Multivariate Poisson hidden Markov models for analysis of spatial counts
Multivariate 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 hid...
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ndltd-USASK-oai-usask.ca-etd-06072007-0910592013-01-08T16:32:48Z Multivariate Poisson hidden Markov models for analysis of spatial counts Karunanayake, Chandima Piyadharshani EM algorithm multivariate Poisson hidden Markov model Weed species counts Multivariate Poisson distribution Multivariate 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. <p>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.<p>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. Srinivasan, Raj Soteros, Chris Miket, Milivoj J. Laverty, William H. Kelly, Ivan W. University of Saskatchewan 2007-06-08 text application/pdf http://library.usask.ca/theses/available/etd-06072007-091059/ http://library.usask.ca/theses/available/etd-06072007-091059/ en unrestricted I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to University of Saskatchewan or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. |
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EM algorithm multivariate Poisson hidden Markov model Weed species counts Multivariate Poisson distribution |
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EM algorithm multivariate Poisson hidden Markov model Weed species counts Multivariate Poisson distribution Karunanayake, Chandima Piyadharshani Multivariate Poisson hidden Markov models for analysis of spatial counts |
description |
Multivariate 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. <p>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.<p>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. |
author2 |
Srinivasan, Raj |
author_facet |
Srinivasan, Raj Karunanayake, Chandima Piyadharshani |
author |
Karunanayake, Chandima Piyadharshani |
author_sort |
Karunanayake, Chandima Piyadharshani |
title |
Multivariate Poisson hidden Markov models for analysis of spatial counts |
title_short |
Multivariate Poisson hidden Markov models for analysis of spatial counts |
title_full |
Multivariate Poisson hidden Markov models for analysis of spatial counts |
title_fullStr |
Multivariate Poisson hidden Markov models for analysis of spatial counts |
title_full_unstemmed |
Multivariate Poisson hidden Markov models for analysis of spatial counts |
title_sort |
multivariate poisson hidden markov models for analysis of spatial counts |
publisher |
University of Saskatchewan |
publishDate |
2007 |
url |
http://library.usask.ca/theses/available/etd-06072007-091059/ |
work_keys_str_mv |
AT karunanayakechandimapiyadharshani multivariatepoissonhiddenmarkovmodelsforanalysisofspatialcounts |
_version_ |
1716532140610420736 |