Related papers: Inference in stochastic differential equations usi…
We recently proposed a method for estimation of states and parameters in stochastic differential equations, which included intermediate time points between observations and used the Laplace approximation to integrate out these intermediate…
We consider the task of generating discrete-time realisations of a nonlinear multivariate diffusion process satisfying an It\^o stochastic differential equation conditional on an observation taken at a fixed future time-point. Such…
Parameter inference for stochastic differential equations is challenging due to the presence of a latent diffusion process. Working with an Euler-Maruyama discretisation for the diffusion, we use variational inference to jointly learn the…
This paper is concerned with fully discrete mixed finite element approximations of the time-dependent stochastic Stokes equations with multiplicative noise. A prototypical method, which comprises of the Euler-Maruyama scheme for time…
State-space models provide an important body of techniques for analyzing time-series, but their use requires estimating unobserved states. The optimal estimate of the state is its conditional expectation given the observation histories, and…
State-space models are used to describe and analyse dynamical systems. They are ubiquitously used in many scientific fields such as signal processing, finance and ecology to name a few. Particle filters are popular inferential methods used…
Ordinary differential equations are arguably the most popular and useful mathematical tool for describing physical and biological processes in the real world. Often, these physical and biological processes are observed with errors, in which…
Inferring dynamical models from low-resolution temporal data continues to be a significant challenge in biophysics, especially within transcriptomics, where separating molecular programs from noise remains an important open problem. We…
We address the problem of estimating unknown model parameters and state variables in stochastic reaction processes when only sparse and noisy measurements are available. Using an asymptotic system size expansion for the backward equation we…
Many stochastic differential equations (SDEs) in the literature have a superlinearly growing nonlinearity in their drift or diffusion coefficient. Unfortunately, moments of the computationally efficient Euler-Maruyama approximation method…
Stochastic Differential Equations (SDEs) serve as a powerful modeling tool in various scientific domains, including systems science, engineering, and ecological science. While the specific form of SDEs is typically known for a given…
A method for sequential inference of the fixed parameters of a dynamic latent Gaussian models is proposed and evaluated that is based on the iterated Laplace approximation. The method provides a useful trade-off between computational…
We introduce a nonparametric approach for estimating drift and diffusion functions in systems of stochastic differential equations from observations of the state vector. Gaussian processes are used as flexible models for these functions and…
Using a hierarchical construction, we develop methods for a wide and flexible class of models by taking a fully parametric approach to generalized linear mixed models with complex covariance dependence. The Laplace approximation is used to…
We consider one-step methods for integrating stochastic differential equations and prove pathwise convergence using ideas from rough path theory. In contrast to alternative theories of pathwise convergence, no knowledge is required of…
Optimal state estimation for linear discrete-time systems is considered. Motivated by the literature on differential privacy, the measurements are assumed to be corrupted by Laplace noise. The optimal least mean square error estimate of the…
In this paper, we construct a type of interacting particle systems to approximate a class of stochastic different equations whose coefficients depend on the conditional probability distributions of the processes given partial observations.…
We study parameter estimation for univariate stochastic differential equations with locally Lipschitz drift and H\"older continuous multiplicative diffusion, a class commonly arising in several applications. Existing inference methods…
A goal of data assimilation is to infer stochastic dynamical behaviors with available observations. We consider transition phenomena between metastable states for a stochastic system with (non-Gaussian) $\alpha-$stable L\'evy noise. With…
We consider a generic and explicit tamed Euler--Maruyama scheme for multidimensional time-inhomogeneous stochastic differential equations with multiplicative Brownian noise. The diffusive coefficient is uniformly elliptic, H\"older…