Marginal likelihoods for finite-support Huber contamination
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910258547392512 |
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| author | Kim, Jaehoan |
| author_facet | Kim, Jaehoan |
| contents | For Huber contamination on a known finite sample space, the unrestricted contaminating law is a probability vector on the support atoms, and domination over all measurable subsets reduces to atomwise inequalities. Placing a Dirichlet prior on this probability vector and a Beta prior on the contamination proportion gives an exact marginal likelihood for the structural parameter after analytic integration of both nuisance quantities. The likelihood is a finite weighted sum over allocations of the observed counts between the structural and contaminating components. For fixed support size, this sum and its score can be evaluated by a dynamic program with quadratic cost in the sample size, enabling gradient-based posterior sampling. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_26723 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Marginal likelihoods for finite-support Huber contamination Kim, Jaehoan Methodology Statistics Theory Computation For Huber contamination on a known finite sample space, the unrestricted contaminating law is a probability vector on the support atoms, and domination over all measurable subsets reduces to atomwise inequalities. Placing a Dirichlet prior on this probability vector and a Beta prior on the contamination proportion gives an exact marginal likelihood for the structural parameter after analytic integration of both nuisance quantities. The likelihood is a finite weighted sum over allocations of the observed counts between the structural and contaminating components. For fixed support size, this sum and its score can be evaluated by a dynamic program with quadratic cost in the sample size, enabling gradient-based posterior sampling. |
| title | Marginal likelihoods for finite-support Huber contamination |
| topic | Methodology Statistics Theory Computation |
| url | https://arxiv.org/abs/2605.26723 |