On the Bayesian analysis of a non-identifiable Binomial model
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910270759108608 |
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| author | Marchand, Éric |
| author_facet | Marchand, Éric |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_30496 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Bayesian analysis of a non-identifiable Binomial model Marchand, Éric Statistics Theory 62E15, 62F15, 62-08 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. |
| title | On the Bayesian analysis of a non-identifiable Binomial model |
| topic | Statistics Theory 62E15, 62F15, 62-08 |
| url | https://arxiv.org/abs/2605.30496 |