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Data is one of the most valuable resources businesses have today. Companies and institutions increasingly invest in tools and platforms to collect and store data about every event that is impacting their business, like their customers, transactions, products, and the market in which they operate. Although the costs for maintaining the huge, expanding volume of data are often considerable, companies are willing to make the investment as it serves their true ambition of being able to extract valuable information from their large quantity of data. As a result, companies increasingly rely on data-driven techniques for developing powerful predictive models to aid them in their decision process. These models, however, are often not well aligned with the core business objective of profit maximization or minimizing financial losses, in the sense that, the models fail to take into account the costs and benefits that are associated with their predictions. In this thesis, we propose new methods for developing models that incorporate costs and gains directly into the construction process of the model.The first method, called ProfTree (Höppner et al., 2018), builds a profit driven decision tree for predicting customer churn. The recently developed expected maximum profit measure for customer churn (EMPC) has been proposed in order to select the most profitable churn model (Verbraken et al., 2013). ProfTree integrates the EMPC metric directly into the model construction and uses an evolutionary algorithm for learning profit driven decision trees.The second and third method, called cslogit and csboost, are approaches for learning a model when the costs due to misclassification vary between instances. An instance-dependent threshold is derived, based on the instance-dependent cost matrix for transfer fraud detection, that allows for making the optimal cost-based decision for each transaction. The two novel classifiers, cslogit and csboost, are based on lasso-regularized logistic regression and gradient tree boosting, respectively, which directly minimize the proposed instance-dependent cost measure when learning a classification model.A major challenge when trying to detect fraud is that the fraudulent activities form a minority class which make up a very small proportion of the data set, often less than 0.5%. Detecting fraud in such a highly imbalanced data set typically leads to predictions that favor the majority group, causing fraud to remain undetected. The third contribution in this thesis is an oversampling technique, called robROSE, that solves the problem of imbalanced data by creating synthetic samples that mimic the minority class while ignoring anomalies that could distort the detection algorithm and spoil the resulting analysis.Besides using methods for making data-driven decisions, businesses often take advantage of statistical techniques to detect anomalies in their data with the goal of discovering new insights. However, the mere detection of an anomalous case does not always answer all questions associated with that data point. In particular, once an outlier is detected, the scientific question why the case has been flagged as an outlier becomes of interest.In this thesis, we propose a fast and efficient method, called SPADIMO (Debruyne et al., 2019), to detect the variables that contribute most to an outlier's abnormal behavior. Thereby, the method helps to understand in which way an outlier lies out.The SPADIMO algorithm allows us to introduce the cellwise robust M regression estimator (Filzmoser et al., 2020) as the first linear regression estimator of its kind that intrinsically yields both a map of cellwise outliers consistent with the linear model, and a vector of regression coefficients that is robust against outliers. As a by-product, the method yields a weighted and imputed data set that contains estimates of what the values in cellwise outliers would need to amount to if they had fit the model.All introduced algorithms are implemented in R and are included in their respective R package together with supporting functions and supplemented documentation on the usage of the algorithms. These R packages are publicly available on CRAN and at github.com/SebastiaanHoppner.

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This dissertation will focus on investigating and improvingtechniques used in the statistical process control field, and particular withregards to control charts, as they pertain to the control of systems whichdisplay autocorrelation, non-stationarity, and exhibit outlier and missingmeasurements. Control chart approaches which will initially be considered areDynamic PCA/PLS, MovingWindow PCA/PLS, and Recursive PCA/PLS. Each of theseapproaches attempts to extend the static control chart model so that it may beapplied in a setting with time series dynamics. As of yet, no comprehensiveoverview of the methods and their extensions has been performed to evaluatetheir relative performance. Furthermore, in all cases, additional innovationsare needed before these methods display the straightforward applicability ofstatic control charts. Therefore, (1) examining the characteristics of thevarious approaches discussed in the literature, and (2) providing innovativeextensions which yield stable and easy to use methods will form two primaryresearch objectives.

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Several observations of astrophysical jets show evidence of a structure in the direction perpendicular to the jet axis, leading to "spine & sheath" models of jets. We will examine such case of a two-component jet: a highly relativistic inner jet and a slower but still relativistic outer jet, surrounded by an unmagnetized environment.Hydrodynamic jets and jets with poloidal magnetic field have already been examined and found susceptible to a relativistically enhanced, Rayleigh-Taylor type instability (Meliani & Keppens 2007, 2009).We first extend this work using a realistic helical magnetic field topology, performing 2.5D & 3D simulations using the MPI-AMRVAC code. The toroidal component of the magnetic field may provide sufficient hoop stress to suppress these instabilities. Differential rotation between the jet components is also incorporated in our study. The stability is determined in terms of the average Lorentz factor (deceleration) and effective cross-section of the jet (decollimation).The next step is to post-process the simulation data with a radiative transfer code to detect effects of the (in)stabilities in the synchrotron emission from the jet and the polarization properties.In the last part, we focus on the interaction between the relativistic jet of the X-ray binary SS433 and a supernova remnant, W50. We perform relativistic 3D simulations, capturing both the initial supernova explosion and the propagation of the jet in order to recreate the observed asymmetric, elongated shape of W50.

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The Sun directly impacts many processes on our planet, from climate to thesustenance of life. While it needs no promoting, this makes it the most importantastrophysical object of study. Despite its obvious importance for us, it is safeto say that the Sun-Earth connection is far from being completely understood.The Sun exerts influence mostly by its luminosity, i.e. electromagnetic radiation,but also through its magnetic activity, leading to the solar wind and spaceweather, i.e. a variable but continuous flux of charged particles originating fromits dynamic atmosphere. Better understanding of space weather is essential aswe rely more and more on space-based technologies and as we fare further awayfrom Earth on space exploration missions. The driving force and origin of spaceweather is the magnetically dominated solar corona, which is still enigmatic froma physical point of view. Foremost, the almost 80-year-old mystery of how it isheated to multi-million degrees constitutes the famous coronal heating problem.The theories put forth to solve this conundrum can be put in two separateboxes (even if they might act together): the so-called direct-current models,in which the slow shear of the magnetic field lines leads to small reconnectionevents called nanoflares, and the alternative-current model, in which waves
generated by the turbulent convection at the Sun's surface get dissipated asthey propagate upwards.In this thesis, we focus on wave behaviour in the solar corona, withinthe framework of magnetohydrodynamics (MHD). The importance of a betterunderstanding of wave phenomena is twofold: on the one hand, as previouslymentioned, waves are a potential candidate for coronal heating; on the otherhand, as properties of waves hold clues about the medium they propagate in,they can be used as diagnostic tools for the elusive physical properties of the solarcorona, within the field of coronal seismology. The corona is not homogeneous,as the complex magnetic field configuration dictates its appearance. In thissense, we distinguish the open magnetic field corona, which are cooler regions,mostly situated at the Sun's poles, and the closed magnetic field corona, whichpresent the majestic coronal loops, arch-like plasma structures outlining themagnetic field. Coronal loops are central to coronal wave studies, as structuringintroduces many interesting phenomena, such as surface waves, wave damping,mode coupling, resonant absorption, phase mixing, and so on. The analyticalframework for these much-studied mechanisms is well developed, however,moving away from symmetric and linear problems to more realistic, nonlineardynamics is made possible with recent advances in numerical computing power.Much of the work carried out and presented in this thesis is thus concerning thenonlinear aspects of wave behaviour in the structured corona, using numericalsimulations, with implications for both the coronal heating problem and coronalseismology, the two prime outcomes of coronal wave studies.The first three studies presented in the results chapter focus on standingkink waves in coronal loops modeled as straight cylindrical flux tubes. Theeffects of radiative cooling, large amplitudes, and a twisted magneticfield on the oscillation properties are presented. In all cases, nonlinearities,among which the most prominent one is the development of the Kelvin-Helmholtzinstability around the loop, are shown to induce considerable deviations fromanalyitical results, e.g. in damping time and oscillation period. These have animpact on some seismological estimates that are based on these values, and onwave heating. Furthermore, it is hinting at the possibly complex and turbulentinternal structure of coronal loops, which is further explainedby studying the effect of propagating transverse waves in aninhomogeneous plasma. It is shown for the first time that turbulence can begenerated from unidirectionally propagating waves, constituting a paradigm shiftin MHD turbulence in general, not only for the coronal setting. Finally, thecapabilities of the promising and emerging field of dynamic coronal seismologyis evaluated. Based on the ubiquity of the transverse propagating Alfvénicwaves observed in the solar corona, the possibility of continuous diagnostics forphysical parameters such as magnetic field strengths would constitute advancesin our understanding of coronal evolution. It is shown that, despite boththeoretical and observational limitations, reliable magnetic field estimates can be achieved, robust to widely different simulated conditions, which are expectedto be present in the corona.