Within our research group Bayesian Risk Solutions we have coined the idea of a Bayesian Risk Management (BRM). It claims (1) a more transparent and diligent data analysis as well as (2)an open-minded incorporation of human expertise in risk management. In this dissertation we formulize a framework for BRM based on the two pillars Hardcore-Bayesianism (HCB) and Softcore-Bayesianism (SCB) providing solutions for the claims above. For data analysis we favor Bayesian statistics with its Markov Chain Monte Carlo (MCMC) simulation algorithm. It provides a full illustration of data-induced uncertainty beyond classical point-estimates. We calibrate twelve different stochastic processes to four years of CO2 price data. Besides, we calculate derived risk measures (ex ante/ post value-at-risks, capital charges, option prices) and compare them to their classical counterparts. When statistics fails because of a lack of reliable data we propose our integrated Bayesian Risk Analysis (iBRA) concept. It is a basic guideline for an expertise-driven quantification of critical risks. We additionally review elicitation techniques and tools supporting experts to express their uncertainty. Unfortunately, Bayesian thinking is often blamed for its arbitrariness. Therefore, we introduce the idea of a Bayesian due diligence judging expert assessments according to their information content and their inter-subjectivity. / Die vorliegende Arbeit befasst sich mit den Ansätzen eines Bayes’schen Risikomanagements zur Messung von Risiken. Dabei konzentriert sich die Arbeit auf folgende zentrale Fragestellungen: (1) Wie ist es möglich, transparent Risiken zu quantifizieren, falls nur eine begrenzte Anzahl an geeigneten historischen Beobachtungen zur Datenanalyse zur Verfügung steht? (2) Wie ist es möglich, transparent Risiken zu quantifizieren, falls mangels geeigneter historischer Beobachtungen keine Datenanalyse möglich ist? (3) Inwieweit ist es möglich, Willkür und Beliebigkeit bei der Risikoquantifizierung zu begrenzen? Zur Beantwortung der ersten Frage schlägt diese Arbeit die Anwendung der Bayes’schen Statistik vor. Im Gegensatz zu klassischen Kleinste-Quadrate bzw. Maximum-Likelihood Punktschätzern können Bayes’sche A-Posteriori Verteilungen die dateninduzierte Parameter- und Modellunsicherheit explizit messen. Als Anwendungsbeispiel werden in der Arbeit zwölf verschiedene stochastische Prozesse an CO2-Preiszeitreihen mittels des effizienten Bayes’schen Markov Chain Monte Carlo (MCMC) Simulationsalgorithmus kalibriert. Da die Bayes’sche Statistik die Berechnung von Modellwahrscheinlichkeiten zur kardinalen Modellgütemessung erlaubt, konnten Log-Varianz Prozesse als mit Abstand beste Modellklasse identifiziert werden. Für ausgewählte Prozesse wurden zusätzlich die Auswirkung von Parameterunsicherheit auf abgeleitete Risikomaße (ex-ante/ ex-post Value-at-Risks, regulatorische Kapitalrücklagen, Optionspreise) untersucht. Generell sind die Unterschiede zwischen Bayes’schen und klassischen Risikomaßen umso größer, je komplexer die Modellannahmen für den CO2-Preis sind. Überdies sind Bayes’sche Value-at-Risks und Kapitalrücklagen konservativer als ihre klassischen Pendants (Risikoprämie für Parameterunsicherheit). Bezüglich der zweiten Frage ist die in dieser Arbeit vertretene Position, dass eine Risikoquantifizierung ohne (ausreichend) verlässliche Daten nur durch die Berücksichtigung von Expertenwissen erfolgen kann. Dies erfordert ein strukturiertes Vorgehen. Daher wird das integrated Bayesian Risk Analysis (iBRA) Konzept vorgestellt, welches Konzepte, Techniken und Werkzeuge zur expertenbasierten Identifizierung und Quantifizierung von Risikofaktoren und deren Abhängigkeiten vereint. Darüber hinaus bietet es Ansätze für den Umgang mit konkurrierenden Expertenmeinungen. Da gerade ressourceneffiziente Werkzeuge zur Quantifizierung von Expertenwissen von besonderem Interesse für die Praxis sind, wurden im Rahmen dieser Arbeit der Onlinemarkt PCXtrade und die Onlinebefragungsplattform PCXquest konzipiert und mehrfach erfolgreich getestet. In zwei empirischen Studien wurde zudem untersucht, inwieweit Menschen überhaupt in der Lage sind, ihre Unsicherheiten zu quantifizieren und inwieweit sie Selbsteinschätzungen von Experten bewerten. Die Ergebnisse deuten an, dass Menschen zu einer Selbstüberschätzung ihrer Prognosefähigkeiten neigen und tendenziell hohes Vertrauen in solche Experteneinschätzungen zeigen, zu denen der jeweilige Experte selbst hohes Zutrauen geäußert hat. Zu letzterer Feststellung ist jedoch zu bemerken, dass ein nicht unbeträchtlicher Teil der Befragten sehr hohe Selbsteinschätzung des Experten als negativ ansehen. Da der Bayesianismus Wahrscheinlichkeiten als Maß für die persönliche Unsicherheit propagiert, bietet er keinerlei Rahmen für die Verifizierung bzw. Falsifizierung von Einschätzungen. Dies wird mitunter mit Beliebigkeit gleichgesetzt und könnte einer der Gründe sein, dass offen praktizierter Bayesianismus in Deutschland ein Schattendasein fristet. Die vorliegende Arbeit stellt daher das Konzept des Bayesian Due Diligence zur Diskussion. Es schlägt eine kriterienbasierte Bewertung von Experteneinschätzungen vor, welche insbesondere die Intersubjektivität und den Informationsgehalt von Einschätzungen beleuchtet.

[pt] Projetos de renovação ferroviária apresentam características de projetos complexos e repetitivos, dado seu grande número de recursos e fatores de influência e atividades repetitivas para determinadas unidades de produção. Neste contexto o presente trabalho buscou aplicar conceitos relativos a gerenciamento de projetos desse nicho e desenvolver uma forma integrada de trabalhar com a incerteza nesse ambiente. Foi aplicada a metodologia de planejamento de projetos chamada Linha de Balanço, utilizando informações do projeto em fase de concepção em uma empresa ferroviária. Em sequência foi desenvolvido um protocolo para obtenção da opinião de especialistas em informações críticas para o processo e obtidas as distribuições betas que melhor representam as informações elicitadas. A partir dessas entradas, foi desenvolvido um modelo de simulação das atividades do projeto para analisar o seu funcionamento em um ambiente virtual e livre de riscos e usar como ferramenta para aprimorar seu planejamento. Como resultados são apresentadas e analisadas as principais saídas do modelo e propostas formas de controle que possam auxiliar na retroalimentação do planejamento com informações do andamento do projeto após iniciado. / [en] Project Planning known as Line of Balance (LoB) was applied, using information from a project in the conception stage of a railway company. Next, a protocol was developed to obtain expert opinion on critical information for the process and beta distributions that best represent the elicited information. From these inputs, it was developed a simulation model of the project activities in order to analyze their operation in a virtual and risk-free environment and optimize their scheduling. As a result, the main outputs of the model are presented and analyzed, in addition with the suggestion of methods of control that can assist in the feedback of the planning process with status information of the ongoing project.

In this thesis a number of statistical methods have been developed and applied to habitat suitability modelling for rare and threatened species. Data available on these species are typically limited. Therefore, developing these models from these data can be problematic and may produce prediction biases. To address these problems there are three aims of this thesis. The _rst aim is to develop and implement frequentist and Bayesian statistical modelling approaches for these types of data. The second aim is develop and implement expert elicitation methods. The third aim is to apply these novel approaches to Australian rare and threatened species case studies with the intention of habitat suitability modelling. The _rst aim is ful_lled by investigating two innovative approaches for habitat suitability modelling and sensitivity analysis of the second approach to priors. The _rst approach is a new multilevel framework developed to model the species distribution at multiple scales and identify excess zeros (absences outside the species range). Applying a statistical modelling approach to the identi_cation of excess zeros has not previously been conducted. The second approach is an extension and application of Bayesian classi_cation trees to modelling the habitat suitability of a threatened species. This is the _rst `real' application of this approach in ecology. Lastly, sensitivity analysis of the priors in Bayesian classi_cation trees are examined for a real case study. Previously, sensitivity analysis of this approach to priors has not been examined. To address the second aim, expert elicitation methods are developed, extended and compared in this thesis. In particular, one elicitation approach is extended from previous research, there is a comparison of three elicitation methods, and one new elicitation approach is proposed. These approaches are illustrated for habitat suitability modelling of a rare species and the opinions of one or two experts are elicited. The _rst approach utilises a simple questionnaire, in which expert opinion is elicited on whether increasing values of a covariate either increases, decreases or does not substantively impact on a response. This approach is extended to express this information as a mixture of three normally distributed prior distributions, which are then combined with available presence/absence data in a logistic regression. This is one of the _rst elicitation approaches within the habitat suitability modelling literature that is appropriate for experts with limited statistical knowledge and can be used to elicit information from single or multiple experts. Three relatively new approaches to eliciting expert knowledge in a form suitable for Bayesian logistic regression are compared, one of which is the questionnaire approach. Included in this comparison of three elicitation methods are a summary of the advantages and disadvantages of these three methods, the results from elicitations and comparison of the prior and posterior distributions. An expert elicitation approach is developed for classi_cation trees, in which the size and structure of the tree is elicited. There have been numerous elicitation approaches proposed for logistic regression, however no approaches have been suggested for classi_cation trees. The last aim of this thesis is addressed in all chapters, since the statistical approaches proposed and extended in this thesis have been applied to real case studies. Two case studies have been examined in this thesis. The _rst is the rare native Australian thistle (Stemmacantha australis), in which the dataset contains a large number of absences distributed over the majority of Queensland, and a small number of presence sites that are only within South-East Queensland. This case study motivated the multilevel modelling framework. The second case study is the threatened Australian brush-tailed rock-wallaby (Petrogale penicillata). The application and sensitivity analysis of Bayesian classi_cation trees, and all expert elicitation approaches investigated in this thesis are applied to this case study. This work has several implications for conservation and management of rare and threatened species. Novel statistical approaches addressing the _rst aim provide extensions to currently existing methods, or propose a new approach, for identi _cation of current and potential habitat. We demonstrate that better model predictions can be achieved using each method, compared to standard techniques. Elicitation approaches addressing the second aim ensure expert knowledge in various forms can be harnessed for habitat modelling, a particular bene_t for rare and threatened species which typically have limited data. Throughout, innovations in statistical methodology are both motivated and illustrated via habitat modelling for two rare and threatened species: the native thistle Stemmacantha australis and the brush-tailed rock wallaby Petrogale penicillata.