The complexity of modern computer and software systems still seems to grow exponentially, while the human user is widely left without explanations on how to understand these systems. One of the central tasks of current computer science therefore lies in the development of methods and tools to build such an understanding. A similar task is addressed by formal verification which gives various verifiable justifications for the functionality of a system. As these still only give knowledge that a system functions properly they only address a portion of the task to make systems easier to comprehend. It is widely believed that cause-effect reasoning plays an important role in forming human understanding of complex relations. Thus, there are already many accounts on causality in modern computer science. However, most of them are focusing on a form of backward looking actual causality. This variant of causality is concerned with actual events after their occurrence and tries to reason about causes mostly in a counterfactual manner. In this thesis we address a probabilistic form of causality which is forward looking by nature. As such, we define and discuss novel notions of probabilistic causes in discrete time Markov chains and Markov decision processes. For this we rely on two central principles of probabilistic causality. On one hand, the probability-raising principle states that a cause should raise the probability of its effect. On the other hand, temporal priority requires that a cause must occur before its effect. We build the mathematical and algorithmic foundations of our so called probability-raising causes. For this we work in a state-based setting where causes and effects are reachability properties of sets of states. In order to measure the predictive power of states we define quality-measures for which we interpret causes as binary classifiers. With these tools we address the algorithmic questions of checking cause-effect relations if both a cause candidate and an effect are given and finding quality-optimal causes if only the effect is given. We discuss possible extensions of this basic state-based framework to more general formulations of causes and effects as ω-regular properties.:Abstract 3 1 Introduction 7 1.1 Contributions and Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2 Preliminaries 21 2.1 Markov Decision Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.1.1 Graph of an MDP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.1.2 Schedulers and Probability Measure . . . . . . . . . . . . . . . . . . . . . 23 2.1.3 Maximal and Minimal Probabilities . . . . . . . . . . . . . . . . . . . . . . 25 2.1.4 Frequencies and Balance Equations . . . . . . . . . . . . . . . . . . . . . 26 2.1.5 MR Scheduler in MDPs without ECs . . . . . . . . . . . . . . . . . . . . . . 26 2.1.6 MEC-Quotient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.2 Automata and ω-Regular Languages . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.3 Probability-Raising Causality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3 Probability-Raising Causality in Markov Decision Processes 33 3.1 Setting and Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.1.1 Related Work revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.2.1 Conceptual Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.2.2 Racetrack MDP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.3 Quality Measures for Probability-Raising Causes . . . . . . . . . . . . . . . . . . 52 3.3.1 PR Causes as Binary Classifiers in MDPs . . . . . . . . . . . . . . . . . . . 53 3.3.2 Quality Measures for a given PR Cause . . . . . . . . . . . . . . . . . . . . 54 4 Algorithmic Considerations 59 4.1 Checking the Probability-Raising Conditions . . . . . . . . . . . . . . . . . . . . . 60 4.1.1 Canonical MDP for given Cause Set . . . . . . . . . . . . . . . . . . . . . . 61 4.1.2 Checking the SPR Condition and the Existence of PR Causes . . . . . . . 72 4.1.3 Checking the GPR Condition . . . . . . . . . . . . . . . . . . . . . . . . . . 77 4.2 Computing the Quality of a PR Cause . . . . . . . . . . . . . . . . . . . . . . . . . 88 4.2.1 Max/Min Ratios for Disjoint Sets of Terminal States . . . . . . . . . . . . 92 4.3 Quality-Optimal Probability-Raising Causes . . . . . . . . . . . . . . . . . . . . . . 97 4.3.1 Quality-Optimal SPR Causes . . . . . . . . . . . . . . . . . . . . . . . . . . 98 4.3.2 Quality-Optimal GPR Causes . . . . . . . . . . . . . . . . . . . . . . . . . . 108 5 Variants of Probability-Raising Causality in MDPs 115 5.1 Probability-Raising Scheduler and Potential PR Causes . . . . . . . . . . . . . . . 116 5.1.1 Checking for SPR Scheduler . . . . . . . . . . . . . . . . . . . . . . . . . . 119 5.1.2 Checking for GPR Scheduler . . . . . . . . . . . . . . . . . . . . . . . . . . 124 5.2 ω-Regular Effects - Reachability Causes . . . . . . . . . . . . . . . . . . . . . . . . 127 5.2.1 Checking Reachability Probability-Raising Causes . . . . . . . . . . . . . . 128 5.2.2 Quality and Optimality of Reachability PR Causes . . . . . . . . . . . . . . 133 5.3 ω-Regular Co-Safety Causes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 5.3.1 Checking Co-Safety PR causes . . . . . . . . . . . . . . . . . . . . . . . . . 139 5.3.2 Quality and Optimality of Co-Safety PR Causes . . . . . . . . . . . . . . . 142 6 Conclusion 147

This thesis aims to analyze some of the available methods that aid in risk estimation based on econometric models, as well as to propose some new ones. Some of the questions that are expected to be answered include which distribution to choose to obtain better risk estimates for series with abnormal behaviours, how to determine whether the distribution in parametric conditional models is a Student’s t, and how to assess whether an asset’s risk helps predict the risk of another asset. In Chapter 1, we estimate several cryptocurrencies’ Expected Shortfall using different error distributions and GARCH-type models for conditional variance. ur goal is to examine which distributions perform better and to check which component of the specification plays a more crucial role in estimating Expected Shortfall. The performance of the estimations is conducted using a backtesting technique with a rolling-window approach. Results show that, in the case of Bitcoin, it is important to use a distribution with at least two parameters that control its shape and an extension of the GARCH model, whether it be the NGARCH or the CGARCH model. On the other hand, other smaller cryptocurrencies yield good enough risk predictions with the Student’s t distribution and a GARCH model. The fact that the main measures of financial risk are focused on the tail of the distribution of returns highlights the importance of the choice of an appropriate distribution model. Chapter 2 develops a procedure for consistently testing the specification of a Student’s t distribution for the innovations of a dynamic model. This contributes to the existing literature by providing a test for Student’s t distributions in conditional mean and variance models with a parameter-free test statistic and, thus, a known asymptotic distribution, avoiding the use of more computationally costly resampling techniques such as bootstrapping. The specific expressions needed for the computation of the test statistic are obtained by adapting the generic test of Bai (2003), which is based on the Khmaladze (1988) transformation of the model residuals. Finally, in Chapter 3, the concept of Granger causality in Expected Shortfall (ES) is introduced, along with a testing procedure to detect this type of predictive relationship between return series. Granger causality in Expected Shortfall is here defined as the predictive ability of tail values of a series over future tail values of another series on average. This definition may help in analyzing whether past values of an asset in extreme risk affect future extreme risk values of another asset. The main contribution of this chapter is a test for detecting this type of causality, based on the test for Granger causality in VaR by Hong et al. (2009). An empirical application on financial institutions from different industries (banking, insurance, and diversified financials) is presented to analyze the risk spillovers in the US financial market. The contribution of this thesis to the field of financial econometrics focuses on the market risk of financial assets, both in its modeling through the metric known as Expected Shortfall suggested in the Basel III Accords and in its utility beyond capital requirements. The results highlight the importance of a good specification of the chosen distribution model for risk estimation - especially in high-risk assets such as cryptocurrencies - and a test is proposed to verify if the conditional distribution in parametric models used for risk predictions is or is not a Student’s t distribution. Finally, a Granger causality test in Expected Shortfall is proposed, which allows for studying risk propagation in tails of return distributions. The proposed test can be used to investigate interconnections within and between markets as a complement when evaluating systemic risk. Other potential applications include improving Expected Shortfall forecasts by including causing variables as regressors in estimations, studying the inclusion of certain asset pairs in the same portfolio based on how they interact in the riskiest situations, or constructing networks of extreme risk propagation. / Esta tesis doctoral ha sido financiada mediante una ayuda FPU por el Ministerio de Educación, Cultura y Deporte (FPU17/06227).

Yes / This study contributes to the existing literature on the relationship between oil market shocks and the green bond market by investigating the impact of the COVID-19 pandemic on their dynamic correlation. We first decompose the oil market shocks into components using a time-frequency framework. Then, we combine wavelet decomposition and quantile coherence and causality methods to discuss changes during the COVID-19 era. We observe positive effects of both supply-driven and demand-driven oil shocks on the green bond market at most quantile levels. However, supply-driven oil price changes play a major role. The results also indicate that long-term changes have a greater impact than short-term changes on the connection between oil and green bond markets. Nevertheless, the COVID-19 pandemic changed the nature of the causal relationship, as we observed no relationship under extreme market conditions during the pandemic era. We argue that the economic and social impacts of the COVID-19 pandemic have left investors focusing on the short-term substitution between oil and green bond markets. / This research was supported by the Major Projects of the National Natural Science Fund of China [NO. 71991483], the Natural Science Fund of Hunan Province [NO. 2022JJ40647] and the Fundamental Research Funds for the Central Universities of Central South University [NO. 2022ZZTS0353].

Civil aviation demands punctual and efficient commercial flights. Flight delays adversely affect passengers, airlines, airports, and the environment (Cook and Tanner, 2015; Cook, Tanner, and Lawes, 2012). Flight delays are typically characterized as the time difference between the actual departure/arrival time of an aircraft and its scheduled departure/arrival time (EUROCONTROL, 2018). Air transportation functions within a complex system and delays are influenced by a multitude of factors. At its core, delays arise due to an imbalance between demand and capacity, where the demand exceeds the available capacity (EUROCONTROL, 2018; Technology Assessment, 1984; Wells and Young, 2004). Air Traffic Flow Management (ATFM) can adjust the demand and balance the imbalance between demand and capacity to achieve a better equilibrium (EUROCONTROL, 2023; Odoni, 1987; Ball et al., 2003; Bertsimas, Lulli, and Odoni, 2011; Murca, 2018; Xu et al., 2020). This dissertation encompasses applications of statistical methods in air transport, such as landing time predictions and weather variable interpolations to enhance ATFM, as well as delay propagation inferences among airports to comprehend patterns of delay transmission, all aiming to understand and mitigate flight delays. Efficient ATFM requires accurate monitoring and prediction of the current capacity and demand imbalance status. Accurate prediction of flight delay helps airports to monitor better, make more informed decisions and increase airport efficiency (Fricke and Schultz, 2009; Lordan, Sallan, and Valenzuela-Arroyo, 2016; Wang et al., 2021). Besides delay prediction, landing time prediction also improves resource monitoring. Many machine learning methods are available to make predictions of landing time. Chapter 2 compares the accuracy of different machine learning methods to predict landing time at Zurich Airport by cross- validation errors. Important factors contributing to the landing time prediction are also identified. The results showcase the effectiveness of the decision tree methods in accurately predicting landing times, which helps improve the management of runways and resources at the local airport. Besides a warning of delays, rerouting can prevent delays by exploring alternative flight routes, which involves re-planning trajectories to bypass congested airspace and hotspots. Weather information serves as a critical input for trajectory planners. The question pertains to choosing interpolation methods to extend the weather data available at 1-degree grid points defined by latitudes, longitudes, and pressure levels with high accuracy. Chapter 3 explores different interpolation techniques for crucial weather variables such as temperature, wind speed, and wind direction. These methods, including Ordinary Kriging, the radial basis function method, neural networks, and decision trees, are compared using cross-validation interpolation errors. A Monte Carlo simulation of a trajectory from Prague to Tunis is conducted to examine the impact of input weather data and the interpolation method (Ordinary Kriging) on planned trajectories. Even though errors in GFS data and Ordinary Kriging are inevitable, the inaccuracy of the data has a minor impact on the planned trajectory. Flight delays negatively affect passengers, airlines, airports, and the environment. Besides mitigating delays at individual airports and for specific flights, considering the potential propagation of delays from other airports is necessary. Assessing delay propagation among airports in the network contributes to understanding the systemic impact of delays. Analyzing delay propagation assists in understanding the patterns of delay transmission and identifying potential strategies for mitigation. Graph network theory has enabled the construction of delay propagation networks to understand the delay transmission pattern using time series data (Belkoura and Zanin, 2016; Zanin, Belkoura, and Zhu, 2017; Du et al., 2018; Mazzarisi et al., 2020b; Xiao et al., 2020; Wang et al., 2020; Jia et al., 2022). However, inferring connections from time series data using statistical methods can introduce biases resulting from excluding airports (Belkoura and Zanin, 2016; Zanin, Belkoura, and Zhu, 2017; Du et al., 2018) or false positives by inappropriate statistical methods (Mazzarisi et al., 2020b), consequently overestimating propagation. Overestimation of delay propagation can undermine the credibility of the reported results, as it becomes dubious to discern whether inaccurate inferences drive the observed delay propagation. Chapter 4 infers Granger causality among airports by avoiding the overestimation of propagation from excluding airports and false positives. The “one-standard-error” rule (Hastie et al., 2009) is recommended to mitigate a high false positive rate during parameter tuning. It is found that the choice of data inputs for model training influences the delay propagation inference results. When early arrivals and punctual flights are included, the observed delay propagation among airports can stem from correlations among punctual and early arrivals rather than delayed flights. In contrast to recent research (Xiao et al., 2020; Jia et al., 2022), this study unveils that large airports exert a substantial influence on the delay propagation network. In summary, this work aims to enhance our understanding of and mitigate flight delays. Chapters 2 and 3 focus on delay mitigation, while Chapter 4 contributes to our understanding of delay interactions.

Text in Afrikaans / Aquinas's five point argument for God's existence views creation as a holistic entity in which synthesis and creative influences are initiated through the interaction between minimal and maximal acts of being. These acts are represented by the per accidens and the per se respectively. Both these acts are fundamental acts which are crucial to the outcome of the argument for the existence of God. The creature who, because of his per accidens dependency, possesses minimal status, is elevated to a place of honour by participation in creation. Both the essence and esse of creatures have their origin in the pure esse of the maximal act of being (God). Maximal being, the efficient cause, grounds the similarity between itself and minimal acts of being. Both the per accidens and the per se have crucial roles to play in the verification of tbe argument. Should any one of these two elements be lacking, the argument would be invalid. / Aquinas se Quinque Via as 'n Holistiese Beredenering is 'n vyfpunt-argument vir die bestaan van God wat die skepping as 'n eenheid beskou waarin sintese en skeppende invloede bewerkstellig word deur interaksie tussen minimale en maksimale bestaansaktes. Die bestaansaktes word deur die per accidens en die per se (wat die fundamentele boustene in die argument vorm) verteenwoordig. Die skepsel wat vanwee sy per accidens- afhanklikheid beperkte status beklee, word deur bemiddeling van die per se of maksimale bestaansakte (God) tot deelgenoot verhef en beklee ·n ereplek in die skepping. Beide die esse en essensie van menslike wesens het hul oorsprong in die suiwer esse van die maksimale bestaansakte. Maksimale bestaan, die effektiewe oorsaak, begrond die ooreenkoms tussen sigself en die minimale bestaansaktes. Die per accidens sowel as die per se vervul 'n onontbeerlike rol in die bewysvoering van die argument. Sou een van die twee fundamentele elemente ontbreek, sou die argument in geheel ongeldig wees. / Philosophy, Practical & Systematic Theology / M.A. (Wysbegeerte)

This paper follows Ghysels, Gourieroux, and Jasiak (1998), examines the causal relation between price and volume in Taiwan Futures Market. I use high frequency intraday data of Taiwan Stock Exchange Capitalization Weighted Stock Index in Taiwan Futures Exchange; and analyze the causality between returns and volume series, which are transformed into Markov chain, with Granger’s causal tests. I analyze the data with two different time category, trading time and calendar time. In our research we find out that Taiwan futures market has a bi-directional causality between price and volume in trading time analysis, as to the calendar time analysis, only price to volume unidirectional causality exists. Unlike the unidirectional causal relation that Ghysels, Gourieroux, and Jasiak (1998) observed in French security market.

The aim of this thesis is to verify and analyse presumed relations between selected macro-fundamentals, namely USD exchange rate, production index, interbank offered rate, inflation, money supply and two exogenous indices ( Standard & Poor's 500 and EURO STOXX 50), and CEE (Austria, Czech Republic, Poland, Hungary) or SEE (Bulgaria, Croatia, Slovenia, Romania) financial markets over the period from December 1995 to December 2015. In order to test the long-run cointegration relationships between studied markets and the set of macroeconomic variables, the Engle-Granger and Johansen tests are applied. The vector error correction model is used to confirm the long-run equilibrium interlinkages and the results show similar trend tendencies between stock indices and some of the macro-fundamentals in Croatia, Czech Republic, Hungary, Poland and Romania. To verify the short-run causal linkages, the Granger causality test is employed. Based on retrieved findings, the efficiency of studied markets with respect to Efficient Market Theory is reviewed. Our findings reveal several pairwise short-run causal impacts between studied macroeconomic indicators and stock indices. The only indicator which does not impact any stock market is the interbank offered rate. Moreover, according to our results, all CEE&SEE stock...

Text in Afrikaans / Aquinas's five point argument for God's existence views creation as a holistic entity in which synthesis and creative influences are initiated through the interaction between minimal and maximal acts of being. These acts are represented by the per accidens and the per se respectively. Both these acts are fundamental acts which are crucial to the outcome of the argument for the existence of God. The creature who, because of his per accidens dependency, possesses minimal status, is elevated to a place of honour by participation in creation. Both the essence and esse of creatures have their origin in the pure esse of the maximal act of being (God). Maximal being, the efficient cause, grounds the similarity between itself and minimal acts of being. Both the per accidens and the per se have crucial roles to play in the verification of tbe argument. Should any one of these two elements be lacking, the argument would be invalid. / Aquinas se Quinque Via as 'n Holistiese Beredenering is 'n vyfpunt-argument vir die bestaan van God wat die skepping as 'n eenheid beskou waarin sintese en skeppende invloede bewerkstellig word deur interaksie tussen minimale en maksimale bestaansaktes. Die bestaansaktes word deur die per accidens en die per se (wat die fundamentele boustene in die argument vorm) verteenwoordig. Die skepsel wat vanwee sy per accidens- afhanklikheid beperkte status beklee, word deur bemiddeling van die per se of maksimale bestaansakte (God) tot deelgenoot verhef en beklee ·n ereplek in die skepping. Beide die esse en essensie van menslike wesens het hul oorsprong in die suiwer esse van die maksimale bestaansakte. Maksimale bestaan, die effektiewe oorsaak, begrond die ooreenkoms tussen sigself en die minimale bestaansaktes. Die per accidens sowel as die per se vervul 'n onontbeerlike rol in die bewysvoering van die argument. Sou een van die twee fundamentele elemente ontbreek, sou die argument in geheel ongeldig wees. / Philosophy, Practical and Systematic Theology / M.A. (Wysbegeerte)

Since the seminal work of Fritz Heider and Marienne Simmel (1944) the study of animacy perception, or the perception and attribution of life from the motion of simple geometrical shapes has intrigued researchers. The intrigue for psychologists and vision scientists then and today centered on the stark disconnect between the simplicity of the visual input and the universal richness of the resulting percept. Infant research in this domain has become critical in examining the ontological processes behind the formation of animated percepts. To date, little is known about how infants process these kinds of stimuli. While numerous habituation studies have shown sensitivity to animate motion in general, none to date has examined whether infants actually perceive animate displays as social interactions. The overarching goal of the present thesis is to answer this question and further augment knowledge about the mechanisms behind the formation of animated percepts in infancy. I, along with my collaborators, do so in three ways, in three separate studies. First, we examined visual attention during online observation of randomly moving geometrical shapes in adults and infants (Study I, using eye tracking). Second, we examine distribution of visual attention in infancy during online observation of non-contact causal interactions, focusing on the most ubiquitous, fitness relevant of interactions – chasing (Study II, using eye tracking). Third, we answer the question whether infants perceive social content in chasing displays by measuring the neural correlates in response to chasing (Study III, using EEG). The collective contribution of the present work is also three fold. First, it demonstrates that starting at the end of the first year of life, human visual system is sensitive to cues that efficiently predict an interaction. Second, at 5-months infants begins allocating attention differently across agents within interactions. Finally, attention to specific objects is not due to low-level saliency but the social nature of the interaction. Subsequently, I present the case that perception of social agents is fast, direct, and reflects the workings of a specialized learning mechanisms whose function is the detection of heat-seeking animates in motion.

L'intérêt en apprentissage machine pour étudier la causalité s'est considérablement accru ces dernières années. Cette approche est cependant encore peu répandue dans le domaine de l’intelligence artificielle (IA) et du droit. Elle devrait l'être. L'approche associative actuelle d’apprentissage machine révèle certaines limites que l'analyse causale peut surmonter. Cette thèse vise à découvrir si les modèles causaux peuvent être utilisés en IA et droit. Nous procédons à une brève revue sur le raisonnement et la causalité en science et en droit. Traditionnellement, les cadres normatifs du raisonnement étaient la logique et la rationalité, mais la théorie duale démontre que la prise de décision humaine dépend de nombreux facteurs qui défient la rationalité. À ce titre, des statistiques et des probabilités étaient nécessaires pour améliorer la prédiction des résultats décisionnels. En droit, les cadres de causalité ont été définis par des décisions historiques, mais la plupart des modèles d’aujourd’hui de l'IA et droit n'impliquent pas d'analyse causale. Nous fournissons un bref résumé de ces modèles, puis appliquons le langage structurel de Judea Pearl et les définitions Halpern-Pearl de la causalité pour modéliser quelques décisions juridiques canadiennes qui impliquent la causalité. Les résultats suggèrent qu'il est non seulement possible d'utiliser des modèles de causalité formels pour décrire les décisions juridiques, mais également utile car un schéma uniforme élimine l'ambiguïté. De plus, les cadres de causalité sont utiles pour promouvoir la responsabilisation et minimiser les biais. / The machine learning community’s interest in causality has significantly increased in recent years. This trend has not yet been made popular in AI & Law. It should be because the current associative ML approach reveals certain limitations that causal analysis may overcome. This research paper aims to discover whether formal causal frameworks can be used in AI & Law. We proceed with a brief account of scholarship on reasoning and causality in science and in law. Traditionally, normative frameworks for reasoning have been logic and rationality, but the dual theory has shown that human decision-making depends on many factors that defy rationality. As such, statistics and probability were called for to improve the prediction of decisional outcomes. In law, causal frameworks have been defined by landmark decisions but most of the AI & Law models today do not involve causal analysis. We provide a brief summary of these models and then attempt to apply Judea Pearl’s structural language and the Halpern-Pearl definitions of actual causality to model a few Canadian legal decisions that involve causality. Results suggest that it is not only possible to use formal causal models to describe legal decisions, but also useful because a uniform schema eliminates ambiguity. Also, causal frameworks are helpful in promoting accountability and minimizing biases.