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

Exact and Efficient Bayesian Inference for Privacy Risk Quantification (Extended Version)