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We introduce the BREASE framework for the Bayesian analysis of randomized controlled trials with a binary treatment and a binary outcome. Approaching the problem from a causal inference perspective, we propose parameterizing the likelihood in terms of the baseline risk, efficacy, and side effects of the treatment, along with a flexible, yet intuitive and tractable jointly independent beta prior distribution on these parameters, which we show to be a generalization of the Dirichlet prior for the joint distribution of potential outcomes. Our approach has a number of desirable characteristics when compared to current mainstream alternatives: (i) it naturally induces prior dependence between expected outcomes in the treatment and control groups; (ii) as the baseline risk, efficacy and side effects are quantities inherently familiar to clinicians, the hyperparameters of the prior are directly interpretable, thus facilitating the elicitation of prior knowledge and sensitivity analysis; and (iii) it admits analytical formulae for the marginal likelihood, Bayes factor, and other posterior quantities,as well as an exact posterior sampling algorithm and an accurate and fast data-augmented Gibbs sampler in cases where traditional MCMC fails. Empirical examples demonstrate the utility of our methods for estimation, hypothesis testing, and sensitivity analysis of treatment effects.
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This content will become publicly available on January 1, 2026
VARIANCE-BASED SENSITIVITY OF BAYESIAN INVERSE PROBLEMS TO THE PRIOR DISTRIBUTION
The formulation of Bayesian inverse problems involves choosing prior distributions; choices that seem equally reason-able may lead to significantly different conclusions. We develop a computational approach to understand the impact of the hyperparameters defining the prior on the posterior statistics of the quantities of interest. Our approach relies on global sensitivity analysis (GSA) of Bayesian inverse problems with respect to the prior hyperparameters. This, however, is a challenging problem-a naive double loop sampling approach would require running a prohibitive number of Markov chain Monte Carlo (MCMC) sampling procedures. The present work takes a foundational step in making such a sensitivity analysis practical by combining efficient surrogate models and a tailored importance sampling approach. In particular, we can perform accurate GSA of posterior statistics of quantities of interest with respect to prior hyperparameters without the need to repeat MCMC runs. We demonstrate the effectiveness of the approach on a simple Bayesian linear inverse problem and a nonlinear inverse problem governed by an epidemiological model.
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- Award ID(s):
- 1745654
- PAR ID:
- 10627874
- Publisher / Repository:
- Begell House
- Date Published:
- Journal Name:
- International Journal for Uncertainty Quantification
- Volume:
- 15
- Issue:
- 2
- ISSN:
- 2152-5080
- Page Range / eLocation ID:
- 65 to 90
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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