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dc.contributor.advisorSethuraman, Sunder
dc.contributor.authorLippitt, William Lindsay
dc.creatorLippitt, William Lindsay
dc.date.accessioned2019-09-17T02:03:30Z
dc.date.available2019-09-17T02:03:30Z
dc.date.issued2019
dc.identifier.urihttp://hdl.handle.net/10150/634359
dc.description.abstractWe study the connections among three types of objects: Residual Allocation Models (RAMs), a generalized class of stick-breaking processes which include Dirichlet processes, and the occupation laws of certain discrete space time-inhomogeneous Markov chains. These connections are established through a new clumping procedure on RAMs according to a clumping sequence. We introduce and analyze two methods of its application with respect to homogeneous Markov chains. Clumping according to the rst method results in a class of stick-breaking measures we later identify as the limit of the empirical occupation measures for particular time-inhomogeneous Markov chains. Clumping according to the second method leads to a general study of self-similarity as a characterization of random probability measures, which we apply in context. We further discuss the occupation law of an inhomogeneous Markov chain related to simulated annealing and its connections to stick-breaking measures. By introducing a reverse-chronological clumping procedure, we dene and study the local occupations up to time n of the Markov chain. As n gets large, these local occupations converge jointly to the clumped RAM structure resulting from the rst method above. We then explore additional properties of the generalized stick-breaking measure uncovered by the connection to the occupation law, and consider potential applications of results.
dc.language.isoen
dc.publisherThe University of Arizona.
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction, presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
dc.subjectclumping
dc.subjectDirichlet
dc.subjectGEM
dc.subjectMarkov
dc.subjectRAM
dc.subjectstick-breaking
dc.titleClumping, Stick-breaking, and an Inhomogeneous Markov Chain
dc.typetext
dc.typeElectronic Dissertation
thesis.degree.grantorUniversity of Arizona
thesis.degree.leveldoctoral
dc.contributor.committeememberGlickenstein, David
dc.contributor.committeememberZhang, Hao Helen
dc.contributor.committeememberBedrick, Edward
thesis.degree.disciplineGraduate College
thesis.degree.disciplineMathematics
thesis.degree.namePh.D.
refterms.dateFOA2019-09-17T02:03:30Z


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