The technical advancements in genomics, functional magnetic-resonance and other areas of scientific research seen in the last two decades have led to a burst of interest in multiple testing procedures. A driving factor for innovations in the field of multiple testing has been the problem of large scale simultaneous testing. There, the goal is to uncover lower--dimensional signals from high--dimensional data. Mathematically speaking, this means that the dimension d is usually in the thousands while the sample size n is relatively small (max. 100 in general, often due to cost constraints) --- a characteristic commonly abbreviated as d >> n. In my thesis I look at several multiple testing problems and corresponding procedures from a false discovery rate (FDR) perspective, a methodology originally introduced in a seminal paper by Benjamini and Hochberg (2005). FDR analysis starts by fitting a two--component mixture model to the observed test statistics. This mixture consists of a null model density and an alternative component density from which the interesting cases are assumed to be drawn. In the thesis I proposed a new approach called log--FDR to the estimation of false discovery rates. Specifically, my new approach to truncated maximum likelihood estimation yields accurate null model estimates. This is complemented by constrained maximum likelihood estimation for the alternative density using log--concave density estimation. A recent competitor to the FDR is the method of \"Higher Criticism\". It has been strongly advocated in the context of variable selection in classification which is deeply linked to multiple comparisons. Hence, I also looked at variable selection in class prediction which can be viewed as a special signal identification problem. Both FDR methods and Higher Criticism can be highly useful for signal identification. This is discussed in the context of variable selection in linear discriminant analysis (LDA), a popular classification method. FDR methods are not only useful for multiple testing situations in the strict sense, they are also applicable to related problems. I looked at several kinds of applications of FDR in linear classification. I present and extend statistical techniques related to effect size estimation using false discovery rates and showed how to use these for variable selection. The resulting fdr--effect method proposed for effect size estimation is shown to work as well as competing approaches while being conceptually simple and computationally inexpensive. Additionally, I applied the fdr--effect method to variable selection by minimizing the misclassification rate and showed that it works very well and leads to compact and interpretable feature sets.

The technical advancements in genomics, functional magnetic-resonance and other areas of scientific research seen in the last two decades have led to a burst of interest in multiple testing procedures. A driving factor for innovations in the field of multiple testing has been the problem of large scale simultaneous testing. There, the goal is to uncover lower--dimensional signals from high--dimensional data. Mathematically speaking, this means that the dimension d is usually in the thousands while the sample size n is relatively small (max. 100 in general, often due to cost constraints) --- a characteristic commonly abbreviated as d >> n. In my thesis I look at several multiple testing problems and corresponding procedures from a false discovery rate (FDR) perspective, a methodology originally introduced in a seminal paper by Benjamini and Hochberg (2005). FDR analysis starts by fitting a two--component mixture model to the observed test statistics. This mixture consists of a null model density and an alternative component density from which the interesting cases are assumed to be drawn. In the thesis I proposed a new approach called log--FDR to the estimation of false discovery rates. Specifically, my new approach to truncated maximum likelihood estimation yields accurate null model estimates. This is complemented by constrained maximum likelihood estimation for the alternative density using log--concave density estimation. A recent competitor to the FDR is the method of \"Higher Criticism\". It has been strongly advocated in the context of variable selection in classification which is deeply linked to multiple comparisons. Hence, I also looked at variable selection in class prediction which can be viewed as a special signal identification problem. Both FDR methods and Higher Criticism can be highly useful for signal identification. This is discussed in the context of variable selection in linear discriminant analysis (LDA), a popular classification method. FDR methods are not only useful for multiple testing situations in the strict sense, they are also applicable to related problems. I looked at several kinds of applications of FDR in linear classification. I present and extend statistical techniques related to effect size estimation using false discovery rates and showed how to use these for variable selection. The resulting fdr--effect method proposed for effect size estimation is shown to work as well as competing approaches while being conceptually simple and computationally inexpensive. Additionally, I applied the fdr--effect method to variable selection by minimizing the misclassification rate and showed that it works very well and leads to compact and interpretable feature sets.

In this dissertation we propose methodology for testing SNP-sets for genetic associations, both for sequencing and genome-wide association studies. Due to the large scale of this kind of data, there is an emphasis on producing methodology that is not only accurate and powerful, but also computationally efficient.

Identifying genes linked to the appearance of certain types of cancers and their phenotypes is a well-known and challenging problem in bioinformatics. Discovering marker genes which, upon genetic mutation, drive the proliferation of different types and subtypes of cancer is critical for the development of advanced tests and therapies that will specifically identify, target, and treat certain cancers. Therefore, it is crucial to find methods that are successful in recovering "cancer-critical genes" from the (usually much larger) set of all genes in the human genome. We approach this problem in the statistical context as a feature (or variable) selection problem for clustering, in the case where the number of important features is typically small (or rare) and the signal of each important feature is typically minimal (or weak). Genetic datasets typically consist of hundreds of samples (n) each with tens of thousands gene-level measurements (p), resulting in the well-known statistical "large p small n" problem. The class or cluster identification is based on the clinical information associated with the type or subtype of the cancer (either known or unknown) for each individual. We discuss and develop novel feature ranking methods, which complement and build upon current methods in the field. These ranking methods are used to select features which contain the most significant information for clustering. Retaining only a small set of useful features based on this ranking aids in both a reduction in data dimensionality, as well as the identification of a set of genes that are crucial in understanding cancer subtypes. In this paper, we present an outline of cutting-edge feature selection methods, and provide a detailed explanation of our own contributions to the field. We explain both the practical properties and theoretical advantages of the new tools that we have developed. Additionally, we explore a well-developed case study applying these new feature selection methods to different levels of genetic data to explore their practical implementation within the field of bioinformatics.

This project studies the signal detection and identification problem in high-dimensional noisy data and the possibility of using it on microbiome data. An extensive simulation study was performed on generated data using as well as a microbiome dataset collected on patients with Parkinson's disease, using Donoho and Jin's Higher criticism, Jager and Wellner's phi-divergence-based goodness-of-fit-test and Stepanova and Pavlenko's CsCsHM statistic . We present some novel approaches based on established theory that perform better than existing methods and show that it is possible to use the signal identification framework to detect differentially abundant features in microbiome data. Although the novel approaches produce good results, they lack substantial mathematical foundations and should be avoided if theoretical rigour is needed. We also conclude that while we have found that it is possible to use signal identification methods to find abundant features in microbiome data, further refinement is necessary before it can be properly used in research. / Detta projekt studerar signaldetekterings- och identifieringsproblemet i högdimensionell brusig data och möjligheten att använda det på mikrobiomdata från människor. En omfattande simuleringsstudie utfördes på genererad data samt ett mikrobiomdataset som samlats in på patienter med Parkinsons sjukdom, med hjälp av ett antal goodness-of-fit-metoder: Donoho och Jins Higher criticis , Jager och Wellners phi-divergenser och Stepanova och Pavelenkos CsCsHM. Vi presenterar några nya tillvägagångssätt baserade på vedertagen teori som visar sig fungera bättre än befintliga metoder och visar att det är möjligt att använda signalidentifiering för att upptäcka olika funktioner i mikrobiomdata. Även om de nya metoderna ger goda resultat saknar de betydande matematiska grunder och bör undvikas om teoretisk formalism är nödvändigt. Vi drar också slutsatsen att medan vi har funnit att det är möjligt att använda signalidentifieringsmetoder för att hitta information i mikrobiomdata, är ytterligare experiment nödvändiga innan de kan användas på ett korrekt sätt i forskning.

Text in Afrikaans, with summaries in Afrikaans and English / Includes bibliographical references (leaves 383-403) / Die woordestryd oor goddelike inspirasie van alles wat in die Bybel staan, as gevolg van die uitgesproke stellings van Johannes Du Plessis, het tot ‘n krisis gelei wat as baken in die annale van die Ned. Geref. Kerk beskou word. Die meeste van sy standpunte word vandag as waarheid aanvaar en hy het bygedra tot die intellektuele debat oor die Bybel as Woord van God wat vandag nog aangaan. Du Plessis se herkoms, opleiding en verdienste as predikant en saakgelastigde van die Kerk word kortliks bespreek. Hy was die talentvolle seun en enigste kind van 'n Afrikaanse predikant en 'n Engelse vrou, die dogter van 'n sendeling van die LMS. Hy word professor aan die Kweekskool en met kennis opgedoen tydens verdere studie oorsee, het hy gewys op dele van die Bybel wat nie aan goddelike inspirasie toegeskryf kan word nie. Hy het dit ook duidelik gestel dat hy as teoloog en leermeester nie kon glo sonder om te probeer verstaan nie. Hy het sy bevindinge bekend gemaak in Het Zoeklicht, 'n maandblad wat bedoel was om as soeklig te dien om verskillende vorms van “duisternis” in beide godsdiens en die politiek, betref, aan die lig te bring. Oortuig van die waarde van die Hoër Kritiek, het hy dit as sy plig geag om wat hy deur wye leeswerk en kritiese ondersoek rakende die oorsprong, vorm en inhoud van die Ou Testamentiese boeke bekom het, bekend te maak. Artikels van dié aard, eers in De Kerkbode en daarna in Het Zoeklicht, het gelei tot beroering onder behoudende lesers wat gekant was teen enige veranderinge in die prediking. Hulle was veral ontstoke oor sy siening dat die belydenisskrifte wat spruit uit die dae van die Hervorming 500 jaar tevore, oop was vir herformulering. Klagtes dat Du Plessis op 'n gevaarlike pad was, was die begin van wat gelei het tot 'n krisis in die Kerk, en uiteindelik tot 'n buitengewone sinode in 1930 toe hy van sy pos onthef is. Die behoudende reaksie van die meerderheid was dat die Bybel die onfeilbare Woord van God is. Die gevolg was dat 'n groot aantal van die leiers van die Kerk, aanhangers van die Nasionale Party wat in 1948 aan bewind gekom het, tekste uit die Bybel gebruik het om die beleid van Apartheid Skriftuurlik te begrond. Ná byna veertig jaar van 'n onkritiese benadering tot die Bybel, is die geloof in 'n foutlose Bybel weer bevraagteken. Tussen die eerlike teoloë wat dit gewaag het om te wys op foute en inkonsekwenthede, was Ferdinand Deist en Willem Vorster. Albei het hulle opleiding as predikante voltooi maar het hulle nie beroepbaar gestel nie omdat hulle met verdere studie voortgegaan het en hulle openlik uitgespreek het teen die misbruik van Bybelse gegewens om apartheid te regverdig. Geskool aan die Kweekskool in Stellenbosch, het Deist hom onderskei as geleerde wat sy drang na dieper ondersoek gepaar het met 'n piëtisme waarop hy uiting gegee het in 'n stortvloed van akademiese en populêre geskrifte ― wat nie altyd gestrook het met sy stelling dat die Woord van God nie met 'n gelyk-aan-teken aan mekaar verbind kan word nie. Vorster, wat sy opleiding aan die Universiteit van Pretoria ontvang het, het ewe bekend geraak en het internasionale erkenning geniet vir sy toepassing van die semantiek op studies van die Nuwe Testament. Daarby het hy sy kennis van die Nabye Oosterse tale toepaslik gevind in sy bydrae tot The New Quest om meer te wete te kom oor die historiese Jesus, 'n Jood en Galileër wat vir 'n kort periode opgetree het as leermeester en eskatologiese profeet. In die studie van bydraes van die drie geleerdes tot ons verstaan van die Bybel, is ook aandag geskenk aan 'n ander aspek van die Bybel as problematiese teks: Die nadruk wat skrywers en redaktors van die Bybelse gebeure, geplaas het op mans as vaders en seuns ten koste van vroue, moeders en dogters. Die gevolg was dat meeste van die sogenaamde Kerkvaders genoeg in die Bybel kon vind om hulle te identifiseer met die neerhalende beeld wat in Die Openbaring (14:3-4) geskep word van vroue, opvallend in stryd met die inhoud van Genesis 1:26-31. / The controversy started by Johannes Du Plessis over the question whether everything in the Bible was inspired by God, caused a crisis in the Dutch Reformed Church, which is listed as a beacon in its history. Most of the points he raised are accepted as truth today, and started an intellectual debate that is still going on. Information relating to Du Plessis’ origins, training, and achievements as a minister and church official is briefly noted. He was the talented son, and only child of an Afrikaner father and minister of religion, and an English mother, the daughter of an LMS missionary. He became a professor at the Seminary in Stellenbosch, after his studies overseas had caused him to question parts of the Old Testament text that could not be regarded as divinely inspired. He also made it quite clear that believing without trying to understand was not possible for him as a theologian and teacher. He proclaimed his findings in Het Zoeklicht, a monthly magazine intended to serve as a searchlight and an organ to reveal the “darkness” that was still prevalent in both religion and politics. Aware of the value of Higher Criticism of the Old Testament, he regarded it his duty to make known what he had found in reading widely and in critical research on the origins, form and content of the books of the Bible. Articles to this effect published first in De Kerkbode and then in Het Zoeklicht, caused an outcry from conservative readers who were opposed to any changes in the teaching of the church. They were especially enraged by his view that the confessions drawn up by Reformers 500 years earlier, were open for review. Complaints that Du Plessis was on a dangerous path, marked the beginning of what was regarded as a crisis in the Church, and in the end led to Du Plessis being relieved of his post by a special Synod convened in 1930. The views of the conservative majority, however, prevailed. As a result, a large number of leading ministers and theologians, who openly supported the Nationalist government that came into power in 1948, provided assurance that the concept of separation of racial groups was in accordance with Scripture. After nearly forty years of an uncritical approach to the Bible, the belief in in-errancy was again questioned. Among the few theologians who dared to point out errors and inconsistencies in various texts, were Ferdinand Deist and Willem Vorster. Both trained as ministers, they chose to continue their studies and openly expressed themselves against the abuse of Biblical texts to support the ideology of apartheid. Trained at the Seminary in Stellenbosch, Deist turned out to be a noted scholar who combined his urge for honest critical study with a pietism expressed in a flood of academic and popular publications ― which were not always consistent with his own statement that The Word of God could not be connected to Scripture with an is-equal-to symbol. Vorster, who received his education at the University of Pretoria, became equally well known as a scholar and gained international recognition for his application of semantics in the study of the Gospels. He also applied his knowledge of languages in what came to be known as The New Quest for the historical Jesus who, as a Jew and a Galilean, distinguished himself during a brief period as a teacher and eschatological prophet. In the study of the contributions of these three outstanding men to our understanding of the Bible, another major aspect of the Bible as problematic text is addressed: The emphasis the authors and redactors of the Scriptures placed on the roles of men, fathers and sons, patently to the exclusion of women, mothers and daughters. As a result many of the so-called Church Fathers found in the Bible sufficient material to look down upon women ― the verdict expressed in Revelations 14:3-4 being one of numerous texts pointing to women as objects of derision in glaring contradiction to the contents of Genesis 1:26-31. / Biblical and Ancient Studies / D. Phil. (Biblical Studies)