Posterior concentration rates for empirical Bayes procedures with applications to Dirichlet process mixtures
We provide conditions on the statistical model and the prior probability law to derive contraction rates of posterior distributions corresponding to data-dependent priors in an empirical Bayes approach for selecting prior hyper-parameter values. We aim at giving conditions in the same spirit as thos...
| Main Authors: | , , , |
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| Format: | Journal article |
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Bernoulli Society for Mathematical Statistics and Probability
2017
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| _version_ | 1826289860536696832 |
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| author | Donnet, S Rivoirard, V Rousseau, J Scricciolo, C |
| author_facet | Donnet, S Rivoirard, V Rousseau, J Scricciolo, C |
| author_sort | Donnet, S |
| collection | OXFORD |
| description | We provide conditions on the statistical model and the prior probability law to derive contraction rates of posterior distributions corresponding to data-dependent priors in an empirical Bayes approach for selecting prior hyper-parameter values. We aim at giving conditions in the same spirit as those in the seminal article of Ghosal and van der Vaart. We then apply the result to specific statistical settings: density estimation using Dirichlet process mixtures of Gaussian densities with base measure depending on data-driven chosen hyper-parameter values and intensity function estimation of counting processes obeying the Aalen model. In the former setting, we also derive recovery rates for the related inverse problem of density deconvolution. In the latter, a simulation study for inhomogeneous Poisson processes illustrates the results. |
| first_indexed | 2024-03-07T02:35:21Z |
| format | Journal article |
| id | oxford-uuid:a8993c97-d0e7-4220-bb86-c796a9f9063f |
| institution | University of Oxford |
| last_indexed | 2024-03-07T02:35:21Z |
| publishDate | 2017 |
| publisher | Bernoulli Society for Mathematical Statistics and Probability |
| record_format | dspace |
| spelling | oxford-uuid:a8993c97-d0e7-4220-bb86-c796a9f9063f2022-03-27T03:02:48ZPosterior concentration rates for empirical Bayes procedures with applications to Dirichlet process mixturesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:a8993c97-d0e7-4220-bb86-c796a9f9063fSymplectic Elements at OxfordBernoulli Society for Mathematical Statistics and Probability2017Donnet, SRivoirard, VRousseau, JScricciolo, CWe provide conditions on the statistical model and the prior probability law to derive contraction rates of posterior distributions corresponding to data-dependent priors in an empirical Bayes approach for selecting prior hyper-parameter values. We aim at giving conditions in the same spirit as those in the seminal article of Ghosal and van der Vaart. We then apply the result to specific statistical settings: density estimation using Dirichlet process mixtures of Gaussian densities with base measure depending on data-driven chosen hyper-parameter values and intensity function estimation of counting processes obeying the Aalen model. In the former setting, we also derive recovery rates for the related inverse problem of density deconvolution. In the latter, a simulation study for inhomogeneous Poisson processes illustrates the results. |
| spellingShingle | Donnet, S Rivoirard, V Rousseau, J Scricciolo, C Posterior concentration rates for empirical Bayes procedures with applications to Dirichlet process mixtures |
| title | Posterior concentration rates for empirical Bayes procedures with applications to Dirichlet process mixtures |
| title_full | Posterior concentration rates for empirical Bayes procedures with applications to Dirichlet process mixtures |
| title_fullStr | Posterior concentration rates for empirical Bayes procedures with applications to Dirichlet process mixtures |
| title_full_unstemmed | Posterior concentration rates for empirical Bayes procedures with applications to Dirichlet process mixtures |
| title_short | Posterior concentration rates for empirical Bayes procedures with applications to Dirichlet process mixtures |
| title_sort | posterior concentration rates for empirical bayes procedures with applications to dirichlet process mixtures |
| work_keys_str_mv | AT donnets posteriorconcentrationratesforempiricalbayesprocedureswithapplicationstodirichletprocessmixtures AT rivoirardv posteriorconcentrationratesforempiricalbayesprocedureswithapplicationstodirichletprocessmixtures AT rousseauj posteriorconcentrationratesforempiricalbayesprocedureswithapplicationstodirichletprocessmixtures AT scriccioloc posteriorconcentrationratesforempiricalbayesprocedureswithapplicationstodirichletprocessmixtures |