A Bayesian Hierarchical Model Approach to Risk Estimation in Statistical Disclosure Limitation

Polettini, Silvia; Stander, Julian

doi:10.1007/978-3-540-25955-8_19

Cited by 8 publications

(7 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Benedetti and Franconi use a Bayesian approach to estimate measure 5, E (1/ F j | f j ), by modeling the distribution of population frequencies given the sample frequencies, or F j | f j . They use the superpopulation approach to model the following:

\begin{matrix} π_{j} & \sim false[π_{j} false] \propto 1 false/ π_{j}, π_{j} > 0, j = 1, ⋯, J, \\ F_{j} false| π_{j} & \sim P o i s s o n false(N π_{j} false), F_{j} = 0, 1, ⋯, \\ f_{j} false| F_{j}, π_{j}, p_{j} & \sim B i n o m i a l false(F_{j}, p_{j} false), f_{j} = 0, 1, ⋯, F_{j} . \end{matrix}

Under these assumptions, the posterior distribution F j | f j has a negative binomial distribution with f j successes and probability of success p j where

P r (F_{j} = r | f_{j}) = (\frac{0}{r - 1}) p_{j}^{f_{j}} {(1 - p_{j})}^{r - f_{j}}, r = 1, 2, ⋯, r \geq f_{j}, f_{j} > 0 .

Polettini and Stander develop a Bayesian hierarchical model with the following model specifications:

\begin{matrix} π_{j} & \sim g a m m a false(α, λ false), π_{j} > 0, j = 1, ⋯, J, \\ F_{j} false| π \end{matrix}

…”

Section: Assessing Disclosure Riskmentioning

confidence: 99%

A tutorial in assessing disclosure risk in microdata

Taylor

Zhou

Rise

2018

Statistics in Medicine

View full text Add to dashboard Cite

Statistical agencies are releasing statistical data to other agencies for research purposes or to inform public policy. Prior to data release, these agencies have a legal and ethical obligation to protect the confidentiality of individuals in the data. Agencies often release altered versions of the data, but there usually remains risks of disclosure. Many well-studied risk measures are available to assess risk; however, many agencies today continue to use subjective judgement, past experience, and ad hoc rules or checklists to assess disclosure risk. More recently, there has been a recognized demand for quantitative risk measures that provide a more objective criteria for data release. This tutorial provides an overview of the statistical disclosure control framework for microdata. We focus on the risk analysis stage within this framework by defining existing disclosure risk measures and how to estimate them with available software.

show abstract

\begin{matrix} π_{j} & \sim false[π_{j} false] \propto 1 false/ π_{j}, π_{j} > 0, j = 1, ⋯, J, \\ F_{j} false| π_{j} & \sim P o i s s o n false(N π_{j} false), F_{j} = 0, 1, ⋯, \\ f_{j} false| F_{j}, π_{j}, p_{j} & \sim B i n o m i a l false(F_{j}, p_{j} false), f_{j} = 0, 1, ⋯, F_{j} . \end{matrix}

Under these assumptions, the posterior distribution F j | f j has a negative binomial distribution with f j successes and probability of success p j where

P r (F_{j} = r | f_{j}) = (\frac{0}{r - 1}) p_{j}^{f_{j}} {(1 - p_{j})}^{r - f_{j}}, r = 1, 2, ⋯, r \geq f_{j}, f_{j} > 0 .

Polettini and Stander develop a Bayesian hierarchical model with the following model specifications:

\begin{matrix} π_{j} & \sim g a m m a false(α, λ false), π_{j} > 0, j = 1, ⋯, J, \\ F_{j} false| π \end{matrix}

…”

Section: Assessing Disclosure Riskmentioning

confidence: 99%

A tutorial in assessing disclosure risk in microdata

Taylor

Zhou

Rise

2018

Statistics in Medicine

View full text Add to dashboard Cite

show abstract

“…More recently, Ting, Fienberg and Trottini (2008) contrasted their method of random orthogonal matrix masking with other microdata perturbation methods, such as additive noise, from the Bayesian perspective of the trade-off between disclosure risk and data utility. This work has yet to be adopted by statistical agencies, but related Bayesian modeling in the same spirit by Franconi and Stander (2002), Polettini and Stander (2004), Rinott and Shlomo (2007) and Forster and Webb (2007) has been done in close collaboration with those in agencies in Israel, Italy and the United Kingdom.…”

Section: Confidentiality and The Risk-utility Trade-offmentioning

confidence: 99%

Bayesian Models and Methods in Public Policy and Government Settings

Fienberg¹

2011

Statist. Sci.

View full text Add to dashboard Cite

Starting with the neo-Bayesian revival of the 1950s, many statisticians argued that it was inappropriate to use Bayesian methods, and in particular subjective Bayesian methods in governmental and public policy settings because of their reliance upon prior distributions. But the Bayesian framework often provides the primary way to respond to questions raised in these settings and the numbers and diversity of Bayesian applications have grown dramatically in recent years. Through a series of examples, both historical and recent, we argue that Bayesian approaches with formal and informal assessments of priors AND likelihood functions are well accepted and should become the norm in public settings. Our examples include census-taking and small area estimation, US election night forecasting, studies reported to the US Food and Drug Administration, assessing global climate change, and measuring potential declines in disability among the elderly.Comment: Published in at http://dx.doi.org/10.1214/10-STS331 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

show abstract

“…Early papers with these statistical risk measures are by Bethlehem et al [6], Fienberg and Makov [25], Benedetti and Franconi [5] and Skinner and Holmes [59]. Later papers with enhanced methods are due to Skinner and Elliot [58], Rinott [53], and Polettini and Stander [47]. The apparent intent is to provide a straightforward, rapid method of estimating the proportion of sample uniques that are also population uniques.…”

Section: Re-identification Of Microdatamentioning

confidence: 99%

Masking and Re-identification Methods for Public-Use Microdata: Overview and Research Problems

Winkler

2004

Privacy in Statistical Databases

View full text Add to dashboard Cite

This paper provides an overview of methods of masking microdata so that the data can be placed in public-use files. It divides the methods according to whether they have been demonstrated to provide analytic properties or not. For those methods that have been shown to provide one or two sets of analytic properties in the masked data, we indicate where the data may have limitations for most analyses and how re-identification might or can be performed. We cover several methods for producing synthetic data and possible computational extensions for better automating the creation of the underlying statistical models. We finish by providing background on analysis-specific and general information-loss metrics to stimulate research. Disclaimer: This report is released to inform interested parties of research and to encourage discussion. The views expressed are those of the author and not necessarily those of the U. S. Census Bureau. The author thanks Nancy Gordon, Cynthia Clark, and two reviewers for comments leading to improved wording and explanation and several additional references.

show abstract

A Bayesian Hierarchical Model Approach to Risk Estimation in Statistical Disclosure Limitation

Cited by 8 publications

References 6 publications

A tutorial in assessing disclosure risk in microdata

A tutorial in assessing disclosure risk in microdata

Bayesian Models and Methods in Public Policy and Government Settings

Masking and Re-identification Methods for Public-Use Microdata: Overview and Research Problems

Contact Info

Product

Resources

About