On Parametric Bootstrapping and Bayesian Prediction
We investigate bootstrapping and Bayesian methods for prediction. The observations and the variable being predicted are distributed according to different distributions. Many important problems can be formulated in this setting. This type of prediction problem appears when we deal with a Poisson pro...
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| Veröffentlicht in: | Scandinavian journal of statistics 2004-09, Vol.31 (3), p.403-416 |
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| container_end_page | 416 |
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| container_issue | 3 |
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| container_title | Scandinavian journal of statistics |
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| creator | Fushiki, Tadayoshi Komaki, Fumiyasu Aihara, Kazuyuki |
| description | We investigate bootstrapping and Bayesian methods for prediction. The observations and the variable being predicted are distributed according to different distributions. Many important problems can be formulated in this setting. This type of prediction problem appears when we deal with a Poisson process. Regression problems can also be formulated in this setting. First, we show that bootstrap predictive distributions are equivalent to Bayesian predictive distributions in the second-order expansion when some conditions are satisfied. Next, the performance of predictive distributions is compared with that of a plug-in distribution with an estimator. The accuracy of prediction is evaluated by using the Kullback-Leibler divergence. Finally, we give some examples. |
| doi_str_mv | 10.1111/j.1467-9469.2004.02_127.x |
| format | Article |
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The observations and the variable being predicted are distributed according to different distributions. Many important problems can be formulated in this setting. This type of prediction problem appears when we deal with a Poisson process. Regression problems can also be formulated in this setting. First, we show that bootstrap predictive distributions are equivalent to Bayesian predictive distributions in the second-order expansion when some conditions are satisfied. Next, the performance of predictive distributions is compared with that of a plug-in distribution with an estimator. The accuracy of prediction is evaluated by using the Kullback-Leibler divergence. Finally, we give some examples.</description><subject>asymptotic theory</subject><subject>Bayes estimators</subject><subject>Bayes theorem</subject><subject>Bayesian analysis</subject><subject>Bayesian prediction</subject><subject>Binomial distributions</subject><subject>Bootstrap method</subject><subject>bootstrap predictive distribution</subject><subject>Coefficients</subject><subject>Exact sciences and technology</subject><subject>Fisher information</subject><subject>Indices of summation</subject><subject>Inference from stochastic processes; time series analysis</subject><subject>information geometry</subject><subject>Kullback-Leibler divergence</subject><subject>Mathematics</subject><subject>Maximum likelihood estimation</subject><subject>Modeling</subject><subject>Parameter estimation</subject><subject>Parametric inference</subject><subject>Predictions</subject><subject>Predictive modeling</subject><subject>Probability and statistics</subject><subject>Sciences and techniques of general use</subject><subject>Statistical models</subject><subject>Statistics</subject><issn>0303-6898</issn><issn>1467-9469</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2004</creationdate><recordtype>article</recordtype><sourceid>X2L</sourceid><recordid>eNqNUMtu1DAUjRBIDIU_YDEgsUzwK35skJgKCqVlkFqE1M3VjeOAw0yS2inM_H2dpppua-naks_DxyfL3lBS0LTetwUVUuVGSFMwQkRBGFCmit2TbHFAnmYLwgnPpTb6efYixpYQKgXVi4yvu-UPDLh1Y_B2uer7MY4Bh8F3v5fY1csV7l30mFjB1d6Ovu9eZs8a3ET36v48yn5-_nR5_CU_W598Pf54lttScpVzRjWxtRBKKETUlFNekrKm2llWiYZVitVGs9JpUpmqrJQtK91Iqqw0jWj4UfZ29h1Cf33j4ghtfxO69CQwotMHlGCJZGaSDX2MwTUwBL_FsAdKYKoIWpiKgKkImCqCuSLYJe3prA1ucPYgrDYYbRtHhH_AkdO07dPcaTn66S7NkEYQDoJK-DNuk9m7-7RJjZsmYGd9fEgjU-dGy8T7MPP--43bPz4tXJyuL7hRyeD1bJAi9uFgICSVmusE5zPs4-h2BxjDX5CKqxJ-fT-Bbyt1dXm-OocrfgujY6qJ</recordid><startdate>200409</startdate><enddate>200409</enddate><creator>Fushiki, Tadayoshi</creator><creator>Komaki, Fumiyasu</creator><creator>Aihara, Kazuyuki</creator><general>Blackwell Publishing Ltd</general><general>Blackwell Publishers</general><general>Blackwell</general><general>Danish Society for Theoretical Statistics</general><scope>BSCLL</scope><scope>IQODW</scope><scope>DKI</scope><scope>X2L</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>H8D</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>200409</creationdate><title>On Parametric Bootstrapping and Bayesian Prediction</title><author>Fushiki, Tadayoshi ; Komaki, Fumiyasu ; Aihara, Kazuyuki</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c5637-32180cd44747aaa81313505d18ec2b4f2b72d9825e80b9b5b7c5b8f617c69f4f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2004</creationdate><topic>asymptotic theory</topic><topic>Bayes estimators</topic><topic>Bayes theorem</topic><topic>Bayesian analysis</topic><topic>Bayesian prediction</topic><topic>Binomial distributions</topic><topic>Bootstrap method</topic><topic>bootstrap predictive distribution</topic><topic>Coefficients</topic><topic>Exact sciences and technology</topic><topic>Fisher information</topic><topic>Indices of summation</topic><topic>Inference from stochastic processes; time series analysis</topic><topic>information geometry</topic><topic>Kullback-Leibler divergence</topic><topic>Mathematics</topic><topic>Maximum likelihood estimation</topic><topic>Modeling</topic><topic>Parameter estimation</topic><topic>Parametric inference</topic><topic>Predictions</topic><topic>Predictive modeling</topic><topic>Probability and statistics</topic><topic>Sciences and techniques of general use</topic><topic>Statistical models</topic><topic>Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Fushiki, Tadayoshi</creatorcontrib><creatorcontrib>Komaki, Fumiyasu</creatorcontrib><creatorcontrib>Aihara, Kazuyuki</creatorcontrib><collection>Istex</collection><collection>Pascal-Francis</collection><collection>RePEc IDEAS</collection><collection>RePEc</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Scandinavian journal of statistics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Fushiki, Tadayoshi</au><au>Komaki, Fumiyasu</au><au>Aihara, Kazuyuki</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On Parametric Bootstrapping and Bayesian Prediction</atitle><jtitle>Scandinavian journal of statistics</jtitle><date>2004-09</date><risdate>2004</risdate><volume>31</volume><issue>3</issue><spage>403</spage><epage>416</epage><pages>403-416</pages><issn>0303-6898</issn><eissn>1467-9469</eissn><abstract>We investigate bootstrapping and Bayesian methods for prediction. The observations and the variable being predicted are distributed according to different distributions. Many important problems can be formulated in this setting. This type of prediction problem appears when we deal with a Poisson process. Regression problems can also be formulated in this setting. First, we show that bootstrap predictive distributions are equivalent to Bayesian predictive distributions in the second-order expansion when some conditions are satisfied. Next, the performance of predictive distributions is compared with that of a plug-in distribution with an estimator. The accuracy of prediction is evaluated by using the Kullback-Leibler divergence. Finally, we give some examples.</abstract><cop>Oxford, UK</cop><pub>Blackwell Publishing Ltd</pub><doi>10.1111/j.1467-9469.2004.02_127.x</doi><tpages>14</tpages></addata></record> |
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| ispartof | Scandinavian journal of statistics, 2004-09, Vol.31 (3), p.403-416 |
| issn | 0303-6898 1467-9469 |
| language | eng |
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| source | JSTOR Mathematics and Statistics; RePEc; Business Source Complete; Wiley Online Library All Journals; JSTOR |
| subjects | asymptotic theory Bayes estimators Bayes theorem Bayesian analysis Bayesian prediction Binomial distributions Bootstrap method bootstrap predictive distribution Coefficients Exact sciences and technology Fisher information Indices of summation Inference from stochastic processes time series analysis information geometry Kullback-Leibler divergence Mathematics Maximum likelihood estimation Modeling Parameter estimation Parametric inference Predictions Predictive modeling Probability and statistics Sciences and techniques of general use Statistical models Statistics |
| title | On Parametric Bootstrapping and Bayesian Prediction |
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