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[{"key": "dc.contributor.advisor", "value": "Taskinen, Sara", "language": null, "element": "contributor", "qualifier": "advisor", "schema": "dc"}, {"key": "dc.contributor.author", "value": "Haapaniemi, Viivi", "language": null, "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2017-06-07T12:04:29Z", "language": null, "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2017-06-07T12:04:29Z", "language": null, "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2017", "language": null, "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.other", "value": "oai:jykdok.linneanet.fi:1703168", "language": null, "element": "identifier", "qualifier": "other", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/54353", "language": null, "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "Tilastollisen mallin parametrit estimoidaan usein suurimman uskottavuuden menetelm\u00e4ll\u00e4. Havaitulla aineistolla ja voimassa olevan mallin vallitessa suurimman uskottavuuden estimointi valitsee malliparametreille arvot, jotka maksimoivat uskottavuusfunktion. Uskottavuusfunktion ollessa integraali yli latenttien eli havaitsemattomien muuttujien, ei uskottavuusfunktiota voida kuitenkaan kirjoittaa suljetussa muodossa. T\u00e4ll\u00f6in uskottavuusfunktio voidaan approksimoida variaatiomenetelm\u00e4ll\u00e4. \n\nVariaatiomenetelm\u00e4ss\u00e4 uskottavuusfunktiolle lasketaan alaraja, jota maksimoimalla saadaan approksimaatiot malliparametrien suurimman uskottavuuden estimaattoreille. Variaatiomenetelm\u00e4 tuottaa malliparametrien lis\u00e4ksi ennusteet ja niiden keskivirheet latenteille muuttujille.\n \nTutkimuksessa sovelletaan variaatiomenetelm\u00e4\u00e4 Poisson-sekamalliin ja -latenttiin muuttujamalliin ordinaatiomenetelm\u00e4lle. Sekamallilla pyrit\u00e4\u00e4n selitt\u00e4m\u00e4\u00e4n simuloinneissa eri lajien m\u00e4\u00e4r\u00e4\u00e4 ja aineistoesimerkiss\u00e4 yhden lajin yksil\u00f6m\u00e4\u00e4r\u00e4\u00e4 eri mittauspaikkoilla. Ordinaatiomenetelm\u00e4ss\u00e4 pyrit\u00e4\u00e4n havainnollistamaan aineisto kaksiulotteisena kuvana, jossa lajien suhteen samankaltaiset mittauspaikat ovat l\u00e4hell\u00e4 toisiaan. Molemmissa tapauksissa implementoidaan menetelm\u00e4 R-ohjelmistolle. Variaatiomenetelm\u00e4n soveltuvuutta laskenta-algoritmiksi tutkitaan simulointikokein. Lis\u00e4ksi sekamalli ja latentti muuttujamalli sovitetaan biologian lukum\u00e4\u00e4r\u00e4aineistoihin, joista lasketaan estimaatit malliparametreille variaatiomenetelm\u00e4ll\u00e4.\n\nTy\u00f6ss\u00e4 osoitetaan ett\u00e4 Poisson-jakauman tapauksessa variaatiomenetelm\u00e4n mukainen uskottavuusfunktion alaraja voidaan kirjoittaa suljetussa muodossa, jolloin parametrien estimointi on yksinkertaista. Poisson-sekamallin tapauksessa lajien m\u00e4\u00e4r\u00e4n lis\u00e4\u00e4minen antaa tarkemman variaatioapproksimaation. Latentissa muuttujamallissa variaatiomenetelm\u00e4 antaa hyvill\u00e4 alkuarvoilla paremman tuloksen kuin perinteisesti k\u00e4ytetty moniulotteiseen skaalaukseen perustuva NMDS-menetelm\u00e4. Kuitenkin variaatiomenetelm\u00e4 n\u00e4ytt\u00e4isi latentin muuttujamallin kohdalla reagoivan herk\u00e4sti huonoihin alkuarvoihin. Kun Poisson-sekamalli sovitetaan lukum\u00e4\u00e4r\u00e4aineistoon, saadaan selville, ett\u00e4 estimaatit ovat samansuuntaiset kuin perinteisesti k\u00e4ytetyll\u00e4 Laplace-menetelm\u00e4ll\u00e4.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted using Plone Publishing form by Viivi Haapaniemi (viemhaap) on 2017-06-07 12:04:29.392139. Form: Pro gradu -lomake (https://kirjasto.jyu.fi/julkaisut/julkaisulomakkeet/pro-gradu-lomake). JyX data: [jyx_publishing-allowed (fi) =True]", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by jyx lomake-julkaisija (jyx-julkaisija.group@korppi.jyu.fi) on 2017-06-07T12:04:29Z\nNo. of bitstreams: 2\nURN:NBN:fi:jyu-201706072724.pdf: 531644 bytes, checksum: b5e0390ba03ca336e96c60560320d18d (MD5)\nlicense.html: 4890 bytes, checksum: c1a56e085cca52bf1d2302dfc439f9af (MD5)", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2017-06-07T12:04:29Z (GMT). No. of bitstreams: 2\nURN:NBN:fi:jyu-201706072724.pdf: 531644 bytes, checksum: b5e0390ba03ca336e96c60560320d18d (MD5)\nlicense.html: 4890 bytes, checksum: c1a56e085cca52bf1d2302dfc439f9af (MD5)\n Previous issue date: 2017", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "1 verkkoaineisto (46 sivua)", "language": null, "element": "format", "qualifier": "extent", "schema": "dc"}, {"key": "dc.format.mimetype", "value": "application/pdf", "language": null, "element": "format", "qualifier": "mimetype", "schema": "dc"}, {"key": "dc.language.iso", "value": "fin", "language": null, "element": "language", "qualifier": "iso", "schema": "dc"}, {"key": "dc.rights", "value": "In Copyright", "language": "en", "element": "rights", "qualifier": null, "schema": "dc"}, {"key": "dc.subject.other", "value": "uskottavuusp\u00e4\u00e4ttely", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "variaatiomenetelm\u00e4", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "sekamalli", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "latentti muuttuja", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "ordinaatiomenetelm\u00e4", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "Poisson-jakauma", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.title", "value": "Uskottavuusfunktion approksimointi gaussisella variaatiomenetelm\u00e4ll\u00e4 Poisson-sekamallin ja -latentin muuttujamallin tapauksessa", "language": null, "element": "title", "qualifier": null, "schema": "dc"}, {"key": "dc.type", "value": "master thesis", "language": null, "element": 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