Extensions of quantal problems
Başlık çevirisi mevcut değil.
- Tez No: 400208
- Danışmanlar: DR. NİCK FİELLER
- Tez Türü: Doktora
- Konular: İstatistik, Statistics
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 2000
- Dil: İngilizce
- Üniversite: The University of Sheffield
- Enstitü: Yurtdışı Enstitü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 298
Özet
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Özet (Çeviri)
A problem which arises in many different contexts is whether a given set of data can beregarded as integral multiples of some basic unit (or quantum), observed subject tosmall errors. Typically, the value of the quantum has to be deduced from the data. Thisthesis is concerned with the investigation of problems in the analysis of such basicquantal models as well as the extensions required to investigate more complex quantalproblems motivated by problems in Biology. These concern lateral rootlet spacings inplants such as onions, tomatoes and ferns and arise in data provided by agriculturalresearch stations in Badajoz, Spain, and Long Ashton, UK.The first chapter begins with a review of the historical development of quantalproblems (notably in relation to atomic weights and megalithic yards) and earlyapproaches to their analyses. The second chapter presents the fundamental statisticaltool of quantogram analysis developed by Kendall and an alternative Bayesian approachprovided by Freeman in their analyses of the .megalithic yard problem., establishingvarious statistical properties of the first of these. The comparative power of statistics fortesting for pure and shifted quantality are investigated in the following chapter. Chapter4 introduces the various sets of data on rootlet spacings with some initial analyses andthe following chapter applies basic quantal analyses to these sets, identifyingdeficiencies in the models in their inability to handle the particular data structures. As aconsequence, various extended quantal models are proposed. The first of these, ahierarchical quantal model, allows for closely related samples to have distinct but.close. values of a quantum, perhaps at various levels, analogous to one-way orhierarchical linear models. The second, a regression quantal model, allows the value ofa quantum to change .slowly. with a covariate (e.g. the position along the parent root).Various computationally intensive algorithmic techniques and graphical tools for theiranalysis are proposed and applied in Chapter 6. Chapter 7 returns to the Bayesianformulation and applies MCMC methods to the analysis, adapting the approach tocover the extended quantal models. Throughout, new techniques for analysis areillustrated and validated on simulated data before application to the data on rootletspacings. Chapter 8 summarises and concludes the thesis.
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