Related papers: Solving inverse problems by combination of maximum…
Importance sampling of target probability distributions belonging to a given convex class is considered. Motivated by previous results, the cost of importance sampling is quantified using the relative entropy of the target with respect to…
Reflected diffusions in polyhedral domains are commonly used as approximate models for stochastic processing networks in heavy traffic. Stationary distributions of such models give useful information on the steady state performance of the…
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 use a Monte Carlo method to assemble finite element matrices for polynomial Chaos approximations of elliptic equations with random coefficients. In this approach, all required expectations are approximated by a Monte Carlo method. The…
Quantum mechanics for many-body systems may be reduced to the evaluation of integrals in 3N dimensions using Monte-Carlo, providing the Quantum Monte Carlo ab initio methods. Here we limit ourselves to expectation values for trial…
Estimating the trace of the inverse of a large matrix is an important problem in lattice quantum chromodynamics. A multilevel Monte Carlo method is proposed for this problem that uses different degree polynomials for the levels. The…
This paper develops an efficient numerical method for the inverse scattering problem of a time-harmonic plane wave incident on a perfectly reflecting random periodic structure. The method is based on a novel combination of the Monte Carlo…
A common way to simulate the transport and spread of pollutants in the atmosphere is via stochastic Lagrangian dispersion models. Mathematically, these models describe turbulent transport processes with stochastic differential equations…
In this paper, we present a probabilistic numerical algorithm combining dynamic programming, Monte Carlo simulations and local basis regressions to solve non-stationary optimal multiple switching problems in infinite horizon. We provide the…
We present a Cross-Entropy based population Monte Carlo algorithm. This methods stands apart from previous work in that we are not optimizing a mixture distribution. Instead, we leverage deterministic mixture weights and optimize the…
Identifying future congestion points in electricity distribution networks is an important challenge distribution system operators face. A proven approach for addressing this challenge is to assess distribution grid adequacy using…
Macroscopically heterogeneous materials, characterised mostly by comparable heterogeneity lengthscale and structural sizes, can no longer be modelled by deterministic approach instead. It is convenient to introduce stochastic approach with…
In this article we consider a Bayesian inverse problem associated to elliptic partial differential equations (PDEs) in two and three dimensions. This class of inverse problems is important in applications such as hydrology, but the…
We revisit the classical problem of inverting dimension-reducing linear mappings using the maximum entropy (MaxEnt) criterion. In the literature, solutions are problem-dependent, inconsistent, and use different entropy measures. We propose…
We translate the problem of calculating the entropy of a set of binary configurations/signals into a sequence of supervised classification tasks. Subsequently, one can use virtually any machine learning classification algorithm for…
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 use the method of Maximum (relative) Entropy to process information in the form of observed data and moment constraints. The generic "canonical" form of the posterior distribution for the problem of simultaneous updating with data and…
Metropolis Monte Carlo simulation is a powerful tool for studying the equilibrium properties of matter. In complex condensed-phase systems, however, it is difficult to design Monte Carlo moves with high acceptance probabilities that also…
In a recent paper, the authors proposed a general methodology for probabilistic learning on manifolds. The method was used to generate numerical samples that are statistically consistent with an existing dataset construed as a realization…
We derive a parallel sampling algorithm for computational inverse problems that present an unknown linear forcing term and a vector of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of…