Related papers: Randomized multilevel Monte Carlo for embarrassing…

Sequential Monte Carlo is a family of algorithms for sampling from a sequence of distributions. Some of these algorithms, such as particle filters, are widely used in the physics and signal processing researches. More recent developments…

Bayesian hierarchical modeling is a popular approach to capturing unobserved heterogeneity across individual units. However, standard estimation methods such as Markov chain Monte Carlo (MCMC) can be impracticable for modeling outcomes from…

This paper discusses the challenges presented by tall data problems associated with Bayesian classification (specifically binary classification) and the existing methods to handle them. Current methods include parallelizing the likelihood,…

In this era of large-scale data, distributed systems built on top of clusters of commodity hardware provide cheap and reliable storage and scalable processing of massive data. Here, we review recent work on developing and implementing…

Bayesian inference involves the specification of a statistical model by a statistician or practitioner, with careful thought about what each parameter represents. This results in particularly interpretable models which can be used to…

This paper considers a new approach to using Markov chain Monte Carlo (MCMC) in contexts where one may adopt multilevel (ML) Monte Carlo. The underlying problem is to approximate expectations w.r.t. an underlying probability measure that is…

Machine learning models, and deep neural networks in particular, are increasingly deployed in risk-sensitive domains such as healthcare, environmental forecasting, and finance, where reliable quantification of predictive uncertainty is…

We describe an embarrassingly parallel, anytime Monte Carlo method for likelihood-free models. The algorithm starts with the view that the stochasticity of the pseudo-samples generated by the simulator can be controlled externally by a…

Many scientific and engineering problems require to perform Bayesian inferences in function spaces, in which the unknowns are of infinite dimension. In such problems, many standard Markov Chain Monte Carlo (MCMC) algorithms become arbitrary…

Multidimensional scaling (MDS) is widely used to reconstruct a low-dimensional representation of high-dimensional data while preserving pairwise distances. However, Bayesian MDS approaches based on Markov chain Monte Carlo (MCMC) face…

This study introduces a computationally efficient algorithm, delayed acceptance Markov chain Monte Carlo (DA-MCMC), designed to improve posterior simulation in quasi-Bayesian inference. Quasi-Bayesian methods, which do not require fully…

The multilevel Monte Carlo (MLMC) method has been used for a wide variety of stochastic applications. In this paper we consider its use in situations in which input random variables can be replaced by similar approximate random variables…

In this paper, we evaluate the performance of the multilevel Monte Carlo method (MLMC) for deterministic and uncertain hyperbolic systems, where randomness is introduced either in the modeling parameters or in the approximation algorithms.…

Drawing a sample from a discrete distribution is one of the building components for Monte Carlo methods. Like other sampling algorithms, discrete sampling suffers from the high computational burden in large-scale inference problems. We…

In many real-world engineering systems, the performance or reliability of the system is characterised by a scalar parameter. The distribution of this performance parameter is important in many uncertainty quantification problems, ranging…

While MCMC methods have become a main work-horse for Bayesian inference, scaling them to large distributed datasets is still a challenge. Embarrassingly parallel MCMC strategies take a divide-and-conquer stance to achieve this by writing…

Due to the potential benefits of parallelization, designing unbiased Monte Carlo estimators, primarily in the setting of randomized multilevel Monte Carlo, has recently become very popular in operations research and computational…

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…

Continuous level Monte Carlo is an unbiased, continuous version of the celebrated multilevel Monte Carlo method. The approximation level is assumed to be continuous resulting in a stochastic process describing the quantity of interest.…

Because of their robustness, efficiency and non-intrusiveness, Monte Carlo methods are probably the most popular approach in uncertainty quantification to computing expected values of quantities of interest (QoIs). Multilevel Monte Carlo…