Non-parametric Inference for Diffusion Processes: A Computational Approach via Bayesian Inversion for PDEs

TL;DR

This paper introduces a Bayesian non-parametric framework for inferring drift and diffusion functions of diffusion processes using PDE-based methods, with initial results on single and multiscale data.

Contribution

It develops a novel computational approach combining PDEs and Bayesian inference for non-parametric analysis of diffusion processes.

Findings

Successful inference of single-scale diffusion processes

Initial results on multiscale process inference

Demonstrates the feasibility of PDE-based Bayesian methods

Abstract

In this paper, we present a theoretical and computational workflow for the non-parametric Bayesian inference of drift and diffusion functions of autonomous diffusion processes. We base the inference on the partial differential equations arising from the infinitesimal generator of the underlying process. Following a problem formulation in the infinite-dimensional setting, we discuss optimization- and sampling-based solution methods. As preliminary results, we showcase the inference of a single-scale, as well as a multiscale process from trajectory data.