Understanding process variations and their impact in silicon photonics remains challenging. To achieve high-yield manufacturing, a key step is to extract the magnitude and spatial distribution of process variations in the actual fabrication, which is usually based on measurements of replicated test structures. In this paper, we develop a Bayesian-based method to infer the distribution of systematic geometric variations in silicon photonics, without requiring replication of identical test structures. We apply this method to characterization data from multiple silicon nitride ring resonators with different design parameters. We extract distributions with standard deviation of 28 nm, 0.8 nm, and 3.8 nm for the width, thickness, and partial etch depth, respectively, as well as the spatial maps of these variations. Our results show that this characterization and extraction approach can serve as an efficient method to study process variation in silicon photonics, facilitating the design of high-yield silicon photonic circuits in the future.