Propriety of the reference posterior distribution in Gaussian Process modeling
In a seminal article, Berger, De Oliveira and Sans\'o (2001) compare several objective prior distributions for the parameters of Gaussian Process regression models with isotropic correlation kernel. The reference prior distribution stands out among them insofar as it always leads to a proper po...
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| creator | Muré, Joseph |
| description | In a seminal article, Berger, De Oliveira and Sans\'o (2001) compare several
objective prior distributions for the parameters of Gaussian Process regression
models with isotropic correlation kernel. The reference prior distribution
stands out among them insofar as it always leads to a proper posterior. They
prove this result for rough correlation kernels - Spherical, Exponential with
power $q |
| doi_str_mv | 10.48550/arxiv.1805.08992 |
| format | Article |
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objective prior distributions for the parameters of Gaussian Process regression
models with isotropic correlation kernel. The reference prior distribution
stands out among them insofar as it always leads to a proper posterior. They
prove this result for rough correlation kernels - Spherical, Exponential with
power $q<2$, Mat\'ern with smoothness $\nu<1$. This paper provides a proof for
smooth correlation kernels - Exponential with power $q=2$, Mat\'ern with
smoothness $\nu \geqslant 1$, Rational Quadratic - along with tail rates of the
reference prior for these kernels.</description><identifier>DOI: 10.48550/arxiv.1805.08992</identifier><language>eng</language><subject>Mathematics - Statistics Theory ; Statistics - Theory</subject><creationdate>2018-05</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1805.08992$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1805.08992$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Muré, Joseph</creatorcontrib><title>Propriety of the reference posterior distribution in Gaussian Process modeling</title><description>In a seminal article, Berger, De Oliveira and Sans\'o (2001) compare several
objective prior distributions for the parameters of Gaussian Process regression
models with isotropic correlation kernel. The reference prior distribution
stands out among them insofar as it always leads to a proper posterior. They
prove this result for rough correlation kernels - Spherical, Exponential with
power $q<2$, Mat\'ern with smoothness $\nu<1$. This paper provides a proof for
smooth correlation kernels - Exponential with power $q=2$, Mat\'ern with
smoothness $\nu \geqslant 1$, Rational Quadratic - along with tail rates of the
reference prior for these kernels.</description><subject>Mathematics - Statistics Theory</subject><subject>Statistics - Theory</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotz8FOAjEUheFuXBj0AVzZF5ix7Z3S6dIQRRMiLthP7rR3oAm0pC1G3l5EV2f1n-Rj7EGKtuu1Fk-Yv8NXK3uhW9Fbq27Zx2dOxxyonnmaeN0RzzRRpuiIH1OplEPK3IdScxhPNaTIQ-RLPJUSMPJL7agUfkie9iFu79jNhPtC9_87Y5vXl83irVmtl--L51WDc6MaZ4mEIXQdQg_QeQ8eNMDcaQlowRhlYZKECpQZvfZyFJMdnQVJpLyAGXv8u72ChgvggPk8_MKGKwx-AFtRSgU</recordid><startdate>20180523</startdate><enddate>20180523</enddate><creator>Muré, Joseph</creator><scope>AKZ</scope><scope>EPD</scope><scope>GOX</scope></search><sort><creationdate>20180523</creationdate><title>Propriety of the reference posterior distribution in Gaussian Process modeling</title><author>Muré, Joseph</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a672-c9ee07eac4a38334dd3d35336c513a9377293f1ea2327bd5d1b0f9bc931ee2d03</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Mathematics - Statistics Theory</topic><topic>Statistics - Theory</topic><toplevel>online_resources</toplevel><creatorcontrib>Muré, Joseph</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv Statistics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Muré, Joseph</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Propriety of the reference posterior distribution in Gaussian Process modeling</atitle><date>2018-05-23</date><risdate>2018</risdate><abstract>In a seminal article, Berger, De Oliveira and Sans\'o (2001) compare several
objective prior distributions for the parameters of Gaussian Process regression
models with isotropic correlation kernel. The reference prior distribution
stands out among them insofar as it always leads to a proper posterior. They
prove this result for rough correlation kernels - Spherical, Exponential with
power $q<2$, Mat\'ern with smoothness $\nu<1$. This paper provides a proof for
smooth correlation kernels - Exponential with power $q=2$, Mat\'ern with
smoothness $\nu \geqslant 1$, Rational Quadratic - along with tail rates of the
reference prior for these kernels.</abstract><doi>10.48550/arxiv.1805.08992</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Statistics Theory Statistics - Theory |
| title | Propriety of the reference posterior distribution in Gaussian Process modeling |
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