Non-linear interpolation for genetic fitness prediction*

In numerical integration based on discrete data points, the choice of integration methods is crucial. Applying Itô or Stratonovich integration that is commonly used in stochastic calculus can lead to significantly different outcomes [1]. In this talk, we propose a stochastic non-linear interpolation method using Bézier’s method [2]. This method is simple and broadly applicable to physical systems. As an example, we apply our approach to the Marginal Path Likelihood method, a genomic fitness inference method based on the stochastic processes and formulated through a path integral [3]. 

[1] Van Kampen, Nicolaas G. "Itô versus stratonovich." Journal of Statistical Physics 24.1 (1981): 175-187.

[2] Bézier, Pierre. "Procédé de définition numérique des courbes et surfaces non mathématiques." Automatisme 13.5 (1968): 189-196.

[3] Sohail, Muhammad Saqib, et al. "MPL resolves genetic linkage in fitness inference from complex evolutionary histories." Nature Biotechnology 39.4 (2021): 472-479.