In this thesis different situations are considered in which the preliminary test estimator is applied and the performance of the preliminary test estimator under different proposed loss functions, namely the reflected normal , linear exponential (LINEX) and bounded LINEX (BLINEX) loss functions is evaluated. In order to motivate the use of the BLINEX loss function rather than the reflected normal loss or the LINEX loss function, the risk for the preliminary test estimator and its component estimators derived under BLINEX loss is compared to the risk of the preliminary test estimator and its components estimators derived under both reflected normal loss and LINEX loss analytically (in some sections) and computationally. It is shown that both the risk under reflected normal loss and the risk under LINEX loss is higher than the risk under BLINEX loss. The key focus point under consideration is the estimation of the regression coefficients of a multiple regression model under two conditions, namely the presence of multicollinearity and linear restrictions imposed on the regression coefficients. In order to address the multicollinearity problem, the regression coefficients were adjusted by making use of Hoerl and Kennard’s (1970) approach in ridge regression. Furthermore, in situations where under- or overestimation exist, symmetric loss functions will not give optimal results and it was necessary to consider asymmetric loss functions. In the economic application, it was shown that a loss function which is both asymmetric and bounded to ensure a maximum upper bound for the loss, is the most appropriate function to use. In order to evaluate the effect that different ridge parameters have on the estimation, the risk values were calculated for all three ridge regression estimators under different conditions, namely an increase in variance, an increase in the level of multicollinearity, an increase in the number of parameters to be estimated in the regression model and an increase in the sample size. These results were compared to each other and summarised for all the proposed estimators and proposed loss functions. The comparison of the three proposed ridge regression estimators under all the proposed loss functions was also summarised for an increase in the sample size and an increase in variance. / Thesis (PhD)--University of Pretoria, 2014. / lk2014 / Statistics / PhD / Unrestricted

We propose in the paper a new solution to the so-called Logical Omniscience Problem of epistemic logic. Almost all attempts in the literature to solve this problem consist in weakening the standard epistemic systems: weaker systems are considered where the agents do not possess the full reasoning capacities of ideal reasoners. We shall argue that this solution is not satisfactory: in this way omniscience can be avoided, but many intuitions about the concepts of knowledge and belief get lost. We shall show that axioms for epistemic logics must have the following form: if the agent knows all premises of a valid inference rule, and if she thinks hard enough, then she will know the conclusion. To formalize such an idea, we propose to \dynamize' epistemic logic, that is, to introduce a dynamic component into the language. We develop a logic based on this idea and show that it is suitable for formalizing the notion of actual, or explicit knowledge.

Economists have convulsively maintained the assumption that humans are able to arrive at decisions by perfect deductive rationality, despite the fact empirical evidences are showing otherwise. The contradicting evidences have resulted in a personal view that instead of finding a unified theory about decision-making, a sound approach would be to study how humans in fact are reasoning in specific contexts. The context of interest for this paper is where it could be assumed humans’ persistence of acting rational is determined by the perceived burden of the problem. In this work, the inductive way of arriving at decisions plays an important role, and the paper will present a way of describing this process in a consistent way. The process will be denoted as the actual level of behavioral change, and represent the core property of this paper. Applying the presented theory is most appropriate for situations where it could be assumed the burden of a problem, expressed as a prevalence rate, will drive the behavioral change. The line of reasoning in this paper will therefore be applied to the important arena of fighting the spread of HIV.

Den genomförda studien syftar till att undersöka transaktionsprocessen och identifiera var det finns störst risk för felbeslut och irrationellt agerande blad fastighetsaktörer i Sverige. Studien bidrar med att skapa en förståelse för läsaren gällande vilka risker som finns i processen samt att framställa var i processen riskerna är som störst. Materialet som ligger till grund för studien består av intervjuer och enkätundersökningar som delats ut till flertalet bolag i branschen. Intervjuerna har genomförts med personer som arbetar med fastighetstransaktioner på väletablerade bolag i branschen. Resultatet av studien indikerar på att det finns stora risker för felbeslut genom hela transaktionsprocessen vilket påverkas av flertalet faktorer i de olika delarna. För den säljande parten är risken för irrationella beslut som störst i början av processen. De förklaras av att det är den säljande parten som i början av processen exempelvis väljer vilken marknadsföringsprocess som ska genomföras, samt vem marknadsföringen ska rikta sig till. Riskerna i processen övergår därefter till köparen. De faktorer som påverkar irrationellt beslutsfattande kan förklaras av de teorier som presenteras i litteraturstudien och teoriavsnittet: ‘Bounded rationality’, ‘principal agent problem’ och ‘ankar effekter’. Det går inte att säkerställa vad som leder till att ett irrationellt beslut genomförs eftersom varje process är unik. Den här studien syftar endast till att identifiera var i transaktionsprocessen det finns risker för aktörerna att agera irrationellt. Nyckelord för studien är: ‘Transaktionsprocess’, ‘bounded rationality’, ‘principal agent problem’, ‘ankar effekt’, ‘due diligence’, ‘fastighetstransaktion’. / The following study aims to examine the transactional process for real estate transactions and establish where there is a risk for irrational decision making amongst real estate investors and advisors in Sweden. The method consists of questionnaires that have been distributed to real estate transaction consultants in Sweden. The study also used semi-structured interviews as a method. The interviews in the study were carried out with real estate consulting companies that focus on real estate transactions in Sweden. The results of the study indicate that there are risks in regards to investment decision making throughout the whole transactionprocess that are affected by various factors for the different parts of the transactionprocess. The underlying explanation is that most of the decision making is done in the initial part of the transactionprocess. The factors that cause irrational decision making can be explained by the theories presented in the literature part of the study and the theory part of the study. Those factors are: Principal agent problems, anchor effects and bounded rationality. It is not possible to ensure exactly what causes irrational behaviour in decision making but the study aims to discover and indicate where in the process there is a risk for the various factors causing irrational behaviour in decision making.

In this article, we propose a new grid-free and exact solution method for computing solutions associated with an hybrid traffic flow model based on the Lighthill- Whitham-Richards (LWR) partial differential equation. In this hybrid flow model, the vehicles satisfy the LWR equation whenever possible, and have a fixed acceleration otherwise. We first present a grid-free solution method for the LWR equation based on the minimization of component functions. We then show that this solution method can be extended to compute the solutions to the hybrid model by proper modification of the component functions, for any concave fundamental diagram. We derive these functions analytically for the specific case of a triangular fundamental diagram. We also show that the proposed computational method can handle fixed or moving bottlenecks.

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It has been shown in many studies that turbulent flows are highly dependent on their initial conditions. This thesis explores turbulent flow using direct numerical simulation (DNS) in a variety of situations, and culminates in the development of physically realizable initial conditions. The reaction of isotropic homogeneous turbulent flow to the instantaneous insertion of a wall is investigated using two-point correlations. A model with which to predict the behavior of the two-point correlations is also proposed. The proposed model utilizes a reflection technique that with a linear operation, it accurately predicts the behavior of the non-linear two point correlations. The model works exceedingly well for correlations involving wall-perpendicular velocities, but does not predict correlations involving only wall-parallel velocities as well. A vorticity approach is covered, in an effort to highlight which parts of the correlation decomposition are important to the prediction of the correlations after wall imposition. The vorticity study also helps highlight why the proposed linear model predicts the flow. The impact of the initial conditions on axisymmetric contraction flow of turbulent flow is examined, and as a consequence new initial conditions are developed based off of a physically realizable flow condition. The development of the new-initial conditions and the resulting fields are covered, as well as a study on the value of the turbulent decay exponent associated with decay of isotropic turbulent velocity fields.

The crossing number of a graph 𝐺 is the minimum number of crossings in any drawing of 𝐺 in the plane. The rectilinear crossing number of 𝐺 is the minimum number of crossings in any straight-line drawing of 𝐺. The Fáry-Wagner theorem states that planar graphs have rectilinear crossing number zero. By Wagner’s theorem, that is equivalent to stating that every graph that excludes 𝐾₅ and 𝐾₃,₃ as minors has rectilinear crossing number 0. We are interested in discovering other proper minor-closed families of graphs which admit strong upper bounds on their rectilinear crossing numbers. Unfortunately, it is known that the crossing number of 𝐾₃,ₙ with 𝑛 ≥ 1, which excludes 𝐾₅ as a minor, is quadratic in 𝑛, more specifically Ω(𝑛²). Since every 𝑛-vertex graph in a proper minor closed family has O(𝑛) edges, the rectilinear crossing number of all such graphs is trivially O(𝑛²). In fact, it is not hard to argue that O(𝑛) bound on the crossing number is the best one can hope for general enough proper minor-closed families of graphs and that to achieve O(𝑛) bounds, one has to both exclude a minor and bound the maximum degree of the graphs in the family. In this thesis, we do that for bounded degree graphs that exclude a single-crossing graph as a minor. A single-crossing graph is a graph whose crossing number is at most one. The main result of this thesis states that every graph 𝐺 that does not contain a single-crossing graph as a minor has a rectilinear crossing number O(∆𝑛), where 𝐺 has 𝑛 vertices and maximum degree ∆. This dependence on 𝑛 and ∆ is best possible. Note that each planar graph is a single-crossing graph, as is the complete graph 𝐾₅ and the complete bipartite graph 𝐾₃,₃. Thus, the result applies to 𝐾₅-minor-free graphs, 𝐾₃,₃-minor free graphs, as well as to bounded treewidth graphs. In the case of bounded treewidth graphs, the result improves on the previous best known bound of O(∆² · 𝑛) by Wood and Telle [New York Journal of Mathematics, 2007]. In the case of 𝐾₃,₃-minor free graphs, our result generalizes the result of Dujmovic, Kawarabayashi, Mohar and Wood [SCG 2008].

This research addresses the decision making process for ESG procurement investments within organizations. Since the decision making process for ESG procurement investments, particularly the consideration of environmental, social, and governance, is not clearly understood or documented, this research aims to investigate the roles, activities, and stakeholders involved in each stage of the decision making process, while exploring the challenges and opportunities associated with using ESG considerations for ESG procurement investments. The research design employs qualitative methods, including semi-structured interviews with sustainability managers and a comprehensive analysis of findings. The key findings indicate that the decision making process follows Herbert Simon's three steps, involving the intelligence, design, and choice stage. Throughout this process, various stakeholders, including management teams, finance teams, and sustainability departments, assume specific roles. Furthermore, the involvement of additional stakeholders can vary from stage to stage, with their roles adapting accordingly. In the intelligence stage, the activities encompassed identifying the situation and problems at hand, as well as collecting data through collaborative efforts. Moving into the design stage, activities involved developing business cases and exploring potential alternatives. Finally, in the choice stage of the decision making process, the activities involved evaluating the best alternative, presenting it to the management team, and making the final decision. Challenges identified using ESG in procurement investments include among others aligning costs and sustainability, limited awareness and competences, and data availability, while opportunities lie in risk reduction, enhanced sustainability, collaboration, and cost reductions. The research contributes to existing literature by providing empirical evidence, development of an analytical framework, and shedding light on the decision making process. In practical terms, this research provides valuable insights for sustainability managers, procurement professionals, and organizational leaders. It highlights the importance of understanding the decision making process and the roles of different stakeholders, which can lead to improved collaboration and coordination among departments involved.

I denna studie undersöks hur intern Business Intelligence påverkar beslutsprocessen i stora svenska bolag. Business Intelligence används mer och mer i beslutsprocessen och anses nu vara essentiellt för organisationer som vill vara konkurrenskraftiga. Organisationer vill också bli alltmer datadrivna i sin beslutsprocess och då basera beslut på data och inte intuition. Genom en kvalitativ undersökning visar studien att BI-analytiker och beslutsfattare som använder sig av Business Intelligence är överens om att ett BI-system påverkar beslutsfattandeprocessen främst positivt. Den största nackdelen som tas upp i studien är kostanden som en implementering av ett BI-system medför, men att de positiva följderna av implementeringen väger tyngre. De främsta positiva följderna som tas upp i studien är att beslutsfattandeprocessen går fortare samt att beslutskvalitén ökar då ett BI-system tillhandahåller beslutsfattarna relevant, smart och riktad information snabbare än det tidigare var möjligt. / This study examines how internal Business Intelligence effects the decision-making process in large Swedish companies. Business Intelligence is used more and more in the decision-making process and is now considered essential for organizations if they want to be competitive. Organizations strive to become more data-driven in their decision-making and thus wants their decision-makers to primarily base their decisions on data and not intuition. Through a qualitative study, it highlights that both BI-analysts and decision-makers who use Business Intelligence agrees that a BI system affects the decision-making process mainly positively. The biggest disadvantage that is addressed in the study is the cost that the implementation of a BI system entails, but that the positive consequences of the implementation of a BI system are bigger. The main positive consequences that are addressed in the study are that the decision-making process becomes faster and that the quality of decisions increases. This is because a BI system provides the decision-makers with relevant, smart and targeted information faster than was previously possible.