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Prevalence is a valuable epidemiological measure about the burden of disease in a community for planning health services; however, true prevalence is typically underestimated and there exists no reliable method of confirming the estimate of this prevalence in question. This thesis studies imprecise priors for the development of a statistical reasoning framework regarding this epidemiological decision making problem. The concept of imprecise probabilities introduced by Walley (1991) is adopted for the construction of this inferential framework in order to model prior ignorance and quantify the degree of imprecision associated with the inferential process. The study is restricted to the standard and zero-truncated Poisson sampling models that give an exponential family with a canonical log-link function because of the mechanism involved with the estimation of population size. A three-parameter exponential family of posteriors which includes the normal and log-gamma as limiting cases is introduced by applying normal priors on the canonical parameter of the Poisson sampling models. The canonical parameters simplify dealing with families of priors as Bayesian updating corresponds to a translation of the family in the canonical hyperparameter space. The canonical link function creates a linear relationship between regression coefficients of explanatory variables and the canonical parameters of the sampling distribution. Thus, normal priors on the regression coefficients induce normal priors on the canonical parameters leading to a higher-dimensional exponential family of posteriors whose limiting cases are again normal or log-gamma. All of these implementations are synthesized to build the ipeglim package (Lee, 2013) that provides a convenient method for characterizing imprecise probabilities and visualizing their translation, soft-linearity, and focusing behaviours. A characterization strategy for imprecise priors is introduced for instances when there exists a state of complete ignorance. The learning process of an individual intentional unit, the agreement process between several intentional units, and situations concerning prior-data conflict are graphically illustrated. Finally, the methodology is applied for re-analyzing the data collected from the epidemiological disease surveillance of three specific cases – Cholera epidemic (Dahiya, 1973), Down’s syndrome (Zelterman, 1988), and the female users of methamphetamine and heroin (B ̈ ohning, 2009).

This thesis considers mathematical models of the interaction between social and territorial behaviour in animals, mainly by probabilistic methods. Chapter 1 introduces the Resource Dispersion Hypothesis, which suggests that territorial behaviour plus dispersed food resources can explain the existence of social groups, and describes an existing model of the process, due to Carr and Macdonald. In Chapter 2 the model of Carr and Macdonald is analysed, and in Chapter 3 an improved model is suggested and its main properties derived, primarily using renewal theory. Chapters 4 and 5 consider various spatial models for territory formation, and the effect, of spatial factors on social behaviour, using analytic and simulation-based methods. Chapter 6 considers the evolution of social behaviour using both discrete-time deterministic models and branching processes to investigate the viability of different strategies of social behaviour in the presence of dispersed resources.

Atmospheric particles play a crucial role in climate, visibility, air pollution, and human health. Reactions between gas-phase molecules and particles (heterogeneous reactions) affect not only the particle composition and morphology, but also the composition of the atmosphere. This thesis investigates the heterogeneous chemistry of organic mixtures and inorganic solutions coated with organic monolayers as proxies for atmospheric particles. The first topic of interest was the reaction between N₂0₅ and aqueous inorganic solutions coated with organic monolayers. The goal of this work was to better understand how organic monolayers on aqueous particles affect the mass transport and kinetics of N₂0₅ uptake by aqueous aerosols, and consequently what effectthe monolayer can have on predicted concentrations of N₂0₅ in the atmosphere. To investigate heterogeneous reactions of inorganic solutions coated with an organic monolayer a new rectangular channel flow reactor was developed. This newly developed flow reactor was described in detail and validated. Subsequently, the new flow reactor was used to study the reactive uptake of N₂0₅ on sulfuric acid solutions in the presence of a variety of 1- and 2-component monolayers with varying functional groups, solubilities, chain lengths, surface pressures, and molecular surface areas. Reactive uptake of N₂0₅ on aqueous sulfuric acid solutions was found to correlate most strongly with the molecular surface area or packing density of the monolayer. These results provide a good foundation for determining the influence of monolayers on heterogeneous reactions in the atmosphere, and highlight the need for characterization of monolayer surface properties of organic monolayers present on atmospheric particles. The second topic of interest was reactions between 0₃ and proxies for meat cooking aerosols with the goal to better understand the effect of the phase and microstructure of the mixtures on the lifetime of oleic acid (OA) in atmospheric particles. The reactive uptake of 0₃ was approximately 1 order of magnitude slower on binarysolid-liquid mixtures and multicomponent mixtures that closely represent compositions of meat-cooking aerosols compared to the liquid solutions. Lifetimes up to 75 min were obtained for these mixtures.

Thesis (Ph. D.)--Texas State University-San Marcos, 2007. / Vita. Appendices: leaves 194-207. Includes bibliographical references (leaves 208-209).

Thesis (Ph.D.)--McMaster University, 2004. / Supervisor: N. Balakrishnan. Includes bibliographical references (p. 186-191).

Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 123-124).

Thesis (Ph. D.)--University of Washington. / Bibliography: l. 99-100.

Thesis (Ph.D.)--University of Melbourne, Dept. of Mathematics and Statistics, 2001. / Typescript (photocopy). Includes bibliographical references (leaves 126-128).

Thesis (Ph.D)--University of Adelaide, Dept. of Pure Mathematics, 2001. / Includes bibliographies and index. Also available in an electronic version via ADT (Australian Digital Theses) Program.