Related papers: Nonparametric Bayesian Inference for Stochastic Re…

An important task in the statistical analysis of inhomogeneous point processes is to investigate the influence of a set of covariates on the point-generating mechanism. In this article, we consider the nonparametric Bayesian approach to…

We construct deterministic particle solutions for linear and fast diffusion equations using a nonlocal approximation. We exploit the $2$-Wasserstein gradient flow structure of the equations in order to obtain the nonlocal approximating PDEs…

Flexible estimation of multiple conditional quantiles is of interest in numerous applications, such as studying the effect of pregnancy-related factors on low and high birth weight. We propose a Bayesian non-parametric method to…

We study the convergence rates of empirical Bayes posterior distributions for nonparametric and high-dimensional inference. We show that as long as the hyperparameter set is discrete, the empirical Bayes posterior distribution induced by…

The use of non parametric hidden Markov models with finite state space is flourishing in practice while few theoretical guarantees are known in this framework. Here, we study asymptotic guarantees for these models in the Bayesian framework.…

The classical Feynman-Kac formula states the connection between linear parabolic partial differential equations (PDEs), like the heat equation, and expectation of stochastic processes driven by Brownian motion. It gives then a method for…

We investigate Bayesian nonparametric density estimation via orthogonal polynomial expansions in weighted Sobolev spaces. A core challenge is establishing minimax optimal posterior convergence rates, especially for densities on unbounded…

Using an asymmetric Laplace distribution, which provides a mechanism for Bayesian inference of quantile regression models, we develop a fully Bayesian approach to fitting single-index models in conditional quantile regression. In this work,…

We study the rate of convergence of posterior distributions in density estimation problems for log-densities in periodic Sobolev classes characterized by a smoothness parameter p. The posterior expected density provides a nonparametric…

Bayesian methods are actively used for parameter identification and uncertainty quantification when solving nonlinear inverse problems with random noise. However, there are only few theoretical results justifying the Bayesian approach.…

Bernstein-von Mises theorems for nonparametric Bayes priors in the Gaussian white noise model are proved. It is demonstrated how such results justify Bayes methods as efficient frequentist inference procedures in a variety of concrete…

In many practical and numerical inverse problems, the exact data log-likelihood is not fully accessible, motivating the use of surrogate models. We study heteroscedastic nonparametric nonlinear regression problems with Gaussian errors and…

We derive the exact evolution equation for the probability density function of particle displacements generated by arbitrary Gaussian velocity processes, when neither Markovianity and nor stationarity are assumed. Starting from the…

The statistical inverse problem of estimating the probability distribution of an infinite-dimensional unknown given its noisy indirect observation is studied in the Bayesian framework. In practice, one often considers only…

A scheme is developed for estimating state-dependent drift and diffusion coefficients in a stochastic differential equation from time-series data. The scheme does not require to specify parametric forms for the drift and diffusion…

A generalisation of the Lie symmetry method is applied to classify a coupled system of reaction-diffusion equations wherein the nonlinearities involve arbitrary functions in the limit case in which one equation of the pair is quasi-steady…

This paper presents a study of the large-sample behavior of the posterior distribution of a structural parameter which is partially identified by moment inequalities. The posterior density is derived based on the limited information…

This work aims to estimate the drift and diffusion functions in stochastic differential equations (SDEs) driven by a particular class of L\'evy processes with finite jump intensity, using neural networks. We propose a framework that…

In Bayesian nonparametric models, Gaussian processes provide a popular prior choice for regression function estimation. Existing literature on the theoretical investigation of the resulting posterior distribution almost exclusively assume a…

We present a Bayesian non-parametric way of inferring stochastic differential equations for both regression tasks and continuous-time dynamical modelling. The work has high emphasis on the stochastic part of the differential equation, also…