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The Monte Carlo algorithm is increasingly utilized, with its central step involving computer-based random sampling from stochastic models. While both Markov Chain Monte Carlo (MCMC) and Reject Monte Carlo serve as sampling methods, the…
Hypothesis tests calibrated by (re)sampling methods (such as permutation, rank and bootstrap tests) are useful tools for statistical analysis, at the computational cost of requiring Monte-Carlo sampling for calibration. It is common and…
In simulations of partial differential equations using particle-in-cell (PIC) methods, it is often advantageous to resample the particle distribution function to increase simulation accuracy, reduce compute cost, and/or avoid numerical…
Two different Reverse Monte Carlo strategies, 'RMC++' and 'RMCPOW', have been compared for determining the microscopic structure of some liquid and amorphous solid systems on the basis of neutron diffraction measurements. The first, '$g(r)$…
Diffusion models enable the synthesis of highly accurate samples from complex distributions and have become foundational in generative modeling. Recently, they have demonstrated significant potential for solving Bayesian inverse problems by…
Monte Carlo methods are widely used in particle physics to integrate and sample probability distributions (differential cross sections or decay rates) on multi-dimensional phase spaces. We present a Neural Network (NN) algorithm optimized…
Probabilistic prediction of sequences from images and other high-dimensional data is a key challenge, particularly in risk-sensitive applications. In these settings, it is often desirable to quantify the uncertainty associated with the…
Quantitative photoacoustic tomography aims at estimating optical parameters from photoacoustic images that are formed utilizing the photoacoustic effect caused by the absorption of an externally introduced light pulse. This optical…
We investigate in this paper an alternative method to simulation based recursive importance sampling procedure to estimate the optimal change of measure for Monte Carlo simulations. We propose an algorithm which combines (vector and…
Markov chain Monte Carlo is a widely-used technique for generating a dependent sequence of samples from complex distributions. Conventionally, these methods require a source of independent random variates. Most implementations use…
In this paper, we present an approach for estimating significant financial metrics within risk management by utilizing quantum phenomena for random number generation. We explore Quantum-Enhanced Monte Carlo, a method that combines…
The Markov Chain Monte Carlo method is at the heart of efficient approximation schemes for a wide range of problems in combinatorial enumeration and statistical physics. It is therefore very natural and important to determine whether…
Least squares Monte Carlo methods are a popular numerical approximation method for solving stochastic control problems. Based on dynamic programming, their key feature is the approximation of the conditional expectation of future rewards by…
We present a sequential Monte Carlo sampler variant of the partial rejection control algorithm, and show that this variant can be considered as a sequential Monte Carlo sampler with a modified mutation kernel. We prove that the new sampler…
We propose a multi-fidelity neural network surrogate sampling method for the uncertainty quantification of physical/biological systems described by ordinary or partial differential equations. We first generate a set of low/high-fidelity…
We describe modern variants of Monte Carlo methods for Uncertainty Quantification (UQ) of the Neutron Transport Equation, when it is approximated by the discrete ordinates method with diamond differencing. We focus on the mono-energetic 1D…
We introduce the Quantization Monte Carlo method to solve thermal radiative transport equations with possibly several collision regimes, ranging from few collisions to massive number of collisions per time unit. For each particle in a given…
Reinforcement learning constantly deals with hard integrals, for example when computing expectations in policy evaluation and policy iteration. These integrals are rarely analytically solvable and typically estimated with the Monte Carlo…
Enriching Brownian motion with regenerations from a fixed regeneration distribution $\mu$ at a particular regeneration rate $\kappa$ results in a Markov process that has a target distribution $\pi$ as its invariant distribution. For the…
Monte Carlo (MC) simulations of many systems, in particular those with conflicting constraints, can be considerably speeded up by using multicanonical or related methods. Some of these approaches sample with a-priori unknown weight factors.…