In this course we consider risk as the quantitative measure describing the potential for realisation of consequences concerning a particular target within a complex system. The target is understood broadly and encompasses human life, health, property, environment, business operations, etc. The consequence can be negative, reflected in loss, or can be positive, reflected in utility. It is uncertain if the event, which the consequence refers to, will occur, in a specified timeframe. We learn about the probability of the event occurring from past data as well as from expert knowledge. We decide what action to take in relation to the possible event given its consequence on the target and the broader implications for the complex system of interest. The action is considered ‘best’, given specified decision criteria.
Numerical and statistical models are used as instruments aimed at assisting the decision-maker in making optimal decisions; the course discusses the decision-maker's attitude towards risk and looks at mechanisms to incorporate attitude in decision analysis models.
The course first introduces influence diagrams and decision trees as tools for building mathematical models of decision problems, which are then analysed. Analysis involves an evaluation of options, modelling the uncertainty in these options through Monte Carlo simulation and considering the influence of preferences and subjectivity in results. To practice the use of influence diagrams and decision trees in decision problems, we employ the DecisionTools suite of software, which comes as an add-on to the course textbook.
A second course component is dedicated to the study of MultiCriteria Decision Analysis (MCDA) methods, which aid in the analysis of complex problems where multiple, sometimes conflicting, criteria exist and tradeoffs must be made. MCDA methods have different theoretical foundations including optimization, goal aspiration and outranking. During the course we review the main MCDA approaches and concentrate on understanding the theoretical foundation of one of these: the Analytic Hierarchy Process (AHP) and its generalisation the Analytic Network Process (ANP). We will illustrate their use with the aid of software.
In the final component of the course we introduce Bayesian Decision Theory and learn how to develop, analyse and interpret the results of a Bayesian Network – a statistical tool that assists us to make decisions when many alternatives, each with a degree of uncertainty, exist. We illustrate the use of Bayesian Networks with the aid of software.
