School of Mathematics and Statistics - Theses
Permanent URI for this collection
Search Results
1 - 3 of 3
-
ItemComputer simulation models for the gravity flow of ore in sublevel caving( 1978-02)In recent years a number of research centres have endeavoured to provide a mathematical model that indicates the chief characteristics of ore flow in the sublevel caving mining method. Optimization of the design parameters for sublevel caving has ensued with the objective of maximizing ore recovery while minimizing waste dilution. Past studies have been confined by two simplifying assumptions: that the region of flow be approximated by a simple mathematical function, and that the flow analysis is static, ie extraction is calculated by employing an idealized ore-waste boundary position for each ring. Further investigation into models of ore flow has been stimulated on two counts.1. full scale tests have indicated that a more complex description is required;2. as a design tool, a dynamic analysis that monitors the displacement of the broken rock mass during extraction would yield more realistic recovery predictions under operating conditions, and enable variations on the method to be evaluated.This study reviews the various formulations currently available, or being developed to describe the flow of granular material. A viable solution in a mining context would be three dimensional, time dependent, and incorporate stress conditions. Although workers in diverse fields have analyzed the problem no solution exists at present. The majority of studies are either empirical in nature, or deficient in one or other of the above criteria. Two approaches are developed and implemented on a digital computer:(i) stochastic flow model(ii) empirical flow model based on the results of modelling studies, and full scale test. Although a number of concepts introduced in these models remain to be verified, the validity of these models would be measured by their success or failure as a simulation tool in a mining environment.
-
ItemConditional inference( 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.
-
ItemDistribution-free inference about quantiles( 1972)This thesis is concerned with the problem of drawing inferences about populations when little or nothing is known about the form of the underlying distribution. Chapter 1 reviews the general problems, but the thesis as a whole is more concerned with problems of estimation than with tests of hypotheses.