Nonparametric inference of doubly stochastic Poisson process data via the kernel method

TL;DR

This paper introduces a nonparametric kernel-based method for inferring doubly stochastic Poisson processes, with applications to biophysical data revealing complex protein dynamics across multiple time scales.

Contribution

It develops a novel kernel inference approach with asymptotic analysis and practical bandwidth selection, specifically tailored for Cox process data in biophysics.

Findings

Conformational fluctuations are common in proteins.

Protein fluctuations occur over a broad range of time scales.

The method effectively analyzes real photon arrival data.

Abstract

Doubly stochastic Poisson processes, also known as the Cox processes, frequently occur in various scientific fields. In this article, motivated primarily by analyzing Cox process data in biophysics, we propose a nonparametric kernel-based inference method. We conduct a detailed study, including an asymptotic analysis, of the proposed method, and provide guidelines for its practical use, introducing a fast and stable regression method for bandwidth selection. We apply our method to real photon arrival data from recent single-molecule biophysical experiments, investigating proteins' conformational dynamics. Our result shows that conformational fluctuation is widely present in protein systems, and that the fluctuation covers a broad range of time scales, highlighting the dynamic and complex nature of proteins' structure.