Some applications of functional networks in statistics and engineering

Functional networks are a general framework useful for solving a wide range of problems in probability, statistics, and engineering applications. In t his article, we demonstrate that functional networks can be used for many g eneral purposes including (a) solving nonlinear regression problems without the rather strong assumption of a known functional form, (b) modeling chao tic time series data, (c) finding conjugate families of distribution Functi ons needed for the applications of Bayesian statistical techniques, (d) ana lyzing the problem of stability with respect to maxima operations, which ar e useful in the theory and applications of extreme values, and (e) modeling the reproductivity and associativity laws that have many applications in a pplied probability. We also give two specific engineering applications-anal yzing the Ikeda map with parameters leading to chaotic behavior and modelin g beam stress subject to a,given load. The main purpose of this article is to introduce functional networks and to show their power and usefulness in engineering and statistical applications. We describe the steps involved in working with functional networks including structural learning (specificat ion and simplification of the initial topology), parametric learning, and m odel-selection procedures. The concepts and methodologies are illustrated u sing several examples of applications.