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Monte Carlo methods are widely used to estimate observables in many-body quantum systems. However, conventional sampling schemes often require a large number of samples to achieve sufficient accuracy. In this work we propose the…
Many questions in quantitative finance, uncertainty quantification, and other disciplines are answered by computing the population mean, $\mu := \mathbb{E}(Y)$, where instances of $Y:=f(\boldsymbol{X})$ may be generated by numerical…
Simulating samples from arbitrary probability distributions is a major research program of statistical computing. Recent work has shown promise in an old idea, that sampling from a discrete distribution can be accomplished by perturbing and…
Quantum Monte Carlo (QMC) methods are essential for the numerical study of large-scale quantum many-body systems, yet their utility has been significantly hampered by the difficulty in computing key quantities such as off-diagonal operators…
Closed-form stochastic filtering equations can be derived in a general setting where probability distributions are replaced by some specific outer measures. In this article, we study how the principles of the sequential Monte Carlo method…
We consider the order of convergence for linear and nonlinear Monte Carlo approximation of compact embeddings from Sobolev spaces of dominating mixed smoothness defined on the torus $\mathbb{T}^d$ into the space $L_{\infty}(\mathbb{T}^d)$…
Randomized quasi-Monte Carlo (RQMC) sampling can bring orders of magnitude reduction in variance compared to plain Monte Carlo (MC) sampling. The extent of the efficiency gain varies from problem to problem and can be hard to predict. This…
Monte Carlo computer simulations are virtually the only way to analyze the thermodynamic behavior of a system in a precise way. However, the various existing methods exhibit extreme differences in their efficiency, depending on model…
Markov chain Monte Carlo (MCMC) methods require a large number of samples to approximate a posterior distribution, which can be costly when the likelihood or prior is expensive to evaluate. The number of samples can be reduced if we can…
When computing quantum-mechanical observables, the ``curse of dimensionality'' limits the naive approach that uses the quantum-mechanical wavefunction. The semiclassical Herman--Kluk propagator mitigates this curse by employing a grid-free…
Bayesian inference for models that have an intractable partition function is known as a doubly intractable problem, where standard Monte Carlo methods are not applicable. The past decade has seen the development of auxiliary variable Monte…
Efficient sampling of many-dimensional and multimodal density functions is a task of great interest in many research fields. We describe an algorithm that allows parallelizing inherently serial Markov chain Monte Carlo (MCMC) sampling by…
Uncertainty quantification (UQ) is an active area of research, and an essential technique used in all fields of science and engineering. The most common methods for UQ are Monte Carlo and surrogate-modelling. The former method is…
Game-theoretic attribution techniques based on Shapley values are used to interpret black-box machine learning models, but their exact calculation is generally NP-hard, requiring approximation methods for non-trivial models. As the…
We introduce an efficient numerical implementation of a Markov Chain Monte Carlo method to sample a probability distribution on a manifold (introduced theoretically in Zappa, Holmes-Cerfon, Goodman (2018)), where the manifold is defined by…
We propose that a combination of the semiclassical approximation with Monte Carlo simulations can be an efficient and reliable impurity solver for dynamical mean field theory equations and their cluster extensions with large cluster sizes.…
Several strategies have been recently proposed in order to improve Monte Carlo sampling efficiency using machine learning tools. Here, we challenge these methods by considering a class of problems that are known to be exponentially hard to…
Bootstrapping was designed to randomly resample data from a fixed sample using Monte Carlo techniques. However, the original sample itself defines a discrete distribution. Convolutional methods are well suited for discrete distributions,…
Sequential Monte Carlo algorithms (also known as particle filters) are popular methods to approximate filtering (and related) distributions of state-space models. However, they converge at the slow $1/\sqrt{N}$ rate, which may be an issue…
Spatially referenced datasets have become increasingly prevalent across many fields, largely driven by advances in data collection methods such as satellite remote sensing. In many applications, predictions at unobserved locations are…