Bayesian Analysis of Variance for Repeat S-Parameter Measurements

We utilize Bayesian analysis of variance to estimate the effects of calibration and disconnect levels for repeated scattering-parameter measurements made with a vector network analyzer. Here, we describe the Bayesian estimation technique, including our random effects model, prior assumptions, Markov chain Monte Carlo simulations, and convergence diagnostics. Our data is structured hierarchically, such that measurements are nested within repeats, which are nested within disconnects, which are further nested within calibrations. We compare our results to a previously developed method-of-moments estimator using measured data involving WR-28 waveguide (26.5 GHz to 40.0 GHz) and show how Bayesian analysis allows us to avoid negative variance estimates by incorporating realistic prior information.