Adaptive density estimation based on a mixture of Gammas
<p>We consider the problem of Bayesian density estimation on the positive semiline for possibly unbounded densities. We propose a hierarchical Bayesian estimator based on the gamma mixture prior which can be viewed as a location mixture. We study convergence rates of Bayesian density estimator...
| প্রধান লেখক: | , |
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| বিন্যাস: | Journal article |
| প্রকাশিত: |
Institute of Mathematical Statistics
2017
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| _version_ | 1826271074564702208 |
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| author | Bochkina, N Rousseau, J |
| author_facet | Bochkina, N Rousseau, J |
| author_sort | Bochkina, N |
| collection | OXFORD |
| description | <p>We consider the problem of Bayesian density estimation on the positive semiline for possibly unbounded densities. We propose a hierarchical Bayesian estimator based on the gamma mixture prior which can be viewed as a location mixture. We study convergence rates of Bayesian density estimators based on such mixtures.We construct approximations of the local Hölder densities, and of their extension to unbounded densities, to be continuous mixtures of gamma distributions, leading to approximations of such densities by finite mixtures. These results are then used to derive posterior concentration rates, with priors based on these mixture models. The rates are minimax (up to a log n term) and since the priors are independent of the smoothness, the rates are adaptive to the smoothness.</p> <br/> <p>One of the novel feature of the paper is that these results hold for densities with polynomial tails. Similar results are obtained using a hierarchical Bayesian model based on the mixture of inverse gamma densities which can be used to estimate adaptively densities with very heavy tails, including Cauchy density.</p> |
| first_indexed | 2024-03-06T21:50:54Z |
| format | Journal article |
| id | oxford-uuid:4b390b08-1df1-4ac3-a39c-74792a50ffc0 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T21:50:54Z |
| publishDate | 2017 |
| publisher | Institute of Mathematical Statistics |
| record_format | dspace |
| spelling | oxford-uuid:4b390b08-1df1-4ac3-a39c-74792a50ffc02022-03-26T15:42:18ZAdaptive density estimation based on a mixture of GammasJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:4b390b08-1df1-4ac3-a39c-74792a50ffc0Symplectic Elements at OxfordInstitute of Mathematical Statistics2017Bochkina, NRousseau, J<p>We consider the problem of Bayesian density estimation on the positive semiline for possibly unbounded densities. We propose a hierarchical Bayesian estimator based on the gamma mixture prior which can be viewed as a location mixture. We study convergence rates of Bayesian density estimators based on such mixtures.We construct approximations of the local Hölder densities, and of their extension to unbounded densities, to be continuous mixtures of gamma distributions, leading to approximations of such densities by finite mixtures. These results are then used to derive posterior concentration rates, with priors based on these mixture models. The rates are minimax (up to a log n term) and since the priors are independent of the smoothness, the rates are adaptive to the smoothness.</p> <br/> <p>One of the novel feature of the paper is that these results hold for densities with polynomial tails. Similar results are obtained using a hierarchical Bayesian model based on the mixture of inverse gamma densities which can be used to estimate adaptively densities with very heavy tails, including Cauchy density.</p> |
| spellingShingle | Bochkina, N Rousseau, J Adaptive density estimation based on a mixture of Gammas |
| title | Adaptive density estimation based on a mixture of Gammas |
| title_full | Adaptive density estimation based on a mixture of Gammas |
| title_fullStr | Adaptive density estimation based on a mixture of Gammas |
| title_full_unstemmed | Adaptive density estimation based on a mixture of Gammas |
| title_short | Adaptive density estimation based on a mixture of Gammas |
| title_sort | adaptive density estimation based on a mixture of gammas |
| work_keys_str_mv | AT bochkinan adaptivedensityestimationbasedonamixtureofgammas AT rousseauj adaptivedensityestimationbasedonamixtureofgammas |