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

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