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dc.contributor.advisorLaverty, William H.en_US
dc.creatorKarunanayake, Chandima Piyadharshanien_US
dc.date.accessioned2007-06-07T09:10:59Zen_US
dc.date.accessioned2013-01-04T04:36:35Z
dc.date.available2007-06-08T08:00:00Zen_US
dc.date.available2013-01-04T04:36:35Z
dc.date.created2007-06en_US
dc.date.issued2007-06-08en_US
dc.date.submittedJune 2007en_US
dc.identifier.urihttp://hdl.handle.net/10388/etd-06072007-091059en_US
dc.description.abstractMultivariate count data are found in a variety of fields. For modeling such data, one may consider the multivariate Poisson distribution. Overdispersion is a problem when modeling the data with the multivariate Poisson distribution. Therefore, in this thesis we propose a new multivariate Poisson hidden Markov model based on the extension of independent multivariate Poisson finite mixture models, as a solution to this problem. This model, which can take into account the spatial nature of weed counts, is applied to weed species counts in an agricultural field. The distribution of counts depends on the underlying sequence of states, which are unobserved or hidden. These hidden states represent the regions where weed counts are relatively homogeneous. Analysis of these data involves the estimation of the number of hidden states, Poisson means and covariances. Parameter estimation is done using a modified EM algorithm for maximum likelihood estimation. We extend the univariate Markov-dependent Poisson finite mixture model to the multivariate Poisson case (bivariate and trivariate) to model counts of two or three species. Also, we contribute to the hidden Markov model research area by developing Splus/R codes for the analysis of the multivariate Poisson hidden Markov model. Splus/R codes are written for the estimation of multivariate Poisson hidden Markov model using the EM algorithm and the forward-backward procedure and the bootstrap estimation of standard errors. The estimated parameters are used to calculate the goodness of fit measures of the models.Results suggest that the multivariate Poisson hidden Markov model, with five states and an independent covariance structure, gives a reasonable fit to this dataset. Since this model deals with overdispersion and spatial information, it will help to get an insight about weed distribution for herbicide applications. This model may lead researchers to find other factors such as soil moisture, fertilizer level, etc., to determine the states, which govern the distribution of the weed counts.en_US
dc.language.isoen_USen_US
dc.subjectEM algorithmen_US
dc.subjectmultivariate Poisson hidden Markov modelen_US
dc.subjectWeed species countsen_US
dc.subjectMultivariate Poisson distributionen_US
dc.titleMultivariate Poisson hidden Markov models for analysis of spatial countsen_US
thesis.degree.departmentMathematics and Statisticsen_US
thesis.degree.disciplineMathematics and Statisticsen_US
thesis.degree.grantorUniversity of Saskatchewanen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophy (Ph.D.)en_US
dc.type.materialtexten_US
dc.type.genreThesisen_US
dc.contributor.committeeMemberSrinivasan, Rajen_US
dc.contributor.committeeMemberSoteros, Chrisen_US
dc.contributor.committeeMemberMiket, Milivoj J.en_US
dc.contributor.committeeMemberKelly, Ivan W.en_US


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