Inference about a Binomial Proportion under Privacy Protection

Adam Hall; Nitul Singha; Bimal Sinha

doi:10.3329/ijss.v26i1.88827

Inference about a Binomial Proportion under Privacy Protection

Authors

Adam Hall Center for Statistical Research and Methodology, US Census Bureau, USA
Nitul Singha Department of Mathematics, Clarkson University, USA
Bimal Sinha Center for Statistical Research and Methodology, US Census Bureau, USA

DOI:

https://doi.org/10.3329/ijss.v26i1.88827

Keywords:

Binomial proportion, Noise addition, Plug-in sampling, Posterior predictive sampling, Privacy, Synthetic data.

Abstract

In this paper we consider the inferential problem for a Binomial proportion in situations when the exact number of units possessing an attribute under consideration is unavailable due to privacy reasons; however a synthesized version of this number is available. The inference problem is addressed under three types of available information: noise added version and plug-in sampling based and posterior sampling based data. A comparison of the three modes of data source is made based on inferential accuracy and a measure of privacy.

IJSS, Vol. 26(1), March, 2026, pp 65-82

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Published

2026-04-21

How to Cite

Hall, A., Singha, N., & Sinha, B. (2026). Inference about a Binomial Proportion under Privacy Protection. International Journal of Statistical Sciences , 26(1), 65–82. https://doi.org/10.3329/ijss.v26i1.88827