Bayesian nonparametric inference for discovery probabilities: credible intervals and large sample asymptotics
<p>Given a sample of size n from a population of individuals belonging to different species with unknown proportions, a problem of practical interest consists in making inference on the probability Dn(l) that the (n + 1)-th draw coincides with a species with frequency l in the sample, for any...
| Main Authors: | , , , |
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| Format: | Journal article |
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Institute of Statistical Science, Academia Sinica
2017
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| _version_ | 1826304443644116992 |
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| author | Arbel, J Favaro, S Nipoti, B Teh, Y |
| author_facet | Arbel, J Favaro, S Nipoti, B Teh, Y |
| author_sort | Arbel, J |
| collection | OXFORD |
| description | <p>Given a sample of size n from a population of individuals belonging to different species with unknown proportions, a problem of practical interest consists in making inference on the probability Dn(l) that the (n + 1)-th draw coincides with a species with frequency l in the sample, for any l = 0, 1, . . . ,n. This paper contributes to the methodology of Bayesian nonparametric inference for Dn(l). Specifically, under the general framework of Gibbs-type priors we show how to derive credible intervals for a Bayesian nonparametric estimation of Dn(l), and we investigate the large n asymptotic behaviour of such an estimator. Of particular interest are special cases of our results obtained under the specification of the two parameter Poisson–Dirichlet prior and the normalized generalized Gamma prior. With respect for these prior specifications, the proposed results are illustrated through a simulation study and a benchmark Expressed Sequence Tags dataset. To the best our knowledge, this provides the first comparative study between the two-parameter Poisson–Dirichlet prior and the normalized generalized Gamma prior in the context of Bayesian nonparemetric inference for Dn(l).</p> |
| first_indexed | 2024-03-07T06:17:54Z |
| format | Journal article |
| id | oxford-uuid:f1b6f10a-5ac3-4d30-bc67-65cbf4e27d4d |
| institution | University of Oxford |
| last_indexed | 2024-03-07T06:17:54Z |
| publishDate | 2017 |
| publisher | Institute of Statistical Science, Academia Sinica |
| record_format | dspace |
| spelling | oxford-uuid:f1b6f10a-5ac3-4d30-bc67-65cbf4e27d4d2022-03-27T11:58:08ZBayesian nonparametric inference for discovery probabilities: credible intervals and large sample asymptoticsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:f1b6f10a-5ac3-4d30-bc67-65cbf4e27d4dSymplectic Elements at OxfordInstitute of Statistical Science, Academia Sinica2017Arbel, JFavaro, SNipoti, BTeh, Y<p>Given a sample of size n from a population of individuals belonging to different species with unknown proportions, a problem of practical interest consists in making inference on the probability Dn(l) that the (n + 1)-th draw coincides with a species with frequency l in the sample, for any l = 0, 1, . . . ,n. This paper contributes to the methodology of Bayesian nonparametric inference for Dn(l). Specifically, under the general framework of Gibbs-type priors we show how to derive credible intervals for a Bayesian nonparametric estimation of Dn(l), and we investigate the large n asymptotic behaviour of such an estimator. Of particular interest are special cases of our results obtained under the specification of the two parameter Poisson–Dirichlet prior and the normalized generalized Gamma prior. With respect for these prior specifications, the proposed results are illustrated through a simulation study and a benchmark Expressed Sequence Tags dataset. To the best our knowledge, this provides the first comparative study between the two-parameter Poisson–Dirichlet prior and the normalized generalized Gamma prior in the context of Bayesian nonparemetric inference for Dn(l).</p> |
| spellingShingle | Arbel, J Favaro, S Nipoti, B Teh, Y Bayesian nonparametric inference for discovery probabilities: credible intervals and large sample asymptotics |
| title | Bayesian nonparametric inference for discovery probabilities: credible intervals and large sample asymptotics |
| title_full | Bayesian nonparametric inference for discovery probabilities: credible intervals and large sample asymptotics |
| title_fullStr | Bayesian nonparametric inference for discovery probabilities: credible intervals and large sample asymptotics |
| title_full_unstemmed | Bayesian nonparametric inference for discovery probabilities: credible intervals and large sample asymptotics |
| title_short | Bayesian nonparametric inference for discovery probabilities: credible intervals and large sample asymptotics |
| title_sort | bayesian nonparametric inference for discovery probabilities credible intervals and large sample asymptotics |
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