Title: Quantifying Statistical Independence in ExperimentalEnsembles of Microwave Measurements
 Abstract: Statistical ensembles underpinexperimental characterization in complex physical systems, yet objectivecriteria for assessing ensemble quality and determining sufficient sample sizeremain limited. In this work, we introduce a quantitative framework formeasuring statistical independence among frequency-dependent scattering matrixrealizations and demonstrate how it can be used to optimize experimental dataacquisition.
Wedefine an independence index derived from pairwise correlations betweenrealizations, formulated through both linear inner-product measures andnonlinear distance-based kernels. A fast, matrix-based implementation enablesefficient computation for large ensembles without explicit pairwise loops. Central to the framework is an interaction matrix that captures the statisticalrelationship between realizations and whose distribution provides insight intoensemble quality.
We applythis methodology to both Random Matrix Theory–generated ensembles andexperimental measurements from a reconfigurable electromagnetic cavity undermechanical, electronic, and mixed mode-stirring conditions. The independenceindex is shown to correlate with physically meaningful parameters such as lossfactor and coupling, while revealing deficiencies in poorly constructedensembles. Leveraging the interaction matrix, we demonstrate that reorderingrealizations to minimize mutual interaction can significantly improve ensembleindependence, reduce parameter estimation error, and enable early stopping ofexperiments with minimal loss of fidelity.
Thisframework provides a general, computationally efficient tool for assessingensemble quality, guiding adaptive experiment design, and balancing accuracyagainst measurement cost, with potential applications across complex andchaotic physical systems.
Advisor: Steve Anlage