Distances between nested densities and a measure of the impact of the prior in Bayesian statistics
In this paper we propose tight upper and lower bounds for the Wasserstein distance between any two {{univariate continuous distributions}} with probability densities $p_1$ and $p_2$ having nested supports. These explicit bounds are expressed in terms of the derivative of the likelihood ratio $p_1/p_...
| المؤلفون الرئيسيون: | , , |
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| التنسيق: | Journal article |
| منشور في: |
2016
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| _version_ | 1826304992712065024 |
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| author | Ley, C Reinert, G Swan, Y |
| author_facet | Ley, C Reinert, G Swan, Y |
| author_sort | Ley, C |
| collection | OXFORD |
| description | In this paper we propose tight upper and lower bounds for the Wasserstein distance between any two {{univariate continuous distributions}} with probability densities $p_1$ and $p_2$ having nested supports. These explicit bounds are expressed in terms of the derivative of the likelihood ratio $p_1/p_2$ as well as the Stein kernel $\tau_1$ of $p_1$. The method of proof relies on a new variant of Stein's method which manipulates Stein operators. We give several applications of these bounds. Our main application is in Bayesian statistics : we derive explicit data-driven bounds on the Wasserstein distance between the posterior distribution based on a given prior and the no-prior posterior based uniquely on the sampling distribution. This is the first finite sample result confirming the well-known fact that with well-identified parameters and large sample sizes, reasonable choices of prior distributions will have only minor effects on posterior inferences if the data are benign. |
| first_indexed | 2024-03-07T06:26:08Z |
| format | Journal article |
| id | oxford-uuid:f45b73a7-f23c-49d9-ab54-5d13ce53c1aa |
| institution | University of Oxford |
| last_indexed | 2024-03-07T06:26:08Z |
| publishDate | 2016 |
| record_format | dspace |
| spelling | oxford-uuid:f45b73a7-f23c-49d9-ab54-5d13ce53c1aa2022-03-27T12:19:11ZDistances between nested densities and a measure of the impact of the prior in Bayesian statisticsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:f45b73a7-f23c-49d9-ab54-5d13ce53c1aaSymplectic Elements at Oxford2016Ley, CReinert, GSwan, YIn this paper we propose tight upper and lower bounds for the Wasserstein distance between any two {{univariate continuous distributions}} with probability densities $p_1$ and $p_2$ having nested supports. These explicit bounds are expressed in terms of the derivative of the likelihood ratio $p_1/p_2$ as well as the Stein kernel $\tau_1$ of $p_1$. The method of proof relies on a new variant of Stein's method which manipulates Stein operators. We give several applications of these bounds. Our main application is in Bayesian statistics : we derive explicit data-driven bounds on the Wasserstein distance between the posterior distribution based on a given prior and the no-prior posterior based uniquely on the sampling distribution. This is the first finite sample result confirming the well-known fact that with well-identified parameters and large sample sizes, reasonable choices of prior distributions will have only minor effects on posterior inferences if the data are benign. |
| spellingShingle | Ley, C Reinert, G Swan, Y Distances between nested densities and a measure of the impact of the prior in Bayesian statistics |
| title | Distances between nested densities and a measure of the impact of the
prior in Bayesian statistics |
| title_full | Distances between nested densities and a measure of the impact of the
prior in Bayesian statistics |
| title_fullStr | Distances between nested densities and a measure of the impact of the
prior in Bayesian statistics |
| title_full_unstemmed | Distances between nested densities and a measure of the impact of the
prior in Bayesian statistics |
| title_short | Distances between nested densities and a measure of the impact of the
prior in Bayesian statistics |
| title_sort | distances between nested densities and a measure of the impact of the prior in bayesian statistics |
| work_keys_str_mv | AT leyc distancesbetweennesteddensitiesandameasureoftheimpactofthepriorinbayesianstatistics AT reinertg distancesbetweennesteddensitiesandameasureoftheimpactofthepriorinbayesianstatistics AT swany distancesbetweennesteddensitiesandameasureoftheimpactofthepriorinbayesianstatistics |