School of Mathematics and Statistics - Theses

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Now showing 1 - 9 of 9
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    On sample size determination for discrete data
    Gordon, Ian Robert. (University of Melbourne, 1993)
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    On sample size determination for discrete data
    Gordon, Ian Robert. (University of Melbourne, 1993)
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    A length preserving geometric heat flow for curves
    Pihan, Denis M. ( 1998)
    This thesis is concerned with the formulation and analysis of a length preserving geometric heat flow for curves, which is the steepest descent flow for the thread problem. The thread problem is the classical problem of minimising the area functional of a surface, subject to the constraint of keeping part of the boundary fixed, while the remainder has some prescribed length. We derive the gradient flow for the thread problem, for the case that the thread has co-dimension one, establish its short-time existence, examine appropriate maximum principles and discuss its properties. Concentrating on the flow of curves in the plane, we establish that closed, convex, embedded curves converge exponentially to a circle, which solves the thread problem and the corresponding isoperimetric problem.
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    Adolescent perceptions of the concept of randomness
    Toohey, Phillip Gerard ( 1994)
    An investigation into adolescents perceptions of concepts of randomness, with a questionnaire trialled on 75 adolescent boys between Year 7 and Year 11 in Catholic schools in Melbourne, Australia.
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    Subcoal seismic exploration in The Gippsland Basin (Australia)
    Dunne, Jarrod Craig ( 1996-10)
    Deep seismic exploration in the Gippsland Basin is hindered by strong, unidentified noise below the Latrobe Group coal sequence. Low velocity events that appeared in field data semblance analyses suggested that an elastic wave modelling study was required to understand the subcoal reflection response. The modified reflectivity method (Kennet, 1980) provided a means for constructing detailed and accurate synthetic seismograms from realistic depth models, under the assumption of an isotropic, plane-layered earth. A study into the effect of each part of an elastic depth model (upon an elastic depth model (upon an elastic synthetic seismogram) resulted in a set of guidelines for obtaining a field data comparison. Excellent ties were obtained at several wells, often using little more than a partial sonic log. The noise contributions to the synthesis were interpreted using additional synthetics computed from variations upon the depth model and by exercising control over the wave types modelled. Subsequent processing of the synthetics revealed three types of persistent noise in progressively deeper parts of the subcoal image: 1) mode converted interbed multiples (generated within the coal sequence); 2) S-wave reflections and long period multiples (generated between the coal sequence and the Miocene carbonates and 3) surface related multiples.
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    Spiritual health: its nature and place in the school curriculum
    Fisher, John W. ( 1998-04)
    As spirituality first appeared in Australian curriculum documents in 1994, it was important to establish how educators thought it related to student well- being. In this research a description and four accounts of spirituality - spiritual rationalism, monism, dualism, and multidimensional unity - were developed from available literature. The literature also revealed four sets of relationships important to spiritual well-being. These were the relationships of a person with themself, others, environment, and Transcendent Other. The model of spiritual health proposed here claims that these four sets of relationships can be developed in corresponding Personal, Communal, Environmental and Global domains of human existence, each of which has two aspects - knowledge and inspiration. Progressive synergism describes the inter-relationship between the four domains. The quality of relationships in the four domains constitutes , spiritual well-being in each domain. Spiritual health is indicated by the combined effect of spiritual well-being in each of the domains embraced by a person. The principles of grounded theory qualitative research methodology were used to investigate the views of 98 teachers from a variety of schools near Melbourne. Feedback from 23 Australian experts, on the researcher’s definitions, is discussed. To encompass all the teachers’ views of spiritual health, to the initial categories of Personalist, Communalist, Environmentalist and Globalist, a fifth category was added for the small group Rationalists, who embraced the knowledge, but not the inspiration/transcendent aspects, of the first three domains of spiritual well-being. All the teachers believed spiritual health should be included in the school curriculum, most rating it of high importance, two-thirds believing it should be integral to the curriculum. The teachers’ major curriculum concerns focussed on Self, Others, the Transcendent, or Wholeness. Investigation of those teacher characteristics seen as important for promoting spiritual health, with associated hindrances and ideals, showed variation by gender, personal view of spiritual health, major curriculum concern, teacher and school type. Greatest variation was noticed when comparing school type. State school teachers emphasised care for the individual student from a humanistic perspective. Catholic school teachers were concerned for the individual, with religious activities being implemented by dedicated teachers. Other Christian school teachers focussed on corporate, not individualistic, activities, and emphasised relationship with God. Other non-government school teachers emphasised tradition, with attendant moral values. Implications of these variations on school choice are discussed. Principals’ behaviour, speech and attitude were considered by the teachers to be vital in providing opportunities for spiritual development in schools. A 30-item Spiritual Health Measure (of Humanistic and Religious Aspects of Spiritual Health) was developed using the researcher’s model of spiritual health and data from 300 UK teachers. The SHM should be useful as a diagnostic for individuals or groups to provide base data from which to plan enhancement of their spiritual health. This thesis contains an analysis of how well the Victorian Curriculum & Standards Framework provides guidelines for promoting spiritual health. A position of responsibility, called Spiritual Facilitator, is proposed to help ensure that the rhetoric about spiritual well-being is put into practice in schools.
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    Flowshop sequencing: a graphic approach
    Park, M. M. ( 1990-03)
    This thesis is concerned with flowshop sequencing which seeks to arrange a variety of different jobs in a sequence which minimizes the total time for the completion of all jobs.
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    On the role of non-uniform smoothness parameters and the probabilistic method in applications of the Stein-Chen Method
    Weinberg, Graham Victor ( 1999-12)
    The purpose of the research presented here is twofold. The first component explores the probabilistic interpretation of Stein’s method, as introduced in Barbour (1988). This is done in the setting of random variable approximations. This probabilistic method, where the Stein equation is interpreted in terms of the generator of an underlying birth and death process having equilibrium distribution equal to that of the approximant, provides a natural explanation of why Stein’s method works. An open problem has been to use this generator approach to obtain bounds on the differences of the solution to the Stein equation. Uniform bounds on these differences produce Stein “magic” factors, which control the bounds. With the choice of unit per capita death rate for the birth and death process, we are able to produce a result giving a new Stein factor bound, which applies to a selection of distributions. The proof is via a probabilistic approach, and we also include a probabilistic proof of a Stein factor bound from Barbour, Holst and Janson (1992). These results generalise the work of Xia (1999), which applies to the Poisson distribution with unit per capita death rate. (For complete abstract open document)
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    Conditional inference
    Senyonyi-Mubiru, John Musisi ( 1984)
    Conditional inference is a branch of statistical inference in which observed data is reduced using either sufficient or ancillary statistics. This often simplifies inference about the parameters. In comparison to full likelihood methods, conditional inference theory’s performance still needs validating in many areas. Some of these are the concern of this thesis. While the definition of an ancillary statistic in single parameter models is unequivocal, the presence of accessory (or nuisance) parameters in a model presents problems in defining an ancillary statistic. Statistical literature abounds with definitions of ancillarity in this case. Some of the commonest and most useful of these are discussed and shown to be interrelated. This facilitates the choice of the strongest eligible ancillary in a problem, i.e. that which offers the biggest reduction of the sample space. The Pitman-Morgan test for variance ratios in bivariate normal populations with unknown correlation coefficient is shown to be a conditional test. We condition on sufficient statistics for the accessory parameters to eliminate them. The test statistic is then derived as an ancillary statistic for the accessory parameters. When a probability model depends on a number of accessory parameters which increases with the sample size, estimation methods based on the full likelihood will often be inconsistent. Using a partial likelihood instead has been suggested. Local maximum partial likelihood estimators are shown to exist, and to be consistent and asymptotically normal under mild conditions. These results also cover conditional and marginal likelihoods, thus considerably strengthening earlier results in this area. In planning statistical inferences, it is useful to choose a sampling scheme which provides only the essential data to our inferences. Jagers’ lemma proposes very general conditions under which maximum likelihood estimation from a subset of the data is identical with that from the full data. However, the lemma is incorrect as given. We show that an additional sufficiency condition repairs the lemma. It is further shown that this lemma cannot be extended to general exponential families.