Hypersonic shock-tunnels replicate high-speed flows in a controlled environment, and are essential for validating hypersonic vehicle designs. Their objective is to produce a spatially uniform freestream. However, extreme operating conditions preclude direct observation of the flow. Freestream properties are thus inferred from indirect measurements, introducing significant uncertainty. Poorly characterized freestream conditions limit the reliability of validation experiments on test-articles. [1,2,3,4] all document errors between experimental sensor-recorded surface quantities on the test-article and CFD across a range of tests. [5] shows that these errors can be dominated by differing freestream conditions between tunnel and CFD. Ray et al[6]. introduce a Bayesian inference framework that maps freestream conditions to surface sensor quantities, enabling Bayesian inversion for freestream characterization. Their results show that the most probable freestream conditions often lie outside uncertainty bounds reported by the facility. However, the inferred posterior distributions exhibit large variance, and their MAP values do not consistently reconcile CFD predictions with experimental measurements. Prior studies[7] further demonstrate that hypersonic tunnels can generate complex, non-ideal freestream conditions, complicating inverse analyses. This work aims to validate and interrogate the Bayesian framework of Ray et al. in a controlled setting. A known, uniform, steady, perfect-gas freestream is prescribed, and synthetic surface sensor data are generated by perturbing modeled responses with a known probability distribution. A Markov Chain Monte Carlo method is then used to solve the Bayesian inverse problem, yielding posterior distributions over the most likely freestream conditions and their associated uncertainty. By validating this Bayesian inference method, we will be able to systematically remove assumptions about freestream conditions, and test the method's ability to construct more complex conditions until we can confidently apply the method to tunnel cases. In doing so, we will learn which freestream impurities play the biggest role in validation mismatches.