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A Probabilistic Procedure for Anonymisation, for Assessing the Risk of Re-identification and for the Analysis of Perturbed Data Sets

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  • Goldstein Harvey

    (Graduate School of Education, University of Bristol, Bristol, BS8 1JA, UK.)

  • Shlomo Natalie

    (University of Manchester, Social Statistics, Humanities Bridgeford Street Manchester, M13 9PL, UK.)

Abstract

The requirement to anonymise data sets that are to be released for secondary analysis should be balanced by the need to allow their analysis to provide efficient and consistent parameter estimates. The proposal in this article is to integrate the process of anonymisation and data analysis. The first stage uses the addition of random noise with known distributional properties to some or all variables in a released (already pseudonymised) data set, in which the values of some identifying and sensitive variables for data subjects of interest are also available to an external ‘attacker’ who wishes to identify those data subjects in order to interrogate their records in the data set. The second stage of the analysis consists of specifying the model of interest so that parameter estimation accounts for the added noise. Where the characteristics of the noise are made available to the analyst by the data provider, we propose a new method that allows a valid analysis. This is formally a measurement error model and we describe a Bayesian MCMC algorithm that recovers consistent estimates of the true model parameters. A new method for handling categorical data is presented. The article shows how an appropriate noise distribution can be determined.

Suggested Citation

  • Goldstein Harvey & Shlomo Natalie, 2020. "A Probabilistic Procedure for Anonymisation, for Assessing the Risk of Re-identification and for the Analysis of Perturbed Data Sets," Journal of Official Statistics, Sciendo, vol. 36(1), pages 89-115, March.
    • Handle: RePEc:vrs:offsta:v:36:y:2020:i:1:p:89-115:n:5
    DOI: 10.2478/jos-2020-0005
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    References listed on IDEAS

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    1. Shlomo, Natalie & Skinner, Chris J., 2010. "Assessing the protection provided by misclassification-based disclosure limitation methods for survey microdata," LSE Research Online Documents on Economics 39119, London School of Economics and Political Science, LSE Library.
    2. Lawrence H. Cox & Alan F. Karr & Satkartar K. Kinney, 2011. "Risk‐Utility Paradigms for Statistical Disclosure Limitation: How to Think, But Not How to Act," International Statistical Review, International Statistical Institute, vol. 79(2), pages 160-183, August.
    3. Harvey Goldstein & James Carpenter & Michael G. Kenward, 2018. "Bayesian models for weighted data with missing values: a bootstrap approach," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 67(4), pages 1071-1081, August.
    4. Delaigle, Aurore & Hall, Peter, 2008. "Using SIMEX for Smoothing-Parameter Choice in Errors-in-Variables Problems," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 280-287, March.
    5. Jerome P. Reiter, 2005. "Releasing multiply imputed, synthetic public use microdata: an illustration and empirical study," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 168(1), pages 185-205, January.
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