  Bayesian inference is applied to the level fluctuations of two coupled
microwave billiards in order to extract the coupling strength. The coupled
resonators provide a model of a chaotic quantum system containing two coupled
symmetry classes of levels. The number variance is used to quantify the level
fluctuations as a function of the coupling and to construct the conditional
probability distribution of the data. The prior distribution of the coupling
parameter is obtained from an invariance argument on the entropy of the
posterior distribution.
