Nonparametric predictive inference for discrete data via Metropolis-adjusted Dirichlet sequences
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912700462792704 |
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| author | Agnoletto, Davide Rigon, Tommaso Dunson, David B. |
| author_facet | Agnoletto, Davide Rigon, Tommaso Dunson, David B. |
| contents | This article is motivated by challenges in conducting Bayesian inferences on unknown discrete distributions, with a particular focus on count data. To avoid the computational disadvantages of traditional mixture models, we develop a novel Bayesian predictive approach. In particular, our Metropolis-adjusted Dirichlet (MAD) sequence model characterizes the predictive measure as a mixture of a base measure and Metropolis-Hastings kernels centered on previous data points. The resulting MAD sequence is asymptotically exchangeable and the posterior on the data generator takes the form of a martingale posterior. This structure leads to straightforward algorithms for inference on count distributions, with easy extensions to multivariate, regression, and binary data cases. We obtain a useful asymptotic Gaussian approximation and illustrate the methodology on a variety of applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_08629 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonparametric predictive inference for discrete data via Metropolis-adjusted Dirichlet sequences Agnoletto, Davide Rigon, Tommaso Dunson, David B. Methodology This article is motivated by challenges in conducting Bayesian inferences on unknown discrete distributions, with a particular focus on count data. To avoid the computational disadvantages of traditional mixture models, we develop a novel Bayesian predictive approach. In particular, our Metropolis-adjusted Dirichlet (MAD) sequence model characterizes the predictive measure as a mixture of a base measure and Metropolis-Hastings kernels centered on previous data points. The resulting MAD sequence is asymptotically exchangeable and the posterior on the data generator takes the form of a martingale posterior. This structure leads to straightforward algorithms for inference on count distributions, with easy extensions to multivariate, regression, and binary data cases. We obtain a useful asymptotic Gaussian approximation and illustrate the methodology on a variety of applications. |
| title | Nonparametric predictive inference for discrete data via Metropolis-adjusted Dirichlet sequences |
| topic | Methodology |
| url | https://arxiv.org/abs/2507.08629 |