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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…

By adopting a Multilevel Monte Carlo (MLMC) framework, we show that only a handful of costly fine scale computations are needed to accurately estimate statistics of the failure of a composite structure, as opposed to the thousands typically…

Numerous capability and safety techniques of Large Language Models (LLMs), including RLHF, automated red-teaming, prompt engineering, and infilling, can be cast as sampling from an unnormalized target distribution defined by a given reward…

Being the most classical generative model for serial data, state-space models (SSM) are fundamental in AI and statistical machine learning. In SSM, any form of parameter learning or latent state inference typically involves the computation…

This article considers the sequential Monte Carlo (SMC) approximation of ratios of normalizing constants associated to posterior distributions which in principle rely on continuum models. Therefore, the Monte Carlo estimation error and the…

Markov Chain Monte Carlo (MCMC) is a well-established family of algorithms primarily used in Bayesian statistics to sample from a target distribution when direct sampling is challenging. Existing work on Bayesian decision trees uses MCMC.…

As it has become common to use many computer cores in routine applications, finding good ways to parallelize popular algorithms has become increasingly important. In this paper, we present a parallelization scheme for Markov chain Monte…

The Multilevel Monte Carlo (MLMC) approach usually works well when estimating the expected value of a quantity which is a Lipschitz function of intermediate quantities, but if it is a discontinuous function it can lead to a much slower…

Distortion risk measures play a critical role in quantifying risks associated with uncertain outcomes. Accurately estimating these risk measures in the context of computationally expensive simulation models that lack analytical tractability…

Markov chain Monte Carlo (MCMC) methods are ubiquitous tools for simulation-based inference in many fields but designing and identifying good MCMC samplers is still an open question. This paper introduces a novel MCMC algorithm, namely,…

Markov chain Monte Carlo (MCMC) is a powerful methodology for the approximation of posterior distributions. However, the iterative nature of MCMC does not naturally facilitate its use with modern highly parallel computation on HPC and cloud…

Many problems in the physical sciences, machine learning, and statistical inference necessitate sampling from a high-dimensional, multi-modal probability distribution. Markov Chain Monte Carlo (MCMC) algorithms, the ubiquitous tool for this…

In parameter estimation problems one computes a posterior distribution over uncertain parameters defined jointly by a prior distribution, a model, and noisy data. Markov Chain Monte Carlo (MCMC) is often used for the numerical solution of…

State space models (SSM) have been widely applied for the analysis and visualization of large sequential datasets. Sequential Monte Carlo (SMC) is a very popular particle-based method to sample latent states from intractable posteriors.…

We introduce a new class of sequential Monte Carlo methods which reformulates the essence of the nested sampling method of Skilling (2006) in terms of sequential Monte Carlo techniques. Two new algorithms are proposed, nested sampling via…

In this work, we introduce a simple modification of the Monte Carlo algorithm, which we call step Monte Carlo (sMC). The sMC approach allows to simulate processes far from equilibrium and obtain information about the dynamic properties of…

Sequential Monte Carlo (SMC) methods comprise one of the most successful approaches to approximate Bayesian filtering. However, SMC without good proposal distributions struggle in high dimensions. We propose nested sequential Monte Carlo…

Bayesian modelling and computational inference by Markov chain Monte Carlo (MCMC) is a principled framework for large-scale uncertainty quantification, though is limited in practice by computational cost when implemented in the simplest…

Random field Monte Carlo (MC) reliability analysis is a robust stochastic method to determine the probability of failure. This method, however, requires a large number of numerical simulations demanding high computational costs. This paper…

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…