[MDS Job Talk] Bayesian Data Analysis with Privatized Data

Speaker: Nianqiao Phyllis Ju (Emory)

Date: 1/16/25

Abstract: Doing data analysis under privacy constraints is like dancing with shackles on: adding privacy protection requires modified analysis procedures and inevitably reduces data utility. This talk begins with some challenges in making statistical inferences from privatized data. Then we present a data augmentation Markov Chain Monte Carlo framework to perform Bayesian inference from the privatized data, which applies to a wide range of statistical models and privacy mechanisms. The algorithm augments the model parameters with the unobserved confidential data and alternately updates each conditional on the other, using Metropolis-within-Gibbs steps. The final part of the talk focuses on the convergence characteristic of data augmentation algorithms. Our analysis reveals that the absolute spectral gap of a data augmentation chain can be bounded based on the absolute spectral gap of the exact Gibbs chain and the absolute spectral gaps of the Metropolis-within-Gibbs kernels.