMC method, an important question is how to…
We demonstrate for the first time that ill-conditioned, non-smooth, constrained distributions in very high dimension, upwards of 100,000, can be sampled efficiently $\textit{in practice}$. Our algorithm incorporates constraints into the…
We show that the mass matrix derived from finite elements can be effectively used as a preconditioner for iteratively solving the linear system arising from finite-difference discretization of the Poisson equation, using the conjugate…
We prove a bound on the finite sample error of sequential Monte Carlo (SMC) on static spaces using the $L_2$ distance between interpolating distributions and the mixing times of Markov kernels. This result is unique in that it is the first…
Hamiltonian Monte Carlo is a popular sampling technique for smooth target densities. The scale lengths of the target have long been known to influence integration error and sampling efficiency. However, quantitative measures intrinsic to…
The Metropolis-Hastings algorithm is a fundamental Markov chain Monte Carlo (MCMC) method for sampling and inference. With the advent of Big Data, distributed and parallel variants of MCMC methods are attracting increased attention. In this…
We propose a minimal generalization of the celebrated Markov-Chain Monte Carlo algorithm which allows for an arbitrary number of configurations to be visited at every Monte Carlo step. This is advantageous when a parallel computing machine…
The paper proposes a Riemannian Manifold Hamiltonian Monte Carlo sampler to resolve the shortcomings of existing Monte Carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlations. The…
A current challenge for many Bayesian analyses is determining when to terminate high-dimensional Markov chain Monte Carlo simulations. To this end, we propose using an automated sequential stopping procedure that terminates the simulation…
This paper proposes a new sampling scheme based on Langevin dynamics that is applicable within pseudo-marginal and particle Markov chain Monte Carlo algorithms. We investigate this algorithm's theoretical properties under standard…
Couplings play a central role in the analysis of Markov chain Monte Carlo algorithms and appear increasingly often in the algorithms themselves, e.g. in convergence diagnostics, parallelization, and variance reduction techniques. Existing…
Monte Carlo (MC) algorithms are commonly employed to explore high-dimensional parameter spaces constrained by data. All the statistical information obtained in the output of these analyses is contained in the Markov chains, which one needs…
Finding effective ways to exploit parallel computing to accelerate Markov chain Monte Carlo methods is an important problem in Bayesian computation and related disciplines. In this paper, we consider the zeroth-order setting where the…
We prove explicit, i.e., non-asymptotic, error bounds for Markov Chain Monte Carlo methods, such as the Metropolis algorithm. The problem is to compute the expectation (or integral) of f with respect to a measure which can be given by a…
The design of the proposal distributions, and most notably the kernel parameters, are crucial for the performance of Markov chain Monte Carlo (MCMC) rendering. A poor selection of parameters can increase the correlation of the Markov chain…
Preconditioning is a key component of MCMC algorithms that improves sampling efficiency by facilitating exploration of geometrically complex target distributions through an invertible map. While linear preconditioners are often sufficient…
We study an overdamped Langevin equation on the $d$-dimensional torus with stationary distribution proportional to~$p = e^{-U / \kappa}$. When~$U$ has multiple wells the mixing time of the associated process is exponentially large (of…
We consider the discrete-time filtering problem in scenarios where the observation noise is degenerate or low. More precisely, one is given access to a discrete time observation sequence which at any time $k$ depends only on the state of an…
We present a novel preconditioning technique for proximal optimization methods that relies on graph algorithms to construct effective preconditioners. Such combinatorial preconditioners arise from partitioning the graph into forests. We…
We show that Markov couplings can be used to improve the accuracy of Markov chain Monte Carlo calculations in some situations where the steady-state probability distribution is not explicitly known. The technique generalizes the notion of…