<p>We introduce a Bayesian framework leveraging synthetic likelihoods to enable uncertainty quantification and robust inference of non-bonded force parameters in three-point water models. The approach integrates multiple experimental observables—enthalpy of vaporization, molecular volume, the radial distribution function, and hydrogen bonding patterns—to explicitly infer model parameters. Beyond parameter estimation, we quantify uncertainty in both inference observables and validation properties, including those that are difficult to target by other means. By systematically analyzing the response of these observables to parameter variations, our method highlights inherent limitations of three-point water models. These findings highlight the utility of our framework in integrating diverse data sources in a principled uncertainty quantification workflow, ultimately improving confidence in the ability of molecular dynamics simulations to reproduce experimental data. Additionally, we evaluate the performance of the mean and the mode of the posterior distribution, demonstrating the limitations of this family of models.</p>