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A Data Disclosure Policy for Count Data Based on the COM-Poisson Distribution

Author

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  • Joseph B. Kadane

    (Department of Statistics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213)

  • Ramayya Krishnan

    (The Heinz School of Public Policy and Management, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213)

  • Galit Shmueli

    (Department of Decision and Information Technologies, Smith School of Business, University of Maryland, College Park, Maryland 20742)

Abstract

Count data arise in various organizational settings. When the release of such data is sensitive, organizations need information-disclosure policies that protect data confidentiality while still providing data access. In contrast to extant disclosure policies, we describe a new policy for count tables that is based on disclosing only the sufficient statistics of a flexible discrete distribution. This distribution, the COM-Poisson, well approximates Poisson counts but also under- and over-dispersed counts. The sufficient statistics mask the exact cell counts and often also the table size. Under the scenario of a data holding agency and a data snooper, we show that this policy has low disclosure risk with no loss of data utility: Usually, many count tables correspond to the disclosed sufficient statistics. Furthermore, these count tables are equally likely to be the undisclosed table. Finding these solutions requires solving a system of linear equations, which are underdetermined for tables with more than three cells, and can be computationally prohibitive for even small tables. We also consider cell-specific interval bounds, a commonly used disclosure limitation policy, and compare them to our policy. We describe several types of snooper knowledge, their integration with the disclosed statistics, and implications. Applying this policy to three real data sets, we illustrate the low associated disclosure risk.

Suggested Citation

  • Joseph B. Kadane & Ramayya Krishnan & Galit Shmueli, 2006. "A Data Disclosure Policy for Count Data Based on the COM-Poisson Distribution," Management Science, INFORMS, vol. 52(10), pages 1610-1617, October.
    • Handle: RePEc:inm:ormnsc:v:52:y:2006:i:10:p:1610-1617
    DOI: 10.1287/mnsc.1060.0562
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    References listed on IDEAS

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    1. Sumit Dutta Chowdhury & George T. Duncan & Ramayya Krishnan & Stephen F. Roehrig & Sumitra Mukherjee, 1999. "Disclosure Detection in Multivariate Categorical Databases: Auditing Confidentiality Protection Through Two New Matrix Operators," Management Science, INFORMS, vol. 45(12), pages 1710-1723, December.
    2. Rathindra Sarathy & Krishnamurty Muralidhar, 2002. "The Security of Confidential Numerical Data in Databases," Information Systems Research, INFORMS, vol. 13(4), pages 389-403, December.
    3. Galit Shmueli & Thomas P. Minka & Joseph B. Kadane & Sharad Borle & Peter Boatwright, 2005. "A useful distribution for fitting discrete data: revival of the Conway–Maxwell–Poisson distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(1), pages 127-142, January.
    4. Robert Garfinkel & Ram Gopal & Paulo Goes, 2002. "Privacy Protection of Binary Confidential Data Against Deterministic, Stochastic, and Insider Threat," Management Science, INFORMS, vol. 48(6), pages 749-764, June.
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    Cited by:

    1. Kimberly F. Sellers & Andrew W. Swift & Kimberly S. Weems, 2017. "A flexible distribution class for count data," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-21, December.
    2. Xiao-Bai Li & Sumit Sarkar, 2013. "Class-Restricted Clustering and Microperturbation for Data Privacy," Management Science, INFORMS, vol. 59(4), pages 796-812, April.
    3. Sunisa Junnumtuam & Sa-Aat Niwitpong & Suparat Niwitpong, 2022. "A Zero-and-One Inflated Cosine Geometric Distribution and Its Application," Mathematics, MDPI, vol. 10(21), pages 1-22, October.
    4. Amalia R. Miller & Catherine Tucker, 2009. "Privacy Protection and Technology Diffusion: The Case of Electronic Medical Records," Management Science, INFORMS, vol. 55(7), pages 1077-1093, July.
    5. Haibing Lu & Jaideep Vaidya & Vijayalakshmi Atluri & Yingjiu Li, 2015. "Statistical Database Auditing Without Query Denial Threat," INFORMS Journal on Computing, INFORMS, vol. 27(1), pages 20-34, February.

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