B\'ezier interpolation improves the inference of dynamical models from data

TL;DR

This paper introduces a Bézier interpolation framework that enhances the accuracy of estimating time-integrated quantities in stochastic dynamical systems from limited, finitely sampled data, reducing bias in inference tasks.

Contribution

The authors develop a novel Bézier interpolation method that improves dynamical inference accuracy from limited data, demonstrated on population fitness and Ornstein-Uhlenbeck processes.

Findings

Bézier interpolation reduces estimation bias in dynamical inference.

The method performs especially well with limited time resolution data.

Broad applicability to various dynamical inference problems.

Abstract

Many dynamical systems, from quantum many-body systems to evolving populations to financial markets, are described by stochastic processes. Parameters characterizing such processes can often be inferred using information integrated over stochastic paths. However, estimating time-integrated quantities from real data with limited time resolution is challenging. Here, we propose a framework for accurately estimating time-integrated quantities using B\'ezier interpolation. We applied our approach to two dynamical inference problems: determining fitness parameters for evolving populations and inferring forces driving Ornstein-Uhlenbeck processes. We found that B\'ezier interpolation reduces the estimation bias for both dynamical inference problems. This improvement was especially noticeable for data sets with limited time resolution. Our method could be broadly applied to improve accuracy for other dynamical inference problems using finitely sampled data.