The primary role of a physical anthropologist is to provide sufficient information to assist in the individualisation of unknown skeletal remains. This is often achieved in establishing a biological profile of the deceased, of which ancestry is an essential aspect. Several successful osteometric and morphological approaches have been developed to facilitate the estimation of ancestry from the cranium. However, the cranium is not always available for analysis, emphasising a need for postcranial alternatives. The postcranial skeleton is frequently labelled as too variable and unreliable to provide an accurate assessment of ancestry. Yet, numerous studies utilise the postcrania for sex and stature estimation, where the a priori knowledge of ancestry results in higher accuracy. Thus, the presence of postcranial differences among populations when investigating other biological parameters inherently demonstrates the potential for the estimation of ancestry. The purpose of this study was to quantify postcranial variation among modern, peer-reported black, white and coloured South Africans. A series of 39 standard measurements were taken from 11 postcranial bones, namely the clavicle, scapula, humerus, radius, ulna, sacrum, pelvis, femur, tibia, fibula and calcaneus. The sample consisted of 360 modern South African individuals (120 black, 120 white, 120 coloured) from the Pretoria Bone and Kirsten Collections housed at the University of Pretoria and the University of Stellenbosch, respectively. Group differences were explored with ANOVA and Tukey’s honestly significant difference test (HSD). Group means were used to create univariate sectioning points for each variable indicated as significant with ANOVA. Where two of the three groups had similar mean values, the groups were pooled for the creation of the sectioning points. Multivariate classification models were employed using linear and flexible discriminant analysis (LDA and FDA, respectively). Classification accuracies were compared to evaluate which model yielded the best results. The results demonstrated variable patterns of group overlap. Black and coloured South Africans displayed similar means for breadth measurements, and black and white South Africans showed similar means for the maximum length of distal limb elements. The majority of group variation is attributed to differences in size and robusticity, where white South Africans are overall larger and more robust than black and coloured South Africans. Accuracies for the univariate sectioning points ranged from 43% to 87%, with iliac breadth performing the best. However, the majority of the univariate sectioning points can only classify individuals into two groups rather than three because of similar group means. Multivariate bone models created using all measurements per bone resulted in accuracies ranging from 46% to 62% (LDA) and 41% to 66% (FDA). Multivariate subsets consisting of numerous different measurement combinations from several skeletal elements achieved accuracies as high as 85% (LDA) and 87% (FDA). Ultimately the best results were achieved using combinations of different variables from several skeletal elements. Overall, the multivariate models yielded better results than the univariate approach, as the inclusion of more variables is generally better for maximising group differences. Furthermore, FDA achieved higher accuracies than the more traditional approach of LDA. Despite the significant overlap among the groups, the postcranial skeleton has proven to be proficient in distinguishing the three groups. Thus, even in a heterogeneous population, a multivariate postcraniometric approach can be used to estimate ancestry with high accuracy. / Dissertation (MSc)--University of Pretoria, 2015. / Anatomy / Unrestricted

Random matrix theory is an outstanding mathematical tool that has demonstrated its usefulness in many areas ranging from wireless communication to finance and economics. The main motivation behind its use comes from the fundamental role that random matrices play in modeling unknown and unpredictable physical quantities. In many situations, meaningful metrics expressed as scalar functionals of these random matrices arise naturally. Along this line, the present work consists in leveraging tools from random matrix theory in an attempt to answer fundamental questions related to applications from statistical signal processing and machine learning. In a first part, this thesis addresses the development of analytical tools for the computation of the inverse moments of random Gram matrices with one side correlation. Such a question is mainly driven by applications in signal processing and wireless communications wherein such matrices naturally arise. In particular, we derive closed-form expressions for the inverse moments and show that the obtained results can help approximate several performance metrics of common estimation techniques. Then, we carry out a large dimensional study of discriminant analysis classifiers. Under mild assumptions, we show that the asymptotic classification error approaches a deterministic quantity that depends only on the means and covariances associated with each class as well as the problem dimensions. Such result permits a better understanding of the underlying classifiers, in practical large but finite dimensions, and can be used to optimize the performance. Finally, we revisit kernel ridge regression and study a centered version of it that we call centered kernel ridge regression or CKRR in short. Relying on recent advances on the asymptotic properties of random kernel matrices, we carry out a large dimensional analysis of CKRR under the assumption that both the data dimesion and the training size grow simultaneiusly large at the same rate. We particularly show that both the empirical and prediction risks converge to a limiting risk that relates the performance to the data statistics and the parameters involved. Such a result is important as it permits a better undertanding of kernel ridge regression and allows to efficiently optimize the performance.

>Magister Scientiae - MSc / The thesis aims to determine the depositional environments, rock types and petrophysical characteristics of the reservoirs in Wells E-S3, E-S5 and F-AH4 of Area X in the Bredasdorp Basin, offshore South Africa. The three wells were studied using methods including core description, petrophysical analysis, seismic facies and multivariate statistics in order to evaluate their reservoir potential. The thesis includes digital wireline log signatures, 2D seismic data, well data and core analysis from selected depths. Based on core description, five lithofacies were identified as claystone (HM1), fine to coarse grained sandstone (HM2), very fine to medium grained sandstone (HM3), fine to medium grained sandstone (HM4) and conglomerate (HM5). Deltaic and shallow marine depositional environments were also interpreted from the core description based on the sedimentary structures and ichnofossils. The results obtained from the petrophysical analysis indicate that the sandstone reservoirs show a relatively fair to good porosity (range 13-20 %), water saturation (range 17-45 %) and a predicted permeability (range 4- 108 mD) for Wells E-S3, E-S5 andF-AH4. The seismic facies model of the study area shows five seismic facies described as parallel, variable amplitude variable continuity, semi-continuous high amplitude, divergent variable amplitude and chaotic seismic facies as well as a probable shallow marine, deltaic and submarine fan depositional system. Linking lithofacies to seismic facies maps helped to understand and predict the distribution and quality of reservoir packages in the studied wells. Multivariate statistical methods of factor, discriminant and cluster analysis were used. For Wells E-S3, E-S5 and F-AH4, two factors were derived from the wireline log data reflecting oil and non- oil bearing depths. Cluster analysis delineated oil and non-oil bearing groups with similar wireline properties. This thesis demonstrates that the approach taken is useful because petrophysical analysis, seismic facies and multivariate statistics has provided useful information on reservoir quality such as net to gross, depths of hydrocarbon saturation and depositional environment.

Travel and tourism marketers face a highly competitive environment brought on by the changing demographics of the U.S. population, the most significant change being the growth in size of the mature segment of the population. In terms of market size, there are currently 73 million people age 50 and older, comprising nearly one-fourth of the U.S. population (U.S. Census Bureau 2000). That number is expected to rise to 96 million by 2010, representing one-third of the population (Rasmusson 2000). A swelling population is not the only enticement that this age group offers. It is important to note that many mature consumers have deep pockets and a strong desire to spend. In fact, they control more than three-quarters of the wealth and one-half of the discretionary income in the nation. It is also estimated that they lay claim to three-fourths of the country's financial assets and boast more than $1 trillion in annual buying power. When all is said and done, this age group accounts for 40 percent of the total consumer demand in the United States (Swartz, 1999). However, even though recognizing the significance of the mature market in terms of their market size and economic potential, little research has been conducted to identify and understand the mature travelers who use the Internet.The main purpose of this study is to profile mature travelers on the basis of Internet use. More specifically, the intention is to examine the demographic and socio-economic characteristics of mature travelers who use the Internet compared to those who do not use the Internet. In addition, the purpose of the present study is to examine whether or not differences exist between Internet users and Internet non-users among mature travelers with respect to travel behavior. Attention is paid to investigate types of trip selected, the preferred activities participated in during the travel, length of stay, travel-related expenditures, type of lodging, type of transportation, number in the travel party, and type of travel party in explaining the differences between Internet users and Internet non-users of the mature market.Data were collected by utilizing a mailed questionnaire. 433 responses (23.44 percent of the total target population) were coded and used for data analysis. Data were analyzed by employing three types of data analysis: chi-square tests of independence; t-tests; and multiple discriminant analysis.The findings in the present study suggest that there are numerous differences in demographics, socio-economic characteristics, and travel characteristics between Internet users and Internet non-users among mature travelers. As a whole, for example, the results revealed that mature travelers who use the Internet were more likely to be younger, have higher annual household incomes, and have higher levels of education than mature travelers who do not use the Internet. Also, the results indicated that mature travelers who are still working are more likely to use the Internet than those who are not working. By understanding and utilizing information gathered from Internet users' and Internet non-users' demographics, socio-economic characteristics, and travel characteristics, tourism planners and marketers can develop appropriate and effective marketing strategies that appeal to mature travelers. / Master of Science

Machine learning is emerging as a powerful tool to data science and is being applied in almost all subjects. In many applications, the number of features is com- parable to the number of samples, and both grow large. This setting is usually named the high-dimensional regime. In this regime, new challenges arise when it comes to the application of machine learning. In this work, we conduct a high-dimensional performance analysis of some popular classification and regression techniques. In a first part, discriminant analysis classifiers are considered. A major challenge towards the use of these classifiers in practice is that they depend on the inverse of covariance matrices that need to be estimated from training data. Several estimators for the inverse of the covariance matrices can be used. The most common ones are estimators based on the regularization approach. In this thesis, we propose new estimators that are shown to yield better performance. The main principle of our proposed approach is the design of an optimized inverse covariance matrix estimator based on the assumption that the covariance matrix is a low-rank perturbation of a scaled identity matrix. We show that not only the proposed classifiers are easier to implement but also, outperform the classical regularization-based discriminant analysis classifiers. In a second part, we carry out a high-dimensional statistical analysis of linear support vector regression. Under some plausible assumptions on the statistical dis- tribution of the data, we characterize the feasibility condition for the hard support vector regression and, when feasible, derive an asymptotic approximation for its risk. Similarly, we study the test risk for the soft support vector regression as a function of its parameters. The analysis is then extended to the case of kernel support vector regression under generalized linear models assumption. Based on our analysis, we illustrate that adding more samples may be harmful to the test performance of these regression algorithms, while it is always beneficial when the parameters are optimally selected. Our results pave the way to understand the effect of the underlying hyper- parameters and provide insights on how to optimally choose the kernel function.

This study develops a bankruptcy prediction model for South African companies listed on the Johannesburg Stock Exchange. The model is of considerable efficiency and the findings reported extend bankruptcy literature to developing countries. 64 financial ratios for 28 companies, grouped into failed and non-failed companies, were tested using multiple discriminant analysis after conducting normality tests. Three variables were found to be significant which are: Times Interest Earned, Cash to Debt and Working Capital to Turnover. The model correctly classified about 75% of failed and non-failed in the original and cross validation procedures. This study went on to conduct an external validation of the model superiority by introducing a sample of failed companies, which showed that the model predictive accuracy is more than chance. Despite the popularity of the topic among researchers this study highlighted the importance and relevance of the topic to corporate managers, policy makers and to investors especially in a developing market perspective, thereby contributing significantly towards understanding the factors that lead to corporate bankruptcy.

The transfer pricing, literature indicates that an investigation of some aspects of this subject could usefully be undertaken in order to contribute to the understanding of transfer pricing in both domestic and international markets. This study aims at exploring the current state of transfer pricing practice and establishing the importance attached to the ranking of transfer pricing determinants (i. e. objectives and environmental variables) and the extent to which the ranking varies across markets, industry, and according to the transfer pricing method used. It also seeks to discover interrelationship among the transfer pricing determinants in order to produce a reduced set of basic factors. Lastly, it aims at evaluating the relationship between transfer pricing determinants and transfer pricing methods and at discovering a means of predicting the latter from the company's perception of the relative importance of these determinants. To achieve the above objectives, an empirical study covering both domestic and international markets was undertaken in UK companies. The conclusions are concerned with transfer pricing policy, methods currently used, and problems apparent in practice. The overall ranking-by survey respondents of the transfer pricing determinants is given as well as the results of tests of certain hypotheses which relate to this ranking. The transfer pricing determinants used in the survey for domestic and international. markets (twelve and twenty respectively) have been reduced by Factor Analysis to four and six factors. The study made use of the results to obtain measures of the ranking of discovered factors. Finally, the relationship between the transfer pricing determinants and transfer pricing methods was quantitatively evaluated in the form of a set of classification functions by using Multi-Discriminant Analysis. The classification functions are able to predict the transfer pricing method actually used in companies with an acceptable degree of success. The study's results have been reviewed with a small number of senior managers who are involved in establishing transfer pricing policy within their companies. / Egyptian Government and Al-Azher University

<p> Application of four statistical techniques of discrimination is made to a set of multivariate data. The techniques, proposed by R.A . Fisher [6], C.R. Rao Q4] , D.F. Andrews [l] and H. Chernoff [4], are reviewed, applied and criticized in an intercomparison of the four methods. Graphic illustrations are also utilized to aid in the classification of sampling units. </p> / Thesis / Master of Science (MSc)

Recent work on fractionally-supervised classification (FSC), an approach that allows classification to be carried out with a fractional amount of weight given to the unla- belled points, is extended in two important ways. First, and of fundamental impor- tance, the question over how to choose the amount of weight given to the unlabelled points is addressed. Then, the FSC approach is extended to mixtures of multivariate t-distributions. The first extension is essential because it makes FSC more readily applicable to real problems. The second, although less fundamental, demonstrates the efficacy of FSC beyond Gaussian mixture models. / Thesis / Master of Science (MSc)

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