Related papers: Explicit error bounds for lazy reversible Markov C…
Adaptive and interacting Markov chain Monte Carlo algorithms (MCMC) have been recently introduced in the literature. These novel simulation algorithms are designed to increase the simulation efficiency to sample complex distributions.…
Probabilistic modeling provides the capability to represent and manipulate uncertainty in data, models, predictions and decisions. We are concerned with the problem of learning probabilistic models of dynamical systems from measured data.…
Approximate Bayesian computation allows for inference of complicated probabilistic models with intractable likelihoods using model simulations. The Markov chain Monte Carlo implementation of approximate Bayesian computation is often…
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…
The Reversible Jump algorithm is one of the most widely used Markov chain Monte Carlo algorithms for Bayesian estimation and model selection. A generalized multiple-try version of this algorithm is proposed. The algorithm is based on…
Metropolis-Hastings estimates intractable expectations - can differentiating the algorithm estimate their gradients? The challenge is that Metropolis-Hastings trajectories are not conventionally differentiable due to the discrete…
In this article, we present an event-driven algorithm that generalizes the recent hard-sphere event-chain Monte Carlo method without introducing discretizations in time or in space. A factorization of the Metropolis filter and the concept…
A classical approach for approximating expectations of functions w.r.t. partially known distributions is to compute the average of function values along a trajectory of a Metropolis-Hastings (MH) Markov chain. A key part in the MH algorithm…
In this paper we address the problem of the prohibitively large computational cost of existing Markov chain Monte Carlo methods for large--scale applications with high dimensional parameter spaces, e.g. in uncertainty quantification in…
This article studies the achievable guarantees on the error rates of certain learning algorithms, with particular focus on refining logarithmic factors. Many of the results are based on a general technique for obtaining bounds on the error…
The missing data issue often complicates the task of estimating generalized linear models (GLMs). We describe why the pseudo-marginal Metropolis-Hastings algorithm, used in this setting, is an effective strategy for parameter estimation.…
A key limitation of sampling algorithms for approximate inference is that it is difficult to quantify their approximation error. Widely used sampling schemes, such as sequential importance sampling with resampling and Metropolis-Hastings,…
In this paper, we provide non-asymptotic upper bounds on the error of sampling from a target density using three schemes of discretized Langevin diffusions. The first scheme is the Langevin Monte Carlo (LMC) algorithm, the Euler…
Markov Chain Monte Carlo methods are widely used in signal processing and communications for statistical inference and stochastic optimization. In this work, we introduce an efficient adaptive Metropolis-Hastings algorithm to draw samples…
We propose a weighting scheme for the proposals within Markov chain Monte Carlo algorithms and show how this can improve statistical efficiency at no extra computational cost. These methods are most powerful when combined with…
Convergence rate analyses of random walk Metropolis-Hastings Markov chains on general state spaces have largely focused on establishing sufficient conditions for geometric ergodicity or on analysis of mixing times. Geometric ergodicity is a…
In this paper we study Markov chains associated with the Metropolis-Hastings algorithm. We consider conditions under which the sequence of the successive densities of such a chain converges to the target density according to the total…
When an unbiased estimator of the likelihood is used within a Metropolis--Hastings chain, it is necessary to trade off the number of Monte Carlo samples used to construct this estimator against the asymptotic variances of averages computed…
A key goal in the design of probabilistic inference algorithms is identifying and exploiting properties of the distribution that make inference tractable. Lifted inference algorithms identify symmetry as a property that enables efficient…
We present a Bayesian approach to estimate the parameters of mathematical models of cardiac electrophysiology with quantified uncertainty. Such models capture the dynamics of the electrical signal that coordinates the muscle cell…