Random irregular histograms
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915855418261504 |
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| author | Simensen, Oskar Høgberg Christensen, Dennis Hjort, Nils Lid |
| author_facet | Simensen, Oskar Høgberg Christensen, Dennis Hjort, Nils Lid |
| contents | We propose a new method of histogram construction, providing a fully Bayesian approach to irregular histograms. Our procedure applies Bayesian model selection to a piecewise constant model of the underlying distribution, resulting in a method that selects both the number of bins as well as their location based on the data in a fully automatic fashion. We show that the histogram estimate is consistent with respect to the Hellinger metric under mild regularity conditions, and that it attains a convergence rate equal to the minimax rate (up to a logarithmic factor) for Hölder continuous densities. Simulation studies indicate that the new method performs comparably to other histogram procedures, both for minimizing the estimation error and for identifying modes. A software implementation is included as supplementary material. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_22034 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Random irregular histograms Simensen, Oskar Høgberg Christensen, Dennis Hjort, Nils Lid Methodology Statistics Theory We propose a new method of histogram construction, providing a fully Bayesian approach to irregular histograms. Our procedure applies Bayesian model selection to a piecewise constant model of the underlying distribution, resulting in a method that selects both the number of bins as well as their location based on the data in a fully automatic fashion. We show that the histogram estimate is consistent with respect to the Hellinger metric under mild regularity conditions, and that it attains a convergence rate equal to the minimax rate (up to a logarithmic factor) for Hölder continuous densities. Simulation studies indicate that the new method performs comparably to other histogram procedures, both for minimizing the estimation error and for identifying modes. A software implementation is included as supplementary material. |
| title | Random irregular histograms |
| topic | Methodology Statistics Theory |
| url | https://arxiv.org/abs/2505.22034 |