Monte Carlo Estimation of Bayesian Credible and HPD Intervals
This article considers how to estimate Bayesian credible and highest probability density (HPD) intervals for parameters of interest and provides a simple Monte Carlo approach to approximate these Bayesian intervals when a sample of the relevant parameters can be generated from their respective margi...
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| Veröffentlicht in: | Journal of computational and graphical statistics 1999-03, Vol.8 (1), p.69-92 |
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| container_end_page | 92 |
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| container_title | Journal of computational and graphical statistics |
| container_volume | 8 |
| creator | Chen, Ming-Hui Shao, Qi-Man |
| description | This article considers how to estimate Bayesian credible and highest probability density (HPD) intervals for parameters of interest and provides a simple Monte Carlo approach to approximate these Bayesian intervals when a sample of the relevant parameters can be generated from their respective marginal posterior distribution using a Markov chain Monte Carlo (MCMC) sampling algorithm. We also develop a Monte Carlo method to compute HPD intervals for the parameters of interest from the desired posterior distribution using a sample from an importance sampling distribution. We apply our methodology to a Bayesian hierarchical model that has a posterior density containing analytically intractable integrals that depend on the (hyper) parameters. We further show that our methods are useful not only for calculating the HPD intervals for the parameters of interest but also for computing the HPD intervals for functions of the parameters. Necessary theory is developed and illustrative examples-including a simulation study-are given. |
| doi_str_mv | 10.1080/10618600.1999.10474802 |
| format | Article |
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We also develop a Monte Carlo method to compute HPD intervals for the parameters of interest from the desired posterior distribution using a sample from an importance sampling distribution. We apply our methodology to a Bayesian hierarchical model that has a posterior density containing analytically intractable integrals that depend on the (hyper) parameters. We further show that our methods are useful not only for calculating the HPD intervals for the parameters of interest but also for computing the HPD intervals for functions of the parameters. 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We also develop a Monte Carlo method to compute HPD intervals for the parameters of interest from the desired posterior distribution using a sample from an importance sampling distribution. We apply our methodology to a Bayesian hierarchical model that has a posterior density containing analytically intractable integrals that depend on the (hyper) parameters. We further show that our methods are useful not only for calculating the HPD intervals for the parameters of interest but also for computing the HPD intervals for functions of the parameters. Necessary theory is developed and illustrative examples-including a simulation study-are given.</description><subject>Bayesian computation</subject><subject>Density estimation</subject><subject>Ergodic theory</subject><subject>Estimation methods</subject><subject>Interval estimators</subject><subject>Markov chain Monte Carlo</subject><subject>Mathematical independent variables</subject><subject>Mathematical intervals</subject><subject>Monte Carlo methods</subject><subject>Musical intervals</subject><subject>Posterior distribution</subject><subject>Sampling distributions</subject><subject>Simulation</subject><subject>Tanneries</subject><issn>1061-8600</issn><issn>1537-2715</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1999</creationdate><recordtype>article</recordtype><recordid>eNqFkEFLAzEQhYMoWKt_QXLwuppJNpvk4KGu1RYqetBzyG4S2LLdSLIo_femrAVvnubN8L2Z4SF0DeQWiCR3QCqQFcmdUiqPSlFKQk_QDDgTBRXAT7POUHGgztFFSltCCFRKzND9SxhGh2sT-4CXaex2ZuzCgIPHD2bvUmcGXEdnu6Z32AwWr94e8Tpb4pfp0yU687m4q986Rx9Py_d6VWxen9f1YlO0jMJYlE1jqhYoWMhKCiesgpK3QlnaGO4UtYIxEBUppeQZo4ZT76QCXlLOPJujatrbxpBSdF5_xvxp3Gsg-hCCPoagDyHoYwjZeDMZt2kM8a-LMiI0MEUUhYwtJqwbfIg78x1ib_Vo9n2IPpqh7ZJm_5z6AUBhbUM</recordid><startdate>19990301</startdate><enddate>19990301</enddate><creator>Chen, Ming-Hui</creator><creator>Shao, Qi-Man</creator><general>Taylor & Francis Group</general><general>American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>19990301</creationdate><title>Monte Carlo Estimation of Bayesian Credible and HPD Intervals</title><author>Chen, Ming-Hui ; Shao, Qi-Man</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c321t-4bba6c121d1bba87e7d9145c79d2ba5e92d7331760488521d2a52fe89154253f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1999</creationdate><topic>Bayesian computation</topic><topic>Density estimation</topic><topic>Ergodic theory</topic><topic>Estimation methods</topic><topic>Interval estimators</topic><topic>Markov chain Monte Carlo</topic><topic>Mathematical independent variables</topic><topic>Mathematical intervals</topic><topic>Monte Carlo methods</topic><topic>Musical intervals</topic><topic>Posterior distribution</topic><topic>Sampling distributions</topic><topic>Simulation</topic><topic>Tanneries</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Chen, Ming-Hui</creatorcontrib><creatorcontrib>Shao, Qi-Man</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of computational and graphical statistics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Chen, Ming-Hui</au><au>Shao, Qi-Man</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Monte Carlo Estimation of Bayesian Credible and HPD Intervals</atitle><jtitle>Journal of computational and graphical statistics</jtitle><date>1999-03-01</date><risdate>1999</risdate><volume>8</volume><issue>1</issue><spage>69</spage><epage>92</epage><pages>69-92</pages><issn>1061-8600</issn><eissn>1537-2715</eissn><abstract>This article considers how to estimate Bayesian credible and highest probability density (HPD) intervals for parameters of interest and provides a simple Monte Carlo approach to approximate these Bayesian intervals when a sample of the relevant parameters can be generated from their respective marginal posterior distribution using a Markov chain Monte Carlo (MCMC) sampling algorithm. We also develop a Monte Carlo method to compute HPD intervals for the parameters of interest from the desired posterior distribution using a sample from an importance sampling distribution. We apply our methodology to a Bayesian hierarchical model that has a posterior density containing analytically intractable integrals that depend on the (hyper) parameters. We further show that our methods are useful not only for calculating the HPD intervals for the parameters of interest but also for computing the HPD intervals for functions of the parameters. Necessary theory is developed and illustrative examples-including a simulation study-are given.</abstract><pub>Taylor & Francis Group</pub><doi>10.1080/10618600.1999.10474802</doi><tpages>24</tpages></addata></record> |
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| ispartof | Journal of computational and graphical statistics, 1999-03, Vol.8 (1), p.69-92 |
| issn | 1061-8600 1537-2715 |
| language | eng |
| recordid | cdi_jstor_primary_10_2307_1390921 |
| source | Jstor Complete Legacy; JSTOR Mathematics & Statistics |
| subjects | Bayesian computation Density estimation Ergodic theory Estimation methods Interval estimators Markov chain Monte Carlo Mathematical independent variables Mathematical intervals Monte Carlo methods Musical intervals Posterior distribution Sampling distributions Simulation Tanneries |
| title | Monte Carlo Estimation of Bayesian Credible and HPD Intervals |
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