Bayesian Sensitivity Analysis Using E-value

American Statistical Association Conference on Statistical Practice (CSP)


Statistical inference in the presence of missing outcome data is an inevitability in almost any application such as those in the social sciences or medical research. However, the quality of inference in these settings rests on strong but unfortunately untestable assumptions on the missingness mechanism. In order to ensure that inference is reliable, Sensitivity Analysis is a necessary step to assess robustness against violations of untestable assumptions. Using motivating examples from Facebook conversion data, we present methodology for conducting an E-value based Sensitivity Analysis at scale with three novel contributions. First, we develop a means for the Bayesian estimation of sensitivity parameters from privacy focused noisy aggregates with empirically derived and objective priors. Second, resting on the estimation of the sensitivity parameters we develop a mechanism for posterior inference via simulation of the E-value. Finally, we derive closed form distributions for the E-value (under a range of assumptions) to make direct inference possible for cases where posterior simulation may be infeasible due to computational constraints. We demonstrate gains in performance over asymptotic inference of the E-value using a data-based simulation supplemented by a case-study on partially missing Facebook conversion data.

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