Browsing by Author "Sinha, Bimal"
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Item Bayesian Analysis of Multiply Imputed Synthetic Data Under the Multiple Linear Regression Model(Center for Statistical Research & Methodology Research and Methodology Directorate U.S. Census Bureau, 2022-04-04) Guin, Abhishek; Roy, Anindya; Sinha, BimalIn this paper we consider Bayesian inference of model parameters in a multiple linear regression model when the response variable is sensitive and the covariates are not, analysis being carried out based on multiple synthetic versions of the response variable. Two scenarios of synthetic data generation are considered - plug-in sampling method and posterior predictive sampling method. We also consider the case when part of the response is sensitive and describe how to carry out full Bayesian analysis based on multiply imputed data.Item Bayesian Analysis of Singly Imputed Partially Synthetic Data Generated by Plug-in Sampling and Posterior Predictive Sampling Under the Multiple Linear Regression Model(United States Census Bureau, 2021-08-25) Guin, Abhishek; Roy, Anindya; Sinha, BimalIn this paper we develop Bayesian inference based on singly imputed partially synthetic data, when the original data are derived from a multiple linear regression model. We assume that the synthetic data are generated by using two methods: plug-in sampling, where unknown parameters in the data model are set equal to observed values of their point estimators based on the original data, and synthetic data are drawn from this estimated version of the model; posterior predictive sampling, where an imputed posterior distribution of the unknown parameters is used to generate a posterior draw, which in turn is plugged in the original model to beget synthetic data. Simulation results are presented to demonstrate how the proposed methodology performs compared to the theoretical predictions. We outline some ways to extend the proposed methodology for certain scenarios where the required set of conditions do not hold.Item Bayesian Analysis of Singly Imputed Synthetic Data under the Multivariate Normal Model(Bangladesh Academy of Sciences, 2023-11-30) Guin, Abhishek; Roy, Anindya; Sinha, BimalWe develop appropriate Bayesian procedures to draw inference about the parameters under a multivariate normal model based on synthetic data. We consider two standard forms of synthetic data, generated under plug in sampling method and posterior predictive sampling method. In addition to point estimates of the mean vector and dispersion matrix, Bayesian credible sets for the mean vector and the generalized variance are also provided under both the scenarios. The analysis in the case when some (partial) features are sensitive and need to be hidden is also briey indicatedItem Multiple Imputation for Parametric Inference Under a Differentially Private Laplace Mechanism(2019-05-09) Klein, Martin; Sinha, BimalIn this paper we consider the scenario where continuous microdata have been noise infused using a differentially private Laplace mechanism for the purpose of statistical disclosure control. We assume the original data are independent and identically distributed, having distribution within a parametric family of continuous distributions. We employ a modification of the standard Laplace mechanism that allows the range of the original data to be unbounded. We propose methodology to analyze the noise infused data using multiple imputation. This approach allows the data user to analyze the released data as if it were original, i.e., not noise infused, and then to obtain inference that accounts for the noise infusion mechanism using standard multiple imputation combining formulas. Methodology is presented for univariate data, and some simulation studies are presented to evaluate the performance of the proposed method. An extension of the proposed methodology to multivariate data is also presented.Item Multivariate Normal Inference based on Singly Imputed Synthetic Data under Plug-in Sampling(2019-05-07) Klein, Martin; Moura, Ricardo; Sinha, BimalIn this paper we consider singly imputed synthetic data generated via plug-in sampling under the multivariate normal model. Based on the observed synthetic dataset, we derive a statistical test for the generalized variance, the sphericity test, a test for independence between two subsets of variables, and a test for the regression of one set of variables on the other. The procedures are based on finite sample theory. Some simulation studies are presented which confirm that the proposed procedures perform as expected