# Doctoral Dissertation Defense: John Zylstra

## Advisors: Dr. Bimal Sinha and Dr. Martin Klein

Friday, April 27, 2018

8:30 AM - 10:30 AM

8:30 AM - 10:30 AM

Sherman Hall : 148C

**Title:**

*Generation and Analysis of Synthetic Data for Privacy Protection Under the Multivariate Linear Regression Model*

**Abstract**

In this dissertation, the author derives likelihood-based exact inference for

*multiply*imputed synthetic data under the multiple (p>1) univariate linear regression model and for

*singly*and

*multiply*imputed data under the multivariate linear regression model. In the former, the synthetic data are generated under plug-in sampling, where unknown parameters in the model are set equal to observed values of point estimators. In the latter, synthetic data are also generated under posterior predictive sampling where they are drawn from a posterior predictive distribution. Simulations are presented to confirm the methodology performs as the theory predicts and to evaluate privacy protection. Robustness studies are also given. Finally, a new idea for privacy protection based on monotone coding is proposed and its performance is evaluated and compared with those of existing procedures.