On the Bayesian analysis of a non-identifiable Binomial model

Éric Marchand

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arXiv · 2605.30496

On the Bayesian analysis of a non-identifiable Binomial model

Éric Marchand

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Abstract

We provide analysis for the posterior distribution and expectation of $(p_1, p_2)$ where $Y|p_1,p_2 \sim \hbox{Binomial}(n, p_1 p_2)$ and $ (p_1, p_2)$ is uniformly distributed on the unit square $[0,1]^2$. We exhibit interesting expressions in terms of a truncated Beta distribution, a finite mixture of Beta distributions and harmonic numbers, and derive a simple large sample size $n$ approximation for the posterior expectations $\mathbb{E}(p_i|y)$ as well as for the normalization constant in the posterior joint density.

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Éric Marchand. 2026-05-28. On the Bayesian analysis of a non-identifiable Binomial model. https://arxiv.org/abs/2605.30496

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