Related papers: Reducing the error of Monte Carlo Algorithms by Le…

Particle MCMC involves using a particle filter within an MCMC algorithm. For inference of a model which involves an unobserved stochastic process, the standard implementation uses the particle filter to propose new values for the stochastic…

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…

This paper addresses the problem of Monte Carlo approximation of posterior probability distributions. In particular, we have considered a recently proposed technique known as population Monte Carlo (PMC), which is based on an iterative…

Adaptive Monte Carlo schemes developed over the last years usually seek to ensure ergodicity of the sampling process in line with MCMC tradition. This poses constraints on what is possible in terms of adaptation. In the general case…

In this paper a novel modification of the multilevel Monte Carlo approach, allowing for further significant complexity reduction, is proposed. The idea of the modification is to use the method of control variates to reduce variance at level…

If the conclusion of a data analysis is sensitive to dropping very few data points, that conclusion might hinge on the particular data at hand rather than representing a more broadly applicable truth. How could we check whether this…

Hamiltonian Monte Carlo (HMC) samples efficiently from high-dimensional posterior distributions with proposed parameter draws obtained by iterating on a discretized version of the Hamiltonian dynamics. The iterations make HMC…

Approximate Bayesian computation (ABC) methods are standard tools for inferring parameters of complex models when the likelihood function is analytically intractable. A popular approach to improving the poor acceptance rate of the basic…

Markov chain Monte Carlo algorithms are used to simulate from complex statistical distributions by way of a local exploration of these distributions. This local feature avoids heavy requests on understanding the nature of the target, but it…

Delayed-acceptance Markov chain Monte Carlo (DA-MCMC) samples from a probability distribution via a two-stages version of the Metropolis-Hastings algorithm, by combining the target distribution with a "surrogate" (i.e. an approximate and…

Stochastic optimization in learning and inference often relies on Markov chain Monte Carlo (MCMC) to approximate gradients when exact computation is intractable. However, finite-time MCMC estimators are biased, and reducing this bias…

Markov chain Monte Carlo (MCMC) methods are one of the most popular classes of algorithms for sampling from a target probability distribution. A rising trend in recent years consists in analyzing the convergence of MCMC algorithms using…

For big data analysis, high computational cost for Bayesian methods often limits their applications in practice. In recent years, there have been many attempts to improve computational efficiency of Bayesian inference. Here we propose an…

Estimating Monte Carlo error is critical to valid simulation results in Markov chain Monte Carlo (MCMC) and initial sequence estimators were one of the first methods introduced for this. Over the last few years, focus has been on…

An efficient simulation-based methodology is proposed for the rolling window estimation of state space models, called particle rolling Markov chain Monte Carlo (MCMC) with double block sampling. In our method, which is based on Sequential…

Bayesian models have become very popular over the last years in several fields such as signal processing, statistics, and machine learning. Bayesian inference requires the approximation of complicated integrals involving posterior…

We consider the problem of adaptive stratified sampling for Monte Carlo integration of a differentiable function given a finite number of evaluations to the function. We construct a sampling scheme that samples more often in regions where…

The stochastic simulation algorithm (SSA) and the corresponding Monte Carlo (MC) method are among the most common approaches for studying stochastic processes. They rely on knowledge of interevent probability density functions (PDFs) and on…

Sequential Monte Carlo (SMC) algorithms were originally designed for estimating intractable conditional expectations within state-space models, but are now routinely used to generate approximate samples in the context of general-purpose…

Sequential Monte Carlo (SMC) methods offer a principled approach to Bayesian uncertainty quantification but are traditionally limited by the need for full-batch gradient evaluations. We introduce a scalable variant by incorporating…