On Classes of Equivalence and Identifiability of Age-Dependent Branching Processes
Age-dependent branching processes are increasingly used in analyses of biological data. Despite being central to most statistical procedures, the identifiability of these models has not been studied. In this paper we partition a family of age-dependent branching processes into equivalence classes ov...
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| Veröffentlicht in: | Advances in applied probability 2014-09, Vol.46 (3), p.704-718 |
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| creator | Chen, Rui Hyrien, Ollivier |
| description | Age-dependent branching processes are increasingly used in analyses of biological data. Despite being central to most statistical procedures, the identifiability of these models has not been studied. In this paper we partition a family of age-dependent branching processes into equivalence classes over which the distribution of the population size remains identical. This result can be used to study identifiability of the offspring and lifespan distributions for parametric families of branching processes. For example, we identify classes of Markov processes that are not identifiable. We show that age-dependent processes with (nonexponential) gamma-distributed lifespans are identifiable and that Smith-Martin processes are not always identifiable. |
| doi_str_mv | 10.1239/aap/1409319556 |
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Despite being central to most statistical procedures, the identifiability of these models has not been studied. In this paper we partition a family of age-dependent branching processes into equivalence classes over which the distribution of the population size remains identical. This result can be used to study identifiability of the offspring and lifespan distributions for parametric families of branching processes. For example, we identify classes of Markov processes that are not identifiable. We show that age-dependent processes with (nonexponential) gamma-distributed lifespans are identifiable and that Smith-Martin processes are not always identifiable.</description><identifier>ISSN: 0001-8678</identifier><identifier>EISSN: 1475-6064</identifier><identifier>DOI: 10.1239/aap/1409319556</identifier><identifier>PMID: 25598541</identifier><identifier>CODEN: AAPBBD</identifier><language>eng</language><publisher>Cambridge, UK: Cambridge University Press</publisher><subject>60J80 ; 60J85 ; Bellman-Harris process ; Biological ; Cumulative distribution functions ; Equivalence ; Equivalence relation ; Factorials ; Genealogy ; General Applied Probability ; Identifiability ; Integers ; Laplace transformation ; Markov analysis ; Markov processes ; Mathematical models ; Parametric models ; Partitions ; Population (statistical) ; Population growth ; Population size ; Probability ; Probability distribution ; Sevastyanov process ; Smith-Martin process ; Studies</subject><ispartof>Advances in applied probability, 2014-09, Vol.46 (3), p.704-718</ispartof><rights>Applied Probability Trust</rights><rights>Copyright © Applied Probability Trust 2014</rights><rights>Copyright Applied Probability Trust Sep 2014</rights><rights>Copyright 2014 Applied Probability Trust</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c526t-ea5c8dc65135f372aabcf33f78368ce3b331474abd47b8e0214f90d45b4467ef3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/43563372$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.cambridge.org/core/product/identifier/S0001867800007333/type/journal_article$$EHTML$$P50$$Gcambridge$$H</linktohtml><link.rule.ids>164,230,314,776,780,799,828,881,27901,27902,55603,57992,57996,58225,58229</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/25598541$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Chen, Rui</creatorcontrib><creatorcontrib>Hyrien, Ollivier</creatorcontrib><title>On Classes of Equivalence and Identifiability of Age-Dependent Branching Processes</title><title>Advances in applied probability</title><addtitle>Advances in Applied Probability</addtitle><description>Age-dependent branching processes are increasingly used in analyses of biological data. Despite being central to most statistical procedures, the identifiability of these models has not been studied. In this paper we partition a family of age-dependent branching processes into equivalence classes over which the distribution of the population size remains identical. This result can be used to study identifiability of the offspring and lifespan distributions for parametric families of branching processes. For example, we identify classes of Markov processes that are not identifiable. We show that age-dependent processes with (nonexponential) gamma-distributed lifespans are identifiable and that Smith-Martin processes are not always identifiable.</description><subject>60J80</subject><subject>60J85</subject><subject>Bellman-Harris process</subject><subject>Biological</subject><subject>Cumulative distribution functions</subject><subject>Equivalence</subject><subject>Equivalence relation</subject><subject>Factorials</subject><subject>Genealogy</subject><subject>General Applied Probability</subject><subject>Identifiability</subject><subject>Integers</subject><subject>Laplace transformation</subject><subject>Markov analysis</subject><subject>Markov processes</subject><subject>Mathematical models</subject><subject>Parametric models</subject><subject>Partitions</subject><subject>Population (statistical)</subject><subject>Population growth</subject><subject>Population size</subject><subject>Probability</subject><subject>Probability distribution</subject><subject>Sevastyanov process</subject><subject>Smith-Martin process</subject><subject>Studies</subject><issn>0001-8678</issn><issn>1475-6064</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><recordid>eNqFkk1v1DAQhi0Eokvhyg0UiQuXtP62c0GUpUCllYoQPVuOM9l6lXW2dlKp_x6HDUsLSPgysuf1M--MjdBLgk8IZdWptbtTwnHFSCWEfIQWhCtRSiz5Y7TAGJNSS6WP0LOUNnnLlMZP0REVotKCkwX6dhmKZWdTglT0bXF-M_pb20FwUNjQFBcNhMG33ta-88PdJDlbQ_kRdhCmVPEh2uCufVgXX2PvYOI8R09a2yV4McdjdPXp_PvyS7m6_HyxPFuVTlA5lGCF042TgjDRMkWtrV3LWKs0k9oBqxnLvXBbN1zVGjAlvK1ww0XNuVTQsmP0bs_djfUWGpftRNuZXfRbG-9Mb715mAn-2qz7W8NpxamSGfB-BsR-A26A0XW-eQBYXq3m0znkeZvf886ItwfEzQhpMFufHHSdDdCPyRBNpcRKKvp_qaQYV4TIifrmD-mmH2PIwzRE5LdVeZGsOtmrXOxTitAenBNsps_xt9nX9wd2kP_6DVnwai_YpKGPhzxn-TL72QKeK9ptHX2zhnvG_l3zBwguzo4</recordid><startdate>20140901</startdate><enddate>20140901</enddate><creator>Chen, Rui</creator><creator>Hyrien, Ollivier</creator><general>Cambridge University Press</general><general>Applied Probability Trust</general><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>7X8</scope><scope>5PM</scope></search><sort><creationdate>20140901</creationdate><title>On Classes of Equivalence and Identifiability of Age-Dependent Branching Processes</title><author>Chen, Rui ; Hyrien, Ollivier</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c526t-ea5c8dc65135f372aabcf33f78368ce3b331474abd47b8e0214f90d45b4467ef3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>60J80</topic><topic>60J85</topic><topic>Bellman-Harris process</topic><topic>Biological</topic><topic>Cumulative distribution functions</topic><topic>Equivalence</topic><topic>Equivalence relation</topic><topic>Factorials</topic><topic>Genealogy</topic><topic>General Applied Probability</topic><topic>Identifiability</topic><topic>Integers</topic><topic>Laplace transformation</topic><topic>Markov analysis</topic><topic>Markov processes</topic><topic>Mathematical models</topic><topic>Parametric models</topic><topic>Partitions</topic><topic>Population (statistical)</topic><topic>Population growth</topic><topic>Population size</topic><topic>Probability</topic><topic>Probability distribution</topic><topic>Sevastyanov process</topic><topic>Smith-Martin process</topic><topic>Studies</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Chen, Rui</creatorcontrib><creatorcontrib>Hyrien, Ollivier</creatorcontrib><collection>PubMed</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research 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><collection>MEDLINE - Academic</collection><collection>PubMed Central (Full Participant titles)</collection><jtitle>Advances in applied probability</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Chen, Rui</au><au>Hyrien, Ollivier</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On Classes of Equivalence and Identifiability of Age-Dependent Branching Processes</atitle><jtitle>Advances in applied probability</jtitle><addtitle>Advances in Applied Probability</addtitle><date>2014-09-01</date><risdate>2014</risdate><volume>46</volume><issue>3</issue><spage>704</spage><epage>718</epage><pages>704-718</pages><issn>0001-8678</issn><eissn>1475-6064</eissn><coden>AAPBBD</coden><abstract>Age-dependent branching processes are increasingly used in analyses of biological data. Despite being central to most statistical procedures, the identifiability of these models has not been studied. In this paper we partition a family of age-dependent branching processes into equivalence classes over which the distribution of the population size remains identical. This result can be used to study identifiability of the offspring and lifespan distributions for parametric families of branching processes. For example, we identify classes of Markov processes that are not identifiable. We show that age-dependent processes with (nonexponential) gamma-distributed lifespans are identifiable and that Smith-Martin processes are not always identifiable.</abstract><cop>Cambridge, UK</cop><pub>Cambridge University Press</pub><pmid>25598541</pmid><doi>10.1239/aap/1409319556</doi><tpages>15</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | Advances in applied probability, 2014-09, Vol.46 (3), p.704-718 |
| issn | 0001-8678 1475-6064 |
| language | eng |
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| source | Jstor Complete Legacy; JSTOR Mathematics & Statistics; Cambridge University Press Journals Complete |
| subjects | 60J80 60J85 Bellman-Harris process Biological Cumulative distribution functions Equivalence Equivalence relation Factorials Genealogy General Applied Probability Identifiability Integers Laplace transformation Markov analysis Markov processes Mathematical models Parametric models Partitions Population (statistical) Population growth Population size Probability Probability distribution Sevastyanov process Smith-Martin process Studies |
| title | On Classes of Equivalence and Identifiability of Age-Dependent Branching Processes |
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