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[{"key": "dc.contributor.advisor", "value": "Luoma, Arto", "language": "", "element": "contributor", "qualifier": "advisor", "schema": "dc"}, {"key": "dc.contributor.author", "value": "L\u00e4hderanta, Tero", "language": "", "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2018-11-30T06:42:06Z", "language": null, "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2018-11-30T06:42:06Z", "language": null, "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2018", "language": "", "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/60393", "language": null, "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "Markovin ketju Monte Carlo -menetelm\u00e4t ovat olleet t\u00e4rke\u00e4 osa Bayes-tilastotiedett\u00e4 jo 90-luvulta saakka. Monet perinteiset MCMC-algoritmit, kuten Metropolis-algoritmi ja Gibbsin otanta, ovat yh\u00e4 suuressa suosiossa tutkijoiden keskuudessa. N\u00e4m\u00e4 yksinkertaiset simulaatioalgoritmit muuttuvat sit\u00e4 tehottomammiksi, mit\u00e4 monimutkaisemmista malleista on kysymys. T\u00e4ss\u00e4 tutkielmassa esitell\u00e4\u00e4n Hamiltonin Monte Carlo, jolla pyrit\u00e4\u00e4n ratkaisemaan monimutkaisten mallien ongelman simuloinnissa. HMC-algoritmin matemaattisen haastavuuden takia algoritmin toiminta esitet\u00e4\u00e4n ensin yksinkertaisten esimerkkien kautta, mink\u00e4 j\u00e4lkeen syvennyt\u00e4\u00e4n sen rakenteeseen ja teoreettiseen taustaan. T\u00e4m\u00e4n lis\u00e4ksi vertaillaan HMC:n ja Metropolis-algoritmin tehokkuutta ja autokorrelaatioita kahdessa finanssimallissa samalla k\u00e4yden l\u00e4pi algoritmin implementoinnin haasteet. \n\nEsimerkinomaisena sovelluskohteena k\u00e4ytet\u00e4\u00e4n kahta finanssimallia, joiden avulla mallinnetaan osake- ja korkosijoitusten tuottoa. Bayesil\u00e4inen l\u00e4hestymistapa on luonteva tapa arvioida finanssimallien parametrien ep\u00e4varmuutta. Molemmissa valituissa malleissa HMC osoittautui ajallisesti hitaammaksi kuin Metropolis-algoritmi: samankaltaisten tulosten saaminen vaati HMC-algoritmissa huomattavasti v\u00e4hemm\u00e4n iteraatioita kuin Metropolis-algoritmissa, mutta yksitt\u00e4isen arvon generoiminen oli HMC:ss\u00e4 huomattavasti hitaampaa. HMC-algoritmin tuottaman ketjun j\u00e4senten v\u00e4linen autokorrelaatio oli kuitenkin merkitt\u00e4v\u00e4sti pienemp\u00e4\u00e4 mit\u00e4 Metropolis-algoritmissa.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by Paivi Vuorio (paelvuor@jyu.fi) on 2018-11-30T06:42:06Z\nNo. of bitstreams: 0", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2018-11-30T06:42:06Z (GMT). No. of bitstreams: 0\n Previous issue date: 2018", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "47", "language": "", "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": "Bayes-tilastotiede", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "Hamiltonin Monte Carlo", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "simulointialgoritmit", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.title", "value": "Hamiltonin Monte Carlon soveltaminen finanssiaikasarjoihin", "language": "", "element": "title", "qualifier": null, "schema": "dc"}, {"key": "dc.type", "value": "master thesis", "language": null, "element": "type", "qualifier": null, "schema": "dc"}, {"key": "dc.identifier.urn", "value": "URN:NBN:fi:jyu-201811304943", "language": "", "element": "identifier", "qualifier": "urn", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Pro gradu -tutkielma", "language": "fi", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Master\u2019s thesis", "language": "en", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Matemaattis-luonnontieteellinen tiedekunta", "language": "fi", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Faculty of Sciences", "language": "en", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Matematiikan ja tilastotieteen laitos", "language": "fi", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Department of Mathematics and Statistics", "language": "en", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "Jyv\u00e4skyl\u00e4n yliopisto", "language": "fi", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "University of Jyv\u00e4skyl\u00e4", "language": "en", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Tilastotiede", "language": "fi", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Statistics", "language": "en", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "yvv.contractresearch.funding", "value": "0", "language": "", "element": "contractresearch", "qualifier": "funding", "schema": "yvv"}, {"key": "dc.type.coar", "value": "http://purl.org/coar/resource_type/c_bdcc", "language": null, "element": "type", "qualifier": "coar", "schema": "dc"}, {"key": "dc.rights.accesslevel", "value": "openAccess", "language": null, "element": "rights", "qualifier": "accesslevel", "schema": "dc"}, {"key": "dc.type.publication", "value": "masterThesis", "language": null, "element": "type", "qualifier": "publication", "schema": "dc"}, {"key": "dc.subject.oppiainekoodi", "value": "4043", "language": "", "element": "subject", "qualifier": "oppiainekoodi", "schema": "dc"}, {"key": "dc.subject.yso", "value": "algoritmit", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "Monte Carlo -menetelm\u00e4t", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "tilastotiede", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.format.content", "value": "fulltext", "language": null, "element": "format", "qualifier": "content", "schema": "dc"}, {"key": "dc.rights.url", "value": "https://rightsstatements.org/page/InC/1.0/", "language": null, "element": "rights", "qualifier": "url", "schema": "dc"}, {"key": "dc.type.okm", "value": "G2", "language": null, "element": "type", "qualifier": "okm", "schema": "dc"}]
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