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In this article we develop a new sequential Monte Carlo (SMC) method for multilevel (ML) Monte Carlo estimation. In particular, the method can be used to estimate expectations with respect to a target probability distribution over an…

We propose a new framework for Hamiltonian Monte Carlo (HMC) on truncated probability distributions with smooth underlying density functions. Traditional HMC requires computing the gradient of potential function associated with the target…

We discuss the efficiency of Monte Carlo methods in solving continuum radiative transfer problems. The sampling of the radiation field and convergence of dust temperature calculations in the case of optically thick clouds are both studied.…

A core problem in statistics and probabilistic machine learning is to compute probability distributions and expectations. This is the fundamental problem of Bayesian statistics and machine learning, which frames all inference as…

Variational Monte Carlo (VMC) is a powerful and fast-growing method for optimizing and evolving parameterized many-body wave functions, especially with modern neural-network quantum states. In practice, however, the stochastic estimators…

Approximate inference in probabilistic graphical models (PGMs) can be grouped into deterministic methods and Monte-Carlo-based methods. The former can often provide accurate and rapid inferences, but are typically associated with biases…

We propose a new framework of variance-reduced Hamiltonian Monte Carlo (HMC) methods for sampling from an $L$-smooth and $m$-strongly log-concave distribution, based on a unified formulation of biased and unbiased variance reduction…

This work introduces a novel multilevel Monte Carlo (MLMC) metamodeling approach for variance function estimation. Although devising an efficient experimental design for simulation metamodeling can be elusive, the MLMC-based approach…

Hamiltonian Monte Carlo (HMC) has been progressively incorporated within the statistician's toolbox as an alternative sampling method in settings when standard Metropolis-Hastings is inefficient. HMC generates a Markov chain on an augmented…

Random sampling of graph partitions under constraints has become a popular tool for evaluating legislative redistricting plans. Analysts detect partisan gerrymandering by comparing a proposed redistricting plan with an ensemble of sampled…

Parameter estimation for discretely observed Markov processes is a challenging problem. However, simulation of Markov processes is straightforward using the Gillespie algorithm. We exploit this ease of simulation to develop an effective…

Traditional gradient-based sampling methods, like standard Hamiltonian Monte Carlo, require that the desired target distribution is continuous and differentiable. This limits the types of models one can define, although the presented models…

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…

Reconstruction of one-dimensional kinematic distributions from calculations based on high-dimensional Monte-Carlo integration is a standard problem in high-energy physics. Traditionally, this is done by collecting randomly-generated events…

Can Monte Carlo (MC) solvers be directly used in gradient-based methods for PDE-constrained optimization problems? In these problems, a gradient of the loss function is typically presented as a product of two PDE solutions, one for the…

The hybrid Monte Carlo (HMC) algorithm is arguably the most efficient sampling method for general probability distributions of continuous variables. Together with exact Fourier acceleration (EFA) the HMC becomes equivalent to direct…

Hamiltonian Monte Carlo (HMC) is an efficient method of simulating smooth distributions and has motivated the widely used No-U-turn Sampler (NUTS) and software Stan. We build on NUTS and the technique of "unbiased sampling" to design HMC…

Monte Carlo (MC) techniques are often used to estimate integrals of a multivariate function using randomly generated samples of the function. In light of the increasing interest in uncertainty quantification and robust design applications…

In this paper we consider sequential joint state and static parameter estimation given discrete time observations associated to a partially observed stochastic partial differential equation (SPDE). It is assumed that one can only estimate…

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…