# Resolution of Local Inconsistency in Identification

### Doug Anderson and Martin Zwick

Presented at the International Institute for General Systems Studies,
Second Workshop, Jan. 9-11, 1997, Southwest Texas State University,
San Marcos, Texas.

### Abstract

This paper reports an algorithm for the resolution of local inconsistency
in information-theoretic identification. This problem was first
pointed out by Klir as an important research area in reconstructability
analysis. Local inconsistency commonly arises when an attempt
is made to integrate multiple data sources, i.e., contingency
tables, which have differing common margins. For example, if one
has an AB table and a BC table, the B margins obtained from the
two tables may disagree. If the disagreement can be assigned to
sampling error, then one can arrive at a compromise B margin,
adjust the original AB and BC tables to this new B margin, and
then obtain the integrated ABC table by the conventional maximum
uncertainty solution.

The problem becomes more complicated when the common margins themselves
have common margins. The algorithm is an iterative procedure which
handles this complexity by sequentially resolving increasingly
higher dimensional inconsistencies. The algorithm is justified
theoretically by maximum likelihood arguments. It opens up the
possibility of many new applications in information theoretic
modeling and forecasting. One such application, involving transportation
studies in the Portland area, will be briefly discussed.