Related papers: Stochastic Series Expansion Methods
In this paper, we compare the performance of two scenario-based numerical methods to solve stochastic optimal control problems: scenario trees and particles. The problem consists in finding strategies to control a dynamical system perturbed…
The "standard" Brownian motion master equation, used to describe thermal damping, is not completely positive, and does not admit a Monte Carlo method, important in numerical simulations. To eliminate both these problems one must add a term…
We investigate the stability of a Sequential Monte Carlo (SMC) method applied to the problem of sampling from a target distribution on $\mathbb{R}^d$ for large $d$. It is well known that using a single importance sampling step one produces…
The time-ordered product framework of quantum field theory can also be used to understand salient phenomena in stochastic biochemical networks. It is used here to derive Gillespie's Stochastic Simulation Algorithm (SSA) for chemical…
Stochastic mathematical models are essential tools for understanding and predicting complex phenomena. The purpose of this work is to study the exit times of a stochastic dynamical system-specifically, the mean exit time and the…
Stochastic Approximation (SA) is a classical algorithm that has had since the early days a huge impact on signal processing, and nowadays on machine learning, due to the necessity to deal with a large amount of data observed with…
Building surrogate models with uncertainty quantification capabilities is essential for many engineering applications where randomness, such as variability in material properties, is unavoidable. Polynomial Chaos Expansion (PCE) is widely…
In the task of predicting spatio-temporal fields in environmental science using statistical methods, introducing statistical models inspired by the physics of the underlying phenomena that are numerically efficient is of growing interest.…
Sparse polynomial chaos expansions (PCE) are a popular surrogate modelling method that takes advantage of the properties of PCE, the sparsity-of-effects principle, and powerful sparse regression solvers to approximate computer models with…
Model comparison for the purposes of selection, averaging and validation is a problem found throughout statistics. Within the Bayesian paradigm, these problems all require the calculation of the posterior probabilities of models within a…
In power system steady-state estimation (PSSE), one needs to consider (1) the need for robust statistics, (2) the nonconvex transmission constraints, (3) the fast-varying nature of the inputs, and the corresponding need to track optimal…
A new class of stochastic field models is constructed using nested stochastic partial differential equations (SPDEs). The model class is computationally efficient, applicable to data on general smooth manifolds, and includes both the…
In the paper, we propose a higher-order geometry-preserving numerical method for stochastic differential equations (SDEs) evolving on the Lie groups SO(n) and SE(n). Most existing Lie group integrators rely on Magnus expansion of the…
Projective measurements of collective observables can be employed to herald the preparation of entangled states of quantum systems, and the resulting conditional dynamics is usually handled by stochastic master equation (SME) for small…
Stochastic differential equations provide a rich class of flexible generative models, capable of describing a wide range of spatio-temporal processes. A host of recent work looks to learn data-representing SDEs, using neural networks and…
In this paper we consider the problem of the limits concerning the physical information that can be extracted from the analysis of one or more time series (light curves) typical of astrophysical objects. On the basis of theoretical…
Epidemics are inherently stochastic, and stochastic models provide an appropriate way to describe and analyse such phenomena. Given temporal incidence data consisting of, for example, the number of new infections or removals in a given time…
We consider a nonlinear state-space model with the state transition and observation functions expressed as basis function expansions. The coefficients in the basis function expansions are learned from data. Using a connection to Gaussian…
A method for analytic continuation of imaginary-time correlation functions (here obtained in quantum Monte Carlo simulations) to real-frequency spectral functions is proposed. Stochastically sampling a spectrum parametrized by a large…
This paper introduces methodology for performing Bayesian inference sequentially on a sequence of posteriors on spaces of different dimensions. We show how this may be achieved through the use of sequential Monte Carlo (SMC) samplers (Del…