Abstract #300825


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JSM 2002 Abstract #300825
Activity Number: 257
Type: Contributed
Date/Time: Tuesday, August 13, 2002 : 2:00 PM to 3:50 PM
Sponsor: Section on Government Statistics*
Abstract - #300825
Title: Disclosure Limitation in Multi-way Contingency Tables
Author(s): Adrian Dobra*+
Affiliation(s): National Institute of Statistical Sciences
Address: 19 T. W. Alexander Dr., Research Triangle Park, North Carolina, 27709-4006,
Keywords: contingency tables ; disclosure limitation ; decomposable models ; markov bases
Abstract:

Disseminating information from a k-way cross classification of non-negative counts typically corresponds to the release of various lower order marginals, or equivalently subsets of the k variables. We show how graphical models can be exploited to characterize classes of tables W induced by several possibly overlapping marginals. In the special case when these marginals correspond to the minimal sufficient statistics of a decomposable graphical model, we develop explicit formulas for the upper and lower bounds on the cell entries of tables in W. In addition, these bounds results are related to the Markov basis used to induce probability distributions over W. The approach for computing bounds and for generating Markov bases generalizes to the case when the released marginals correspond to a reducible independence graph. We illustrate the practical values of the bound and distribution results for assessing the disclosure risk for categorical data. We also present a simulated annealing approach for finding an optimal configuration of released marginals.


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