published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

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Broadly, the objective of this dissertation is to contribute to the ongoing studies on the biblical theology of the Acts of the Apostles. CHAPTER ONE examines the canonical critical approach and its underlying presuppositions. Foundational to the present study is the supposition that the whole Scripture is word of God and thus, the expectation of a theological unity that is centered on “the Son” (John 1:1-4; Heb 1:1-4). It is my thesis that some specifics of that theological and Christological unity can be discerned when Acts is read in the light of the preceding canonical contexts which were ordered by the post-Ireneaus early church as hermeneutical guides for interpreting the NT Scriptures. The canonical contexts that are examined are: (1) the immediately preceding context of the Fourth Gospel [CHAPTERS TWO AND THREE], (2) the four Gospels as a unified whole [CHAPTER 4] and, ultimately, (3) the Old Testament [CHAPTER FOUR]. It is proposed that a canonically informed reading may yield significant insight into the theology that not only is inherent in the history Luke records in Acts about the continuation of “all that Jesus began to do and teach” following his ascension, but also guides the literary choices Luke makes in narrating that history. The present study proceeds from the rhetorical critical observation that the ascension of Jesus, recorded in the opening discourse of Acts, creates the primary rhetorical ‘problem’ addressed in Acts: how will the mission to establish the kingdom of God on earth, inaugurated by Jesus as narrated in the Gospels, continue postascension? CHAPTER TWO makes a case from a canonical point of view that, among the four gospels, the rhetorical ‘problem’ posed by the ascension of Jesus in the opening discourse of Acts is most anticipated, most intentionally and comprehensively addressed by Jesus in the second half of the Fourth Gospel. It is proposed and argued in this chapter that Jesus’ teaching in the Fourth Gospel about the postascension roles of the Holy Spirit and the apostles best facilitates an introduction to and understanding of the theology intrinsic to the history and narrative art in the opening scenes of Acts. CHAPTER THREE views the opening discourses of Acts from the perspective of the exegetical insights argued in chapter two. Chapter three assesses whether Jesus’ anticipation of and pre-planned response to the “problem” of the ascension is actualized in the opening scenes of Acts. CHAPTER FOUR addresses the “problem” created by the ascension in Acts from the broader canonical perspective of the four-fold Gospel testimony about Jesus’ mission. It is argued that Jesus’ mission was defined by Old Testament messianic categories and fulfills the mission of Israel. It is proposed that the reader of Acts, being familiar with the four-fold Gospel, may perceive the striking resemblance of Jesus’ mission, gospel and the concurrent conflict and controversy he provoked manifest in the church’s life and ministry in the narrative of Acts. This chapter argues from a broader canonical approach that the tri-fold Old Testament missional roles of prophet, priest and king, which Jesus fulfills as the Messianic servant in the Gospels is clearly exhibited in Luke’s literary choices and underlying missional theology in Acts. The church’s continuation of Jesus’ tri-fold missional roles in Acts yields a second major plot dynamic that permeates the historical narrative of Acts: persecution. It is argued that these two core elements of theology endemic to the canonical history of God’s people work in literary counterpoint in the history and literary art of Luke in Acts. As the post-ascension manifestation of the body of Christ on earth, the church continues to live out the tri-fold messianic, missional roles of Jesus in fulfillment of his words: “If they persecuted me, they will persecute you also. If they obeyed my teaching, they will obey yours also” (John 15:20). These two contrapuntal themes set forth the core theology that guides Luke’s literary artistic choices and explains the ebb and flow and interconnectedness of the narratives of the continuation of Jesus’ mission by the church in Acts. / Thesis (PhD)--University of Pretoria, 2012. / New Testament Studies / unrestricted

Research pertaining to the distortion of the squared canonical correlation coefficient has traditionally been limited to the effects of sampling error and associated correction formulas. The purpose of this study was to compare the degree of attenuation of the squared canonical correlation coefficient under varying conditions of score reliability. Monte Carlo simulation methodology was used to fulfill the purpose of this study. Initially, data populations with various manipulated conditions were generated (N = 100,000). Subsequently, 500 random samples were drawn with replacement from each population, and data was subjected to canonical correlation analyses. The canonical correlation results were then analyzed using descriptive statistics and an ANOVA design to determine under which condition(s) the squared canonical correlation coefficient was most attenuated when compared to population Rc2 values. This information was analyzed and used to determine what effect, if any, the different conditions considered in this study had on Rc2. The results from this Monte Carlo investigation clearly illustrated the importance of score reliability when interpreting study results. As evidenced by the outcomes presented, the more measurement error (lower reliability) present in the variables included in an analysis, the more attenuation experienced by the effect size(s) produced in the analysis, in this case Rc2. These results also demonstrated the role between and within set correlation, variable set size, and sample size played in the attenuation levels of the squared canonical correlation coefficient.

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We adopt a Bayes linear approach to tackle design problems with many variables cross-classified in many ways. We investigate designs where we wish to sample individuals belonging to different groups, exploiting the powerful properties of the adjustment of infinitely second-order exchangeable vectors. The types of information we gain by sampling are identified with the orthogonal canonical directions. We show how we may express these directions in terms of the different factors of the model. This allows us to solve a series of lower dimensional problems, through which we may identify the different aspects of our adjusted beliefs with the different aspects of the choice of design, leading both to qualitative insights and quantitative guidance for the optimal choice of design. These subproblems have an interpretable form in terms of adjustment upon subspaces of the full problem and remain valid when we consider adjusting the underlying population structure and also for predicting future observables from past observation. We then examine the adjustment of finitely second-order exchangeable vectors, and show that the adjustment shares the same powerful properties as the adjustment in the infinite case. We show how if the finite sequence of vectors is extendible, then the differences in the adjustment of the sequence is quantitatively the same for all sequence lengths and it is easy to compare the qualitative differences. Extending to an infinite sequence allows us to draw comparisons between the finite and infinite modelling. Such comparisons may also be made when we consider sampling individuals belonging to different groups, where each group contains only a finite number of individuals.

This dissertation: (a) investigated the degree to which the squared canonical correlation coefficient is biased in multivariate nonnormal distributions and (b) identified formulae that adjust the squared canonical correlation coefficient (Rc2) such that it most closely approximates the true population effect under normal and nonnormal data conditions. Five conditions were manipulated in a fully-crossed design to determine the degree of bias associated with Rc2: distribution shape, variable sets, sample size to variable ratios, and within- and between-set correlations. Very few of the condition combinations produced acceptable amounts of bias in Rc2, but those that did were all found with first function results. The sample size to variable ratio (n:v)was determined to have the greatest impact on the bias associated with the Rc2 for the first, second, and third functions. The variable set condition also affected the accuracy of Rc2, but for the second and third functions only. The kurtosis levels of the marginal distributions (b2), and the between- and within-set correlations demonstrated little or no impact on the bias associated with Rc2. Therefore, it is recommended that researchers use n:v ratios of at least 10:1 in canonical analyses, although greater n:v ratios have the potential to produce even less bias. Furthermore,because it was determined that b2 did not impact the accuracy of Rc2, one can be somewhat confident that, with marginal distributions possessing homogenous kurtosis levels ranging anywhere from -1 to 8, Rc2 will likely be as accurate as that resulting from a normal distribution. Because the majority of Rc2 estimates were extremely biased, it is recommended that all Rc2 effects, regardless of which function from which they result, be adjusted using an appropriate adjustment formula. If no rationale exists for the use of another formula, the Rozeboom-2 would likely be a safe choice given that it produced the greatest number of unbiased Rc2 estimates for the greatest number of condition combinations in this study.

A lot of attention has been drawn recently to global log canonical thresholds of Fano varieties, which are algebraic counterparts of the α-invariant of Tian for smooth Fano varieties. In particular, global log canonical thresholds are related to the existence of Kahler-Einstein metrics on Fano varieties. The purpose of this thesis is to apply techniques from singularity theory in order to compute the global log canonical thresholds of all Del Pezzo surfaces of degree 1 with Du Val singularities, as well as the global log canonical thresholds of all Del Pezzo surfaces of Picard rank 1 with Du Val singularities. As a consequence, it is proven that Del Pezzo surfaces of degree 1 with Du Val singularities admit a Kahler-Einstein metric if the singular locus consists of only A1, or A3, or A4 type Du Val singular points.

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