Aspects of inference for the Influence Model and related graphical models

Abstract

The Influence Model (IM), developed with the primary motivation of describing network dynamics in power systems, has proved to be very useful in a variety of contexts. It consists of a directed graph of interacting sites whose Markov state transition probabilities depend on their present state and that of their neighbors. The major goals of this thesis are (1) to place the Influence Model in the broader framework of graphical models, such as Bayesian networks, (2) to provide and discuss a hybrid model between the IM and dynamic Bayesian networks, (3) to discuss the use of inference tools available for such graphical models in the context of the IM, and (4) to provide some methods of estimating the unknown parameters that describe the IM. We hope each of these developments will enhance the use of IM as a tool for studying networked interact ions.