Bayesian curve‐fitting with free‐knot splines
We describe a Bayesian method, for fitting curves to data drawn from an exponential family, that uses splines for which the number and locations of knots are free parameters. The method uses reversible‐jump Markov chain Monte Carlo to change the knot configurations and a locality heuristic to speed...
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| Veröffentlicht in: | Biometrika 2001-12, Vol.88 (4), p.1055-1071 |
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| container_end_page | 1071 |
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| container_issue | 4 |
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| container_title | Biometrika |
| container_volume | 88 |
| creator | Dimatteo, Ilaria Genovese, Christopher R. Kass, Robert E. |
| description | We describe a Bayesian method, for fitting curves to data drawn from an exponential family, that uses splines for which the number and locations of knots are free parameters. The method uses reversible‐jump Markov chain Monte Carlo to change the knot configurations and a locality heuristic to speed up mixing. For nonnormal models, we approximate the integrated likelihood ratios needed to compute acceptance probabilities by using the Bayesian information criterion, BIC, under priors that make this approximation accurate. Our technique is based on a marginalised chain on the knot number and locations, but we provide methods for inference about the regression coefficients, and functions of them, in both normal and nonnormal models. Simulation results suggest that the method performs well, and we illustrate the method in two neuroscience applications. |
| doi_str_mv | 10.1093/biomet/88.4.1055 |
| format | Article |
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Simulation results suggest that the method performs well, and we illustrate the method in two neuroscience applications.</description><identifier>ISSN: 0006-3444</identifier><identifier>EISSN: 1464-3510</identifier><identifier>DOI: 10.1093/biomet/88.4.1055</identifier><identifier>CODEN: BIOKAX</identifier><language>eng</language><publisher>Oxford: Oxford University Press</publisher><subject>Approximation ; BIC ; Data smoothing ; Exact sciences and technology ; Generalised linear model ; Heuristics ; Knots ; Magnetic resonance ; Magnetic resonance imaging ; Markov analysis ; Markov chains ; Mathematical foundations ; Mathematical functions ; Mathematics ; Modeling ; Monte Carlo simulation ; Nonparametric regression ; Parametric inference ; Parametric models ; Probability and statistics ; Reversible‐jump Markov chain Monte Carlo ; Sciences and techniques of general use ; Signal noise ; Smoothing ; Statistics ; Unit‐information prior</subject><ispartof>Biometrika, 2001-12, Vol.88 (4), p.1055-1071</ispartof><rights>Copyright 2001 Biometrika Trust</rights><rights>2002 INIST-CNRS</rights><rights>Copyright Oxford University Press(England) Dec 2001</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c357t-f800b6513ace95b4a58e8e30e64274f7002b17aa013eb1072b4bfe24be33ec893</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/2673701$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/2673701$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>314,780,784,803,832,27924,27925,58017,58021,58250,58254</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=14123002$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Dimatteo, Ilaria</creatorcontrib><creatorcontrib>Genovese, Christopher R.</creatorcontrib><creatorcontrib>Kass, Robert E.</creatorcontrib><title>Bayesian curve‐fitting with free‐knot splines</title><title>Biometrika</title><addtitle>Biometrika</addtitle><description>We describe a Bayesian method, for fitting curves to data drawn from an exponential family, that uses splines for which the number and locations of knots are free parameters. The method uses reversible‐jump Markov chain Monte Carlo to change the knot configurations and a locality heuristic to speed up mixing. For nonnormal models, we approximate the integrated likelihood ratios needed to compute acceptance probabilities by using the Bayesian information criterion, BIC, under priors that make this approximation accurate. Our technique is based on a marginalised chain on the knot number and locations, but we provide methods for inference about the regression coefficients, and functions of them, in both normal and nonnormal models. Simulation results suggest that the method performs well, and we illustrate the method in two neuroscience applications.</description><subject>Approximation</subject><subject>BIC</subject><subject>Data smoothing</subject><subject>Exact sciences and technology</subject><subject>Generalised linear model</subject><subject>Heuristics</subject><subject>Knots</subject><subject>Magnetic resonance</subject><subject>Magnetic resonance imaging</subject><subject>Markov analysis</subject><subject>Markov chains</subject><subject>Mathematical foundations</subject><subject>Mathematical functions</subject><subject>Mathematics</subject><subject>Modeling</subject><subject>Monte Carlo simulation</subject><subject>Nonparametric regression</subject><subject>Parametric inference</subject><subject>Parametric models</subject><subject>Probability and statistics</subject><subject>Reversible‐jump Markov chain Monte Carlo</subject><subject>Sciences and techniques of general use</subject><subject>Signal noise</subject><subject>Smoothing</subject><subject>Statistics</subject><subject>Unit‐information prior</subject><issn>0006-3444</issn><issn>1464-3510</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2001</creationdate><recordtype>article</recordtype><recordid>eNpFkE1Lw0AQhhdRsFbvHjwEwWPa_cxujlrUWgqCHyBelk2Y1e1HUne3am_-BH-jv8SESD0NM-8zMy8vQscEDwjO2bBw9RLiUKkBbwZC7KAe4RlPmSB4F_UwxlnKOOf76CCEWdtmIushcmE2EJypknLt3-Hn69u6GF31kny4-JpYD-1sXtUxCauFqyAcoj1rFgGO_mofPV5dPozG6fT2-mZ0Pk1LJmRMrcK4yARhpoRcFNwIBQoYhoxTya3EmBZEGoMJg4JgSQteWKC8AMagVDnro9Pu7srXb2sIUc_qta-al5pikuWKctpAuINKX4fgweqVd0vjN5pg3eaiu1y0UprrNpdm5ezvrgmlWVhvqtKF_z1OKGvMNdxJx81CrP1Wp5lksjHdR2knuxDhcysbP9ctIfT46VnLyd3kXo5yLdkvElB9tQ</recordid><startdate>20011201</startdate><enddate>20011201</enddate><creator>Dimatteo, Ilaria</creator><creator>Genovese, Christopher R.</creator><creator>Kass, Robert E.</creator><general>Oxford University Press</general><general>Biometrika Trust</general><general>Oxford Publishing Limited (England)</general><scope>BSCLL</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7QO</scope><scope>8FD</scope><scope>FR3</scope><scope>P64</scope></search><sort><creationdate>20011201</creationdate><title>Bayesian curve‐fitting with free‐knot splines</title><author>Dimatteo, Ilaria ; Genovese, Christopher R. ; Kass, Robert E.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c357t-f800b6513ace95b4a58e8e30e64274f7002b17aa013eb1072b4bfe24be33ec893</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2001</creationdate><topic>Approximation</topic><topic>BIC</topic><topic>Data smoothing</topic><topic>Exact sciences and technology</topic><topic>Generalised linear model</topic><topic>Heuristics</topic><topic>Knots</topic><topic>Magnetic resonance</topic><topic>Magnetic resonance imaging</topic><topic>Markov analysis</topic><topic>Markov chains</topic><topic>Mathematical foundations</topic><topic>Mathematical functions</topic><topic>Mathematics</topic><topic>Modeling</topic><topic>Monte Carlo simulation</topic><topic>Nonparametric regression</topic><topic>Parametric inference</topic><topic>Parametric models</topic><topic>Probability and statistics</topic><topic>Reversible‐jump Markov chain Monte Carlo</topic><topic>Sciences and techniques of general use</topic><topic>Signal noise</topic><topic>Smoothing</topic><topic>Statistics</topic><topic>Unit‐information prior</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Dimatteo, Ilaria</creatorcontrib><creatorcontrib>Genovese, Christopher R.</creatorcontrib><creatorcontrib>Kass, Robert E.</creatorcontrib><collection>Istex</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Biotechnology Research Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Biotechnology and BioEngineering Abstracts</collection><jtitle>Biometrika</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Dimatteo, Ilaria</au><au>Genovese, Christopher R.</au><au>Kass, Robert E.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Bayesian curve‐fitting with free‐knot splines</atitle><jtitle>Biometrika</jtitle><addtitle>Biometrika</addtitle><date>2001-12-01</date><risdate>2001</risdate><volume>88</volume><issue>4</issue><spage>1055</spage><epage>1071</epage><pages>1055-1071</pages><issn>0006-3444</issn><eissn>1464-3510</eissn><coden>BIOKAX</coden><abstract>We describe a Bayesian method, for fitting curves to data drawn from an exponential family, that uses splines for which the number and locations of knots are free parameters. The method uses reversible‐jump Markov chain Monte Carlo to change the knot configurations and a locality heuristic to speed up mixing. For nonnormal models, we approximate the integrated likelihood ratios needed to compute acceptance probabilities by using the Bayesian information criterion, BIC, under priors that make this approximation accurate. Our technique is based on a marginalised chain on the knot number and locations, but we provide methods for inference about the regression coefficients, and functions of them, in both normal and nonnormal models. Simulation results suggest that the method performs well, and we illustrate the method in two neuroscience applications.</abstract><cop>Oxford</cop><pub>Oxford University Press</pub><doi>10.1093/biomet/88.4.1055</doi><tpages>17</tpages></addata></record> |
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| ispartof | Biometrika, 2001-12, Vol.88 (4), p.1055-1071 |
| issn | 0006-3444 1464-3510 |
| language | eng |
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| source | JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing; Oxford University Press Journals All Titles (1996-Current) |
| subjects | Approximation BIC Data smoothing Exact sciences and technology Generalised linear model Heuristics Knots Magnetic resonance Magnetic resonance imaging Markov analysis Markov chains Mathematical foundations Mathematical functions Mathematics Modeling Monte Carlo simulation Nonparametric regression Parametric inference Parametric models Probability and statistics Reversible‐jump Markov chain Monte Carlo Sciences and techniques of general use Signal noise Smoothing Statistics Unit‐information prior |
| title | Bayesian curve‐fitting with free‐knot splines |
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