National soccer teams are currently ranked by soccer's governing body, the Federation Internationale de Football Association (FIFA). Although the system used by FIFA is thorough, taking into account many different factors, many of the weights used in the system's calculations are somewhat arbitrary. It is investigated here how the use of a statistical model might better compare the teams for ranking purposes. By treating each game played as a pairwise comparison experiment and by using the Bradley-Terry model as a starting point some suitable models are presented. A key component of the final model introduced here its ability to differentiate between friendly matches and competitive matches when determining the impact of a match on a teams ranking. Posterior distributions of the rating parameters are obtained, and the rankings and results obtained from each model are compared to FIFA's rankings and each other.

Analyzing ranking data is an essential component in a wide range of important applications including web-search and recommendation systems. Rankings are difficult to visualize or model due to the computational difficulties associated with the large number of items. On the other hand, partial or incomplete rankings induce more difficulties since approaches that adapt well to typical types of rankings cannot apply generally to all types. While analyzing ranking data has a long history in statistics, construction of an efficient framework to analyze incomplete ranking data (with or without ties) is currently an open problem. This thesis addresses the problem of scalability for visualizing and modeling partial incomplete rankings. In particular, we propose a distance measure for top-k rankings with the following three properties: (1) metric, (2) emphasis on top ranks, and (3) computational efficiency. Given the distance measure, the data can be projected into a low dimensional continuous vector space via multi-dimensional scaling (MDS) for easy visualization. We further propose a non-parametric model for estimating distributions of partial incomplete rankings. For the non-parametric estimator, we use a triangular kernel that is a direct analogue of the Euclidean triangular kernel. The computational difficulties for large n are simplified using combinatorial properties and generating functions associated with symmetric groups. We show that our estimator is computational efficient for rankings of arbitrary incompleteness and tie structure. Moreover, we propose an efficient learning algorithm to construct a preference elicitation system from partial incomplete rankings, which can be used to solve the cold-start problems in ranking recommendations. The proposed approaches are examined in experiments with real search engine and movie recommendation data.

Multinomial selection problem procedures are ranking and selection techniques that aim to select the best (most probable) alternative based upon a sequence of multinomial observations. The classical formulation of the procedure design problem is to find a decision rule for terminating sampling. The decision rule should minimize the expected number of observations taken while achieving a specified indifference zone requirement on the prior probability of making a correct selection when the alternative configurations are in a particular subset of the probability space called the preference zone. We study the constrained version of the design problem in which there is a given maximum number of allowed observations. Numerous procedures have been proposed over the past 50 years, all of them suboptimal. In this thesis, we find via linear programming the optimal selection procedure for any given probability configuration. The optimal procedure turns out to be necessarily randomized in many cases. We also find via mixed integer programming the optimal non-randomized procedure. We demonstrate the performance of the methodology on a number of examples. We then reformulate the mathematical programs to make them more efficient to implement, thereby significantly expanding the range of computationally feasible problems. We prove that there exists an optimal policy which has at most one randomized decision point and we develop a procedure for finding such a policy. We also extend our formulation to replicate existing procedures. Next, we show that there is very little difference between the relative performances of the optimal randomized and non-randomized procedures. Additionally, we compare existing procedures using the optimal procedure as a benchmark, and produce updated tables for a number of those procedures. Then, we develop a methodology that guarantees the optimal randomized and non-randomized procedures for a broad class of variable observation cost functions -- the first of its kind. We examine procedure performance under a variety of cost functions, demonstrating that incorrect assumptions regarding marginal observation costs may lead to increased total costs. Finally, we investigate and challenge key assumptions concerning the indifference zone parameter and the conditional probability of correct selection, revealing some interesting implications.

Opsomming Daar bestaan 'n behoefte aan 'n objektiewe maatstaf om die gehalte van akademiese publikasies te bepaal en te vergelyk. Hierdie navorsing het die invloed of reaksie wat deur 'n publikasie gegenereer is uit verwysingsdata bepaal. Daar is van 'n iteratiewe algoritme gebruik gemaak wat gewigte aan verwysings toeken. In die Internetomgewing word hierdie benadering reeds met groot sukses toegepas deur onder andere die PageRank-algoritme van die Google soekenjin. Hierdie en ander algoritmes in die Internetomgewing is bestudeer om 'n algoritme vir akademiese artikels te ontwerp. Daar is op 'n variasie van die PageRank-algoritme besluit wat 'n Invloedwaarde bepaal. Die algoritme is op gevallestudies getoets. Die empiriese studie dui daarop dat hierdie variasie spesialisnavorsers se intu¨ıtiewe gevoel beter weergee as net die blote tel van verwysings. Abstract Ranking of journals are often used as an indicator of quality, and is extensively used as a mechanism for determining promotion and funding. This research studied ways of extracting the impact, or influence, of a journal from citation data, using an iterative process that allocates a weight to the source of a citation. After evaluating and discussing the characteristics that influence quality and importance of research with specialist researchers, a measure called the Influence factor was introduced, emulating the PageRankalgorithm used by Google to rank web pages. The Influence factor can be seen as a measure of the reaction that was generated by a publication, based on the number of scientists who read and cited itA good correlation between the rankings produced by the Influence factor and that given by specialist researchers were found. / Mathematical Sciences / M.Sc. (Operasionele Navorsing)

Text in Afrikaans / Weens die veeleisende aard van sorggewing aan VIGS-weeskinders, bevind die sorggewers hulle dikwels in 'n posisie waar hulle self sorg en ondersteuning nodig het. Die vraag het begin ontstaan op watter manier hierdie sorggewers ondersteun kan word. Dit het duidelik geword dat die kerk vanuit hul sosiale verantwoordelikheid sorg en ondersteuning aan die sorggewers kan bied. Sorggewers van een instansie wat aan die navorsingsreis deelgeneem het, het inderdaad nie genoeg sorg en ondersteuning van die kerk ontvang nie. Hierdie gebrek aan ondersteuning het 'n direkte invloed op die sorggewers se hantering van sorggewingseise. Sorggewers van die ander twee deelnemende instansies ontvang genoeg ondersteuning van lidmate, en dit maak 'n groot verskil aan hoe sorggewingspanning beleef word. In hierdie studie is daar krities gekyk na wyses waarop die kerk betrokke is en verder kan betrokke raak by die sorggewers van VIGSweeskinders. / Philosophy, Practical & Systematic Theology / M.Th. (Praktiese Teologie)

Text in Afrikaans / Weens die veeleisende aard van sorggewing aan VIGS-weeskinders, bevind die sorggewers hulle dikwels in 'n posisie waar hulle self sorg en ondersteuning nodig het. Die vraag het begin ontstaan op watter manier hierdie sorggewers ondersteun kan word. Dit het duidelik geword dat die kerk vanuit hul sosiale verantwoordelikheid sorg en ondersteuning aan die sorggewers kan bied. Sorggewers van een instansie wat aan die navorsingsreis deelgeneem het, het inderdaad nie genoeg sorg en ondersteuning van die kerk ontvang nie. Hierdie gebrek aan ondersteuning het 'n direkte invloed op die sorggewers se hantering van sorggewingseise. Sorggewers van die ander twee deelnemende instansies ontvang genoeg ondersteuning van lidmate, en dit maak 'n groot verskil aan hoe sorggewingspanning beleef word. In hierdie studie is daar krities gekyk na wyses waarop die kerk betrokke is en verder kan betrokke raak by die sorggewers van VIGSweeskinders. / Philosophy, Practical and Systematic Theology / M.Th. (Praktiese Teologie)