  Data analysis has high value both for commercial and research purposes.
However, disclosing analysis results may pose severe privacy risk to
individuals. Privug is a method to quantify privacy risks of data analytics
programs by analyzing their source code. The method uses probability
distributions to model attacker knowledge and Bayesian inference to update said
knowledge based on observable outputs. Currently, Privug uses Markov Chain
Monte Carlo (MCMC) to perform inference, which is a flexible but approximate
solution. This paper presents an exact Bayesian inference engine based on
multivariate Gaussian distributions to accurately and efficiently quantify
privacy risks. The inference engine is implemented for a subset of Python
programs that can be modeled as multivariate Gaussian models. We evaluate the
method by analyzing privacy risks in programs to release public statistics. The
evaluation shows that our method accurately and efficiently analyzes privacy
risks, and outperforms existing methods. Furthermore, we demonstrate the use of
our engine to analyze the effect of differential privacy in public statistics.
