Bayesian and pseudo-likelihood interval estimation for comparing two Poisson rate parameters using under-reported data.

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dc.contributor.advisorYoung, Dean M.
dc.contributor.authorGreer, Brandi A.
dc.contributor.departmentStatistical Sciences.en
dc.contributor.otherBaylor University. Dept. of Statistical Sciences.en
dc.date.accessioned2009-04-01T15:56:04Z
dc.date.available2009-04-01T15:56:04Z
dc.date.copyright2008-12
dc.date.issued2009-04-01T15:56:04Z
dc.descriptionIncludes bibliographical references (p. 99-101).en
dc.description.abstractWe present interval estimation methods for comparing Poisson rate parameters from two independent populations with under-reported data for the rate difference and the rate ratio. In addition, we apply the Bayesian paradigm to derive credible intervals for both the ratio and the difference of the Poisson rates. We also construct pseudo-likelihood-based confidence intervals for the ratio of the rates. We begin by considering two cases for analyzing under-reported Poisson counts: inference when training data are available and inference when they are not. From these cases we derive two marginal posterior densities for the difference in Poisson rates and corresponding credible sets. First, we perform Monte Carlo simulation analyses to examine the effects of differing model parameters on the posterior density. Then we perform additional simulations to study the robustness of the posterior density to misspecified priors. In addition, we apply the new Bayesian credible intervals for the difference of Poisson rates to an example concerning the mortality rates due to acute lower respiratory infection in two age groups for children in the Upper River Division in Gambia and to an example comparing automobile accident injury rates for male and female drivers. We also use the Bayesian paradigm to derive two closed-form posterior densities and credible intervals for the Poisson rate ratio, again in the presence of training data and without it. We perform a series of Monte Carlo simulation studies to examine the properties of our new posterior densities for the Poisson rate ratio and apply our Bayesian credible intervals for the rate ratio to the same two examples mentioned above. Lastly, we derive three new pseudo-likelihood-based confidence intervals for the ratio of two Poisson rates using the double-sampling paradigm for under-reported data. Specifically, we derive profile likelihood-, integrated likelihood-, and approximate integrated likelihood-based intervals. We compare coverage properties and interval widths of the newly derived confidence intervals via a Monte Carlo simulation. Then we apply our newly derived confidence intervals to an example comparing cervical cancer rates.en
dc.description.degreePh.D.en
dc.description.statementofresponsibilityby Brandi A. Greer.en
dc.format.extentxii, 101 p. : ill.en
dc.format.extent520612 bytes
dc.format.extent2363703 bytes
dc.format.mimetypeapplication/pdf
dc.format.mimetypeapplication/pdf
dc.identifier.urihttp://hdl.handle.net/2104/5283
dc.language.isoen_USen
dc.rightsBaylor University theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Contact librarywebmaster@baylor.edu for inquiries about permission.en
dc.rights.accessrightsBaylor University access onlyen
dc.subjectConfidence intervals.en
dc.subjectPoisson distribution.en
dc.subjectBayesian statistical decision theory.en
dc.subjectSampling (Statistics)en
dc.subjectMonte Carlo method.en
dc.subjectMathematical statistics.en
dc.titleBayesian and pseudo-likelihood interval estimation for comparing two Poisson rate parameters using under-reported data.en
dc.typeThesisen

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