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 Bézier 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 Bézier 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.

SUMMARY: Deep mutational scanning (DMS) experiments provide a powerful method to measure the functional effects of genetic mutations at massive scales. However, the data generated from these experiments can be difficult to analyze, with significant variation between experimental replicates. To overcome this challenge, we developed popDMS, a computational method based on population genetics theory, to infer the functional effects of mutations from DMS data. Through extensive tests, we found that the functional effects of single mutations and epistasis inferred by popDMS are highly consistent across replicates, comparing favorably with existing methods. Our approach is flexible and can be widely applied to DMS data that includes multiple time points, multiple replicates, and different experimental conditions. AVAILABILITY AND IMPLEMENTATION: popDMS is implemented in Python and Julia, and is freely available on GitHub at https://github.com/bartonlab/popDMS.