Related papers: A Multilevel Approach towards Unbiased Sampling of…
Markov chain Monte Carlo (MCMC) methods provide consistent of integrals as the number of iterations goes to infinity. MCMC estimators are generally biased after any fixed number of iterations. We propose to remove this bias by using…
Many probabilistic models introduce strong dependencies between variables using a latent multivariate Gaussian distribution or a Gaussian process. We present a new Markov chain Monte Carlo algorithm for performing inference in models with…
Sequential Monte Carlo methods, also known as particle methods, are a popular set of techniques for approximating high-dimensional probability distributions and their normalizing constants. These methods have found numerous applications in…
The expected information gain is an important quality criterion of Bayesian experimental designs, which measures how much the information entropy about uncertain quantity of interest $\theta$ is reduced on average by collecting relevant…
The safety concern for unmanned systems, namely the concern for the potential casualty caused by system abnormalities, has been a bottleneck for their development, especially in populated areas. Evidently, the collision between the unmanned…
In this review, we address the use of Monte Carlo methods for approximating definite integrals of the form $Z = \int L(x) d P(x)$, where $L$ is a target function (often a likelihood) and $P$ a finite measure. We present vertical-likelihood…
This work describes a domain embedding technique between two non-matching meshes used for generating realizations of spatially correlated random fields with applications to large-scale sampling-based uncertainty quantification. The goal is…
This paper focuses on the study of an original combination of the Multilevel Monte Carlo method introduced by Giles [10] and the popular importance sampling technique. To compute the optimal choice of the parameter involved in the…
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…
Multifidelity Monte Carlo methods rely on a hierarchy of possibly less accurate but statistically correlated simplified or reduced models, in order to accelerate the estimation of statistics of high-fidelity models without compromising the…
In this article, we consider multilevel Monte Carlo for the numerical computation of expectations for stochastic differential equations driven by L\'{e}vy processes. The underlying numerical schemes are based on jump-adapted Euler schemes.…
We consider the numerical approximation of $\mathbb{P}[G\in \Omega]$ where the $d$-dimensional random variable $G$ cannot be sampled directly, but there is a hierarchy of increasingly accurate approximations $\{G_\ell\}_{\ell\in\mathbb{N}}$…
When solving partial differential equations with random fields as coefficients the efficient sampling of random field realisations can be challenging. In this paper we focus on the fast sampling of Gaussian fields using quasi-random points…
The expectation-maximization (EM) algorithm is a powerful computational technique for finding the maximum likelihood estimates for parametric models when the data are not fully observed. The EM is best suited for situations where the…
The simulation of the expectation of a stochastic quantity E[Y] by Monte Carlo methods is known to be computationally expensive especially if the stochastic quantity or its approximation Y_n is expensive to simulate, e.g., the solution of a…
The aim of this paper is to introduce a new Monte Carlo method based on importance sampling techniques for the simulation of stochastic differential equations. The main idea is to combine random walk on squares or rectangles methods with…
In this study, we give an extension of Montanaro's arXiv/archive:1504.06987 quantum Monte Carlo method, tailored for computing expected values of random variables that exhibit infinite variance. This addresses a challenge in analyzing…
The estimation of repeatedly nested expectations is a challenging task that arises in many real-world systems. However, existing methods generally suffer from high computational costs when the number of nestings becomes large. Fix any…
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…
In the following article we consider approximate Bayesian computation (ABC) inference. We introduce a method for numerically approximating ABC posteriors using the multilevel Monte Carlo (MLMC). A sequential Monte Carlo version of the…