Sensitivity and statistical inference in Markov decision models and collective risk models

The first part of this thesis deals with the sensitivity and statistical estimation of the optimal value of a Markov decision model (MDM) in the transition probability function, i.e.\ the family of all transition probabilities. Such models are used for modelling {\color{black}stochastic optimization problems with sequential decision making} which appear in many application areas. Since in practice, the used MDM is most often less complex than the underlying `true' MDM, we first discuss the impact of a reduction of the model complexity in the transition probability function on the optimal value of the MDM, i.e.\ the solution of the underlying stochastic control problem. Besides a statement on the continuity of the optimal value regarded as a real-valued functional on a set of transition probability functions, we will in particular introduce a sort of derivative of this functional which can be used to measure the (first-order) sensitivity of the optimal value w.r.t.\ deviations in the transition probability function. In addition, we perform a statistical analysis of the optimal value of a MDM where the underlying transition probability function is unknown, a situation that often occurs in practice. By limiting ourselves to a simple MDM in which the transition probability function is generated only by a single distribution function, we show that the optimal value construed as a real-valued functional defined on a set of distribution functions is continuous and functionally differentiable in a certain sense. By means of these regularity properties, we discuss the asymptotics of suitable estimators for the optimal value of the MDM in nonparametric and parametric statistical models. Our theoretical findings in the first part of this thesis are illustrated by means of optimization problems in inventory control and mathematical finance. The second part of this thesis is devoted to the nonparametric estimation of risk measures of collective risks in a non-homogeneous individual risk model in connection with the determination of appropriate insurance premiums. We present two nonparametric candidates for the estimator of the exact insurance individual premium and show several asymptotic properties for the estimated premiums, such as strong consistency, asymptotic normality, and qualitative robustness, that are applicable in `large' insurance collectives.Der erste Teil dieser Arbeit befasst sich mit der Sensitivität und statistischen Schätzung des optimalen Wertes eines Markov Entscheidungsmodells (MEMs) in der Übergangswahrscheinlichkeitsfunktion, d. h. der Familie aller Übergangswahrscheinlichkeiten. Solche Modelle werden zur Modellierung von stochastischen Optimierungsproblemen mit sequentieller Entscheidungsfindung verwendet, die in vielen Anwendungsbereichen auftreten. Da das verwendete MEM in der Praxis meist weniger komplex ist als das zugrundeliegende "wahre" MEM, diskutieren wir zunächst den Einfluss einer Reduktion der Modellkomplexität in der Übergangswahrscheinlichkeitsfunktion auf den optimalen Wert des MEM, d.h. der Lösung des zugrundeliegenden stochastischen Kontrollproblems. Neben einer Aussage über die Stetigkeit des optimalen Wertes, aufgefasst als ein reellwertiges Funktional definiert auf einer Menge von Übergangswahrscheinlichkeitsfunktionen, werden wir insbesondere eine Art Ableitung dieses Funktionals vorstellen, die zur Messung der Sensitivität (ersten Ordnung) des optimalen Wertes bezüglich Abweichungen in der Übergangswahrscheinlichkeitsfunktion verwendet werden kann. Darüber hinaus führen wir eine statistische Untersuchung des optimalen Wertes eines MEMs durch, bei dem die zugrundeliegende Übergangswahrscheinlichkeitsfunktion unbekannt ist, eine Situation, die in der Praxis häufig vorkommt. Indem wir uns auf ein einfaches MEMs beschränken, in welchem die Übergangswahrscheinlichkeitsfunktion nur durch eine einzelne Verteilungsfunktion erzeugt wird, zeigen wir, dass der optimale Wert, welcher als ein Funktional auf einer Menge von Verteilungsfunktionen betrachtet wird, stetig und funktional differenzierbar in einem gewissen Sinn ist. Mit Hilfe dieser Regularitätseigenschaften diskutieren wir in nichtparametrischen und parametrischen statistischen Modellen die Asymptotiken geeigneter Schätzer für den optimalen Wert des MEM. Unsere theoretischen Erkenntnisse im ersten Teil dieser Arbeit werden anhand von Optimierungsproblemen in der Lagerbestandskontrolle und der Finanzmathematik veranschaulicht. Der zweite Teil dieser Arbeit widmet sich der nichtparametrischen Schätzung von Risikomaßen kollektiver Risiken in einem individuellen Risikomodell im Zusammenhang mit der Bestimmung geeigneter Versicherungsprämien. Wir stellen zwei nichtparametrische Kandidaten für den Schätzer der exakten individuellen Versicherungs -prämie vor und zeigen für die geschätzten Prämien mehrere asymptotische Eigenschaften wie starke Konsistenz, asymptotische Normalität und qualitative Robustheit, welche in "großen" Versicherungskollektiven anwendbar sind

Effects of Laryngeal Restriction on Pharyngeal Peristalsis and Biomechanics: Clinical Implications

To date, rehabilitative exercises aimed at strengthening the pharyngeal muscles have not been developed due to the inability to successfully overload and fatigue these muscles during their contraction, a necessary requirement for strength training. The purpose of this study was to test the hypothesis that applying resistance against anterosuperior movement of the hyolaryngeal complex will overload the pharyngeal muscles and by repetitive swallowing will result in their fatigue manifested by a reduction in pharyngeal peristaltic amplitude. Studies were done in two groups. In group 1 studies 15 healthy subjects (age: 42 ± 14 yr, 11 females) were studied to determine whether imposing resistance to swallowing using a handmade device can affect the swallow-induced hyolaryngeal excursion and related upper esophageal sphincter (UES) opening. In group 2, an additional 15 healthy subjects (age 56 ± 25 yr, 7 females) were studied to determine whether imposing resistance to the anterosuperior excursion of the hyolaryngeal complex induces fatigue manifested as reduction in pharyngeal contractile pressure during repeated swallowing. Analysis of the video recordings showed significant decrease in maximum deglutitive superior laryngeal excursion and UES opening diameter (P \u3c 0.01) due to resistive load. Consecutive swallows against the resistive load showed significant decrease in pharyngeal contractile integral (PhCI) values (P \u3c 0.01). Correlation analysis showed a significant negative correlation between PhCI and successive swallows, suggesting “fatigue” (P \u3c 0.001). In conclusion, repeated swallows against a resistive load induced by restricting the anterosuperior excursion of the larynx safely induces fatigue in pharyngeal peristalsis and thus has the potential to strengthen the pharyngeal contractile function

Uncertainty-aware predictive modeling for fair data-driven decisions

Both industry and academia have made considerable progress in developing trustworthy and responsible machine learning (ML) systems. While critical concepts like fairness and explainability are often addressed, the safety of systems is typically not sufficiently taken into account. By viewing data-driven decision systems as socio-technical systems, we draw on the uncertainty in ML literature to show how fairML systems can also be safeML systems. We posit that a fair model needs to be an uncertainty-aware model, e.g. by drawing on distributional regression. For fair decisions, we argue that a safe fail option should be used for individuals with uncertain categorization. We introduce semi-structured deep distributional regression as a modeling framework which addresses multiple concerns brought against standard ML models and show its use in a real-world example of algorithmic profiling of job seekers

First-order sensitivity of the optimal value in a Markov decision model with respect to deviations in the transition probability function

Markov decision models (MDM) used in practical applications are most often less complex than the underlying ‘true’ MDM. The reduction of model complexity is performed for several reasons. However, it is obviously of interest to know what kind of model reduction is reasonable (in regard to the optimal value) and what kind is not. In this article we propose a way how to address this question. We introduce a sort of derivative of the optimal value as a function of the transition probabilities, which can be used to measure the (first-order) sensitivity of the optimal value w.r.t. changes in the transition probabilities. ‘Differentiability’ is obtained for a fairly broad class of MDMs, and the ‘derivative’ is specified explicitly. Our theoretical findings are illustrated by means of optimization problems in inventory control and mathematical finance

Elastomerreibung und Kraftübertragung beim Abscheren von aktiv betriebenen Vakuumgreifern auf rauen Oberflächen

Die vorliegende Arbeit beinhaltet die Analyse der Kraftübertragung und die Modellierung des Reibwertes μ auf rauen Oberflächen beim Abscheren von aktiv betriebenen Vakuumgreifern. Es werden die beiden Hauptkomponenten bei der Elastomerreibung (Hysterese und Adhäsion) modelliert. Zusätzlich wird der Formschluss untersucht und im Detail beschrieben. Mit Hilfe des vorgestellten Reibmodells können Angaben für den Reibwert zur Auslegung von Haltesystemen mit Vakuumgreifern gemacht werden

Benchmarking Function Hook Latency in Cloud-Native Environments

Researchers and engineers are increasingly adopting cloud-native technologies for application development and performance evaluation. While this has improved the reproducibility of benchmarks in the cloud, the complexity of cloud-native environments makes it difficult to run benchmarks reliably. Cloud-native applications are often instrumented or altered at runtime, by dynamically patching or hooking them, which introduces a significant performance overhead. Our work discusses the benchmarking-related pitfalls of the dominant cloud-native technology, Kubernetes, and how they affect performance measurements of dynamically patched or hooked applications. We present recommendations to mitigate these risks and demonstrate how an improper experimental setup can negatively impact latency measurements.Comment: to be published in the 14th Symposium on Software Performance (SSP 2023), source code available at https://github.com/dynatrace-research/function-hook-latency-benchmarkin

College Housing Fire Safety

This project was sponsored by the U.S. Consumer Product Safety Commission (CPSC) to address the issue of fire safety in college residences and to assist in the achievement of the CPSC\u27s strategic goal of a 20% reduction in fire-related deaths over the period of 1998-2013. We researched and analyzed the causes of fires, fire education programs, and fire detection and suppression. From this, we developed recommendations for the CPSC to address the issue of college housing fire safety

Leader autonomy support in the workplace: A meta-analytic review

Leader autonomy support (LAS) refers to a cluster of supervisory behaviors that are theorized to facilitate self-determined motivation in employees, potentially enabling well-being and performance. We report the results of a meta-analysis of perceived LAS in work settings, drawing from a database of 754 correlations across 72 studies (83 unique samples, N = 32,870). Results showed LAS correlated strongly and positively with autonomous work motivation, and was unrelated to controlled work motivation. Correlations became increasingly positive with the more internalized forms of work motivation described by self-determination theory. LAS was positively associated with basic needs, well-being, and positive work behaviors, and was negatively associated with distress. Correlations were not moderated by the source of LAS, country of the sample, publication status, or the operationalization of autonomy support. In addition, a meta-analytic path analysis supported motivational processes that underlie LAS and its consequences in workplaces. Overall, our findings lend support for autonomy support as a leadership approach that is consistent with self-determination and optimal functioning in work settings