  This two-part paper presents a new approach to predictive analysis for social
processes. In Part I, we begin by identifying a class of social processes which
are simultaneously important in applications and difficult to predict using
existing methods. It is shown that these processes can be modeled within a
multi-scale, stochastic hybrid system framework that is sociologically
sensible, expressive, illuminating, and amenable to formal analysis. Among
other advantages, the proposed modeling framework enables proper
characterization of the interplay between the intrinsic aspects of a social
process (e.g., the appeal of a political movement) and the social dynamics
which are its realization; this characterization is key to successful social
process prediction. The utility of the modeling methodology is illustrated
through a case study involving the global SARS epidemic of 2002-2003. Part II
of the paper then leverages this modeling framework to develop a rigorous,
computationally tractable approach to social process predictive analysis.
