{"data":{"id":"10.6084/m9.figshare.c.2032223","type":"dois","attributes":{"doi":"10.6084/m9.figshare.c.2032223","prefix":"10.6084","suffix":"m9.figshare.c.2032223","identifiers":[],"alternateIdentifiers":[],"creators":[{"name":"Titsias, Michalis K.","nameType":"Personal","givenName":"Michalis K.","familyName":"Titsias","affiliation":[],"nameIdentifiers":[]},{"name":"Holmes, Christopher C.","nameType":"Personal","givenName":"Christopher C.","familyName":"Holmes","affiliation":[],"nameIdentifiers":[]},{"name":"Yau, Christopher","nameType":"Personal","givenName":"Christopher","familyName":"Yau","affiliation":[],"nameIdentifiers":[]}],"titles":[{"title":"Statistical Inference in Hidden Markov Models Using \u003ci\u003ek\u003c/i\u003e-Segment Constraints"}],"publisher":"Figshare","container":{},"publicationYear":2015,"subjects":[{"subject":"Biophysics"},{"subject":"Molecular Biology"},{"subject":"Neuroscience"},{"subject":"Biotechnology"},{"subject":"69999 Biological Sciences not elsewhere classified","subjectScheme":"FOR"},{"subject":"FOS: Biological sciences","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"FOS: Biological sciences","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"80699 Information Systems not elsewhere classified","subjectScheme":"FOR"},{"subject":"FOS: Computer and information sciences","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"FOS: Computer and information sciences","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"19999 Mathematical Sciences not elsewhere classified","subjectScheme":"FOR"},{"subject":"FOS: Mathematics","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"FOS: Mathematics","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"Mental Health"}],"contributors":[],"dates":[{"date":"2015-12-05","dateType":"Created"},{"date":"2016-05-05","dateType":"Updated"},{"date":"2015","dateType":"Issued"}],"language":null,"types":{"ris":"GEN","bibtex":"misc","citeproc":"article","schemaOrg":"Collection","resourceType":"Collection","resourceTypeGeneral":"Collection"},"relatedIdentifiers":[],"relatedItems":[],"sizes":[],"formats":[],"version":null,"rightsList":[{"rights":"CC-BY","rightsUri":"http://creativecommons.org/licenses/by/3.0/us"}],"descriptions":[{"description":"Hidden Markov models (HMMs) are one of the most widely used statistical methods for analyzing sequence data. However, the reporting of output from HMMs has largely been restricted to the presentation of the most-probable (MAP) hidden state sequence, found via the Viterbi algorithm, or the sequence of most probable marginals using the forward–backward algorithm. In this article, we expand the amount of information we could obtain from the posterior distribution of an HMM by introducing linear-time dynamic programming recursions that, conditional on a user-specified constraint in the number of segments, allow us to (i) find MAP sequences, (ii) compute posterior probabilities, and (iii) simulate sample paths. We collectively call these recursions \u003ci\u003ek\u003c/i\u003e-segment algorithms and illustrate their utility using simulated and real examples. We also highlight the prospective and retrospective use of \u003ci\u003ek\u003c/i\u003e-segment constraints for fitting HMMs or exploring existing model fits. Supplementary materials for this article are available online.","descriptionType":"Abstract"}],"geoLocations":[],"fundingReferences":[],"xml":"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","url":"https://figshare.com/collections/Statistical_Inference_in_Hidden_Markov_Models_using_i_k_i_segment_constraints/2032223","contentUrl":null,"metadataVersion":3,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"api","isActive":true,"state":"findable","reason":null,"viewCount":0,"viewsOverTime":[],"downloadCount":0,"downloadsOverTime":[],"referenceCount":0,"citationCount":0,"citationsOverTime":[],"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":0,"created":"2015-12-05T17:11:09.000Z","registered":"2015-12-05T17:11:10.000Z","published":"2015","updated":"2024-12-12T14:57:30.000Z"},"relationships":{"client":{"data":{"id":"figshare.ars","type":"clients"}},"provider":{"data":{"id":"otjm","type":"providers"}},"media":{"data":{"id":"10.6084/m9.figshare.c.2032223","type":"media"}},"references":{"data":[]},"citations":{"data":[]},"parts":{"data":[]},"partOf":{"data":[]},"versions":{"data":[]},"versionOf":{"data":[]}}}}