Simple stochastic models are widely used to describe complex phenomena, as they provide an interpretable connection between minimal microscopic descriptions and macroscopic statistical patterns. A central challenge in this approach is selecting the appropriate model—and its parameters—to accurately capture specific datasets. In this talk, I present a framework based on change-of-measure theory and bridge processes to perform parametric inference and assess model distinguishability using path statistics. With this tool, we identify optimal sampling protocols that minimize errors in parameter estimation, while also revealing fundamental limits of inference: the ability to discriminate between competing models is intrinsically constrained by data quality (e.g., sampling frequency and dataset size). We illustrate the framework with applications to diverse datasets (particle trapped with optical tweezers, human microbiome, topic mentions in social media, and forest population dynamics) showing how inference limits manifest in practice and inform ongoing modeling debates. The talk aims to give an overview of the state of the art in model inference, highlighting both current methodologies and their inherent limitations.