The identification problem of reconstructability analysis: A general method for estimation and optimal resolution of local inconsistency.

摘要

Reconstructability Analysis is a field within systems theory that studies relationships between systems and their subsystems. The Identification Problem (IP) of reconstructability analysis is concerned with estimating the distribution of states of an overall system, given observations on its subsystems. For discrete probabilistic systems, the conventional IP solution is the probability distribution having maximum uncertainty (Shannon entropy), subject to the constraint that projections of this system match the observed subsystems.;A general solution to IP in the presence of local inconsistency is provided in this dissertation. The methodology involves, first, estimation of a locally consistent set of subsystems from the data, then identification of the overall system from this locally consistent set using the conventional maximum uncertainty approach. The first step is the main contribution of this dissertation.;Local inconsistencies are viewed as arising from sampling or measurement error. Under this assumption, there exists a "true" set of locally consistent subsystems, of which the data are an imperfectly observed realization. The problem lies in estimating the "true" set. In this research, the "best" estimate is specified as that set of subsystems for which a discrimination information statistic from the data is globally minimized, subject to the constraint of local consistency. Solution of this minimization leads to two computational steps which are iterated on the data until a stopping criterion is reached.;This method is applied to estimation of the spatial distribution of households, by socio-economic characteristics, in order to estimate trip generation for a transportation simulation model. Locally inconsistent data are common in this field, and systemic information is therefore ignored due to lack of methods for resolving local inconsistencies. The application shows that resolution of local inconsistencies is feasible for very large problems involving thousands of states; and that simulation results are significantly improved when information in the overall system is utilized.;In practice, observed subsystems often exhibit "local inconsistency," characterized by inequality of marginal distributions that are common to two or more subsystems. An overall system cannot be identified from a locally inconsistent data set because the feasible region for the constrained uncertainty optimization is empty.