Related papers: A Scrambled Method of Moments
Monte Carlo integration using quantum computers has been widely investigated, including applications to concrete problems. It is known that quantum algorithms based on quantum amplitude estimation (QAE) can compute an integral with a…
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…
The ongoing progress in quantum technologies has fueled a sustained exploration of their potential applications across various domains. One particularly promising field is quantitative finance, where a central challenge is the pricing of…
The stochastic simulation algorithm (SSA) and the corresponding Monte Carlo (MC) method are among the most common approaches for studying stochastic processes. They rely on knowledge of interevent probability density functions (PDFs) and on…
The present work addresses the question how sampling algorithms for commonly applied copula models can be adapted to account for quasi-random numbers. Besides sampling methods such as the conditional distribution method (based on a…
Quantum Monte Carlo and quantum simulation are both important tools for understanding quantum many-body systems. As a classical algorithm, quantum Monte Carlo suffers from the sign problem, preventing its application to most fermion systems…
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…
We introduce a Hamiltonian Monte Carlo (HMC) methodology based on a randomized selection of integration times, referred to as eHMC, where "e" stands for empirical. The approach relies on an offline calibration phase that leverages…
Most quasi-Monte Carlo research focuses on sampling from the unit cube. Many problems, especially in computer graphics, are defined via quadrature over the unit triangle. Quasi-Monte Carlo methods for the triangle have been developed by…
This article provides an overview of some interfaces between the theory of quasi-Monte Carlo (QMC) methods and applications. We summarize three QMC theoretical settings: first order QMC methods in the unit cube $[0,1]^s$ and in…
We propose Subsampling MCMC, a Markov Chain Monte Carlo (MCMC) framework where the likelihood function for $n$ observations is estimated from a random subset of $m$ observations. We introduce a highly efficient unbiased estimator of the…
Hamiltonian Monte Carlo (HMC) is a powerful Markov chain Monte Carlo (MCMC) algorithm for estimating expectations with respect to continuous un-normalized probability distributions. MCMC estimators typically have higher variance than…
Computational methods both open the frontiers of economic analysis and serve as a bottleneck in what can be achieved. We are the first to study whether Quantum Monte Carlo (QMC) algorithm can improve the runtime of economic applications and…
We present a Hamiltonian Monte Carlo algorithm to sample from multivariate Gaussian distributions in which the target space is constrained by linear and quadratic inequalities or products thereof. The Hamiltonian equations of motion can be…
SMC (Sequential Monte Carlo) is a class of Monte Carlo algorithms for filtering and related sequential problems. Gerber and Chopin (2015) introduced SQMC (Sequential quasi-Monte Carlo), a QMC version of SMC. This paper has two objectives:…
Recent advances in quasi-Monte Carlo integration have shown that for linearly scrambled digital net estimators, the convergence rate can be dramatically improved by taking the median rather than the mean of multiple independent replicates.…
This paper concerns the use of sequential Monte Carlo methods (SMC) for smoothing in general state space models. A well-known problem when applying the standard SMC technique in the smoothing mode is that the resampling mechanism introduces…
In general, the statistical simulation approaches are referred to as the Monte Carlo methods as a whole. The broad class of the Monte Carlo methods involves the Markov chain Monte Carlo (MCMC) techniques that attract the attention of…
The mean of a random variable can be understood as a linear functional on the space of probability distributions. Quantum computing is known to provide a quadratic speedup over classical Monte Carlo methods for mean estimation. In this…
We present a unified theory of the variational Monte Carlo (VMC) and determinant quantum Monte Carlo (DQMC) methods using a novel density matrix formulation of VMC. We introduce an efficient algorithm for VMC to compute correlation…