Related papers: Maximum Likelihood Estimation for Stochastic Diffe…

Monte Carlo sampling for Bayesian posterior inference is a common approach used in machine learning. The Markov Chain Monte Carlo procedures that are used are often discrete-time analogues of associated stochastic differential equations…

We develop a framework that allows the use of the multi-level Monte Carlo (MLMC) methodology (Giles2015) to calculate expectations with respect to the invariant measure of an ergodic SDE. In that context, we study the (over-damped) Langevin…

Estimating copulas with discrete marginal distributions is challenging, especially in high dimensions, because computing the likelihood contribution of each observation requires evaluating $2^{J}$ terms, with $J$ the number of discrete…

Multivariate Hawkes Processes (MHPs) are a class of point processes that can account for complex temporal dynamics among event sequences. In this work, we study the accuracy and computational efficiency of three classes of algorithms which,…

This article describes a method for using optimization to derive efficient independent transition functions for Markov chain Monte Carlo simulations. Our interest is in sampling from a posterior density $\pi(x)$ for problems in which the…

We consider systems of stochastic differential equations with multiple scales and small noise and assume that the coefficients of the equations are ergodic and stationary random fields. Our goal is to construct provably-efficient importance…

It is one of the most challenging problems in applied mathematics to approximatively solve high-dimensional partial differential equations (PDEs). Recently, several deep learning-based approximation algorithms for attacking this problem…

In this article, we propose a Milstein finite difference scheme for a stochastic partial differential equation (SPDE) describing a large particle system. We show, by means of Fourier analysis, that the discretisation on an unbounded domain…

Neural Stochastic Differential Equations (NSDEs) model the drift and diffusion functions of a stochastic process as neural networks. While NSDEs are known to make accurate predictions, their uncertainty quantification properties have been…

Dynamical models of cognition play an increasingly important role in driving theoretical and experimental research in psychology. Therefore, parameter estimation, model analysis and comparison of dynamical models are of essential…

We develop the method of stochastic modified equations (SME), in which stochastic gradient algorithms are approximated in the weak sense by continuous-time stochastic differential equations. We exploit the continuous formulation together…

A method based on multicanonical Monte Carlo is applied to the calculation of large deviations in the largest eigenvalue of random matrices. The method is successfully tested with the Gaussian orthogonal ensemble (GOE), sparse random…

Monte Carlo approximations for random linear elliptic PDE constrained optimization problems are studied. We use empirical process theory to obtain best possible mean convergence rates $O(n^{-\frac{1}{2}})$ for optimal values and solutions,…

We present a novel multilevel Monte Carlo approach for estimating quantities of interest for stochastic partial differential equations (SPDEs). Drawing inspiration from [Giles and Szpruch: Antithetic multilevel Monte Carlo estimation for…

This paper proposes a new approach for Bayesian and maximum likelihood parameter estimation for stationary Gaussian processes observed on a large lattice with missing values. We propose an MCMC approach for Bayesian inference, and a Monte…

Partial differential equations (PDEs) with spatially-varying coefficients arise throughout science and engineering, modeling rich heterogeneous material behavior. Yet conventional PDE solvers struggle with the immense complexity found in…

A maximum likelihood methodology for the parameters of models with an intractable likelihood is introduced. We produce a likelihood-free version of the stochastic approximation expectation-maximization (SAEM) algorithm to maximize the…

We consider the problem of Bayesian parameter estimation for deep neural networks, which is important in problem settings where we may have little data, and/ or where we need accurate posterior predictive densities, e.g., for applications…

We address numerical differentiation under coarse, non-uniform sampling and Gaussian noise. A maximum-likelihood estimator with $L_2$-norm constraint on a higher-order derivative is obtained, yielding spline-based solution. We introduce a…

In this paper we consider sequential joint state and static parameter estimation given discrete time observations associated to a partially observed stochastic partial differential equation (SPDE). It is assumed that one can only estimate…