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A Bayesian hierarchical framework based on a beta-binomial mixture model for testing for differential biomarker expression using single-cell assays. MIMOSA allows the inference to be subject specific, as is typically required when assessing vaccine responses, while borrowing strength across subjects through common prior distributions. We propose two approaches for parameter estimation: an empirical-Bayes approach using an Expectation–Maximization algorithm and a fully Bayesian one based on a Markov chain Monte Carlo algorithm. Cell counts are modeled by a binomial (or multinomial in the multivariate case) distribution and information is shared across subjects through a prior distribution on the unknown proportion(s) of the binomial (or multinomial) likelihood. In order to discriminate between responders and non-responders, the prior is written as a mixture of two beta (or Dirichlet) distributions where the hyper-parameters for each mixture component are shared across subjects.