Recent advances in experimental biology provide time-resolved datasets that capture key features of complex dynamical systems. Recovering the underlying interactions from such data is a nontrivial inverse problem, especially when one must disentangle deterministic dynamics, intrinsic fluctuations, and measurement noise from limited observations.

We build on the inference framework introduced by Bruckner et al. (2020), which is designed to operate in the moderate-data regime. Our main contribution is to replace the heuristic choices in the original derivation by a controlled expansion of the inference error. This leads to more accurate approximations, identifies the relevant small parameters, and makes the associated validity conditions explicit. The result is an efficient and broadly applicable framework for inferring stochastic dynamics from limited, sparsely sampled data.