Browsing by Author "Guin, Abhishek"
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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 Bayesian Analysis of Synthetic Data under Multiple Linear Regression, Multivariate Normal and Multivariate Regression Models(2020-01-01) Guin, Abhishek; Sinha, Bimal Prof.; Roy, Anindya Prof.; Mathematics and Statistics; StatisticsStatistical Disclosure Control (SDC) methods are used to preserve confidentiality of publicly released microdata, without compromising on its fundamental structure, so as to ensure adequate and accurate statistical analysis of the data. The synthetic data approach is a popular form of SDC methodology where (all or part of) the real data are not released, but are instead used to create synthetic data which are released. In this dissertations we develop Bayesian inference based on singly or multiply imputed synthetic data, when the original data are derived from the following models: multiple linear regression, multivariate normal and multivariate regression. 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 produce synthetic data. In the single imputation case, the procedures developed here fill the gap in the existing literature where inferential methods are only available for multiple imputation and by being based on exact distributions, it may even be applied to cases where the sample size is small. Simulation results are presented to demonstrate how the proposed methodology performs compared to the theoretical predictions. We also outline some ways to extend the proposed methodology for certain scenarios where the required set of conditions do not hold.