## 1. Introduction

[2] The increasing spatial and spectral density of the electromagnetic (EM) environment in which modern electronic equipment is operating calls for accurate, efficient and reliable EM characterization methods. Precise and quantified statements regarding the confidence limits and expected value for EM quantities of interest are essential and critical in estimating safety, integrity, reliability and compatibility of interacting electronic systems and their elements or subsystems. With regard to modeling of such systems, a range of full wave computational EM methods is now available and routinely used for their numerical simulation. However, these methods carry large data processing efforts and computational costs with them when applied to complex, intricately detailed or electrically large objects. Moreover, the discretization (meshing) performed when numerically implementing these methods introduces an inevitable staircasing effect. This poses an inherent limitation on their accuracy, especially for those electrically large or resonant systems that exhibit extreme, that is, nonperturbative sensitivity of the field to relatively small changes in the configuration or EM properties of boundary surfaces, as well as to their inherent mechanical or constitutive uncertainties (tolerances).

[3] Statistical electromagnetism offers an efficient alternative method of analysis with experimentally demonstrated validity in a variety of application areas. Crucially, unlike deterministic numerical methods, its accuracy and simplicity increase with increasing complexity of the configuration. Information on uncertainty and sensitivity of the fields and related quantities is inherent to such a formulation, making it ideally suited for benchmarking, validation and standardization. Some of the main challenges of statistical EM are the extension of ideal first- and second-order statistical characterizations to realistic conditions of operation (e.g., extension to relatively low frequency, finite regions, finite conductivity of boundaries, partial coherence, etc.), by introducing an appropriate number of additional distribution parameters and degrees of freedom, and the independent calculation of the statistics of physical quantities based on an adequate EM model (i.e., expressing the mean, standard deviation, etc., in terms of geometrical, topological and EM quantities, independently, without recourse to statistical estimation methods using collected numerical data). The latter is needed for proper validation of the model, because a simple comparison between the statistical distributions of theoretical and experimental data is only based on variates that have been normalized or standardized with the aid of their own estimated sample statistics (typically the experimental sample mean or sample standard deviation), thus cancelling quantitative information on the dimensioned quantities of interest. In other words, such a comparison only confirms the validity of the type of distribution and “noise color,” not the accuracy of the EM parameters characterizing this distribution in absolute as opposed to relative terms.