Risk Assessment. Marvin Rausand

Risk Assessment

approach to probability is applicable in only a limited set of situations, where we consider experiments with a finite number images

of possible outcomes, and where each outcome has the same likelihood of occurring. This is appropriate for many simple games of chance, such as tossing coins, rolling dice, dealing cards, and spinning a roulette wheel.

We use the following terminology: An outcome is the result of a single experiment, and a sample space images is the set of all the possible outcomes. An event images is a set of (one or more) outcomes in images that have some common properties. When an outcome that is a member of images occurs, we say that the event images occurs. These and many other terms are defined in Appendix A.

Because all images possible outcomes have the same likelihood of occurring, we can find the likelihood that event images will occur as the number images of outcomes that belong to images divided by the number images of possible outcomes. The outcomes that belong to images are sometimes called the favorable outcomes for images . The likelihood of getting an outcome from the experiment that belongs to images is called the probability of images :

(2.1) equation

The event images can also be a single outcome. The likelihood of getting a particular outcome is then called the probability of the outcome and is given by images .

When – as in this case – all the outcomes in images have the same probability of occurrence, we say that we have a uniform model.

2.4.1.2 Frequentist Approach

The frequentist approach restricts our attention to phenomena that are inherently repeatable under essentially the same conditions. We call each repetition an experiment and assume that each experiment may or may not give the event images . The experiment is repeated images times as we count the number images of the images experiments that end up in the event images . The relative frequency of images is defined as

Because the conditions are the same for all experiments, the relative frequency approaches a limit when images . This limit is called the probability of images and is denoted by images

(2.2) equation

If we do a single experiment, we say that the probability of getting the outcome images is images and consider this probability a property of the experiment.

2.4.1.3 Bayesian Approach

In a risk analysis, we almost never have a finite sample space of outcomes that occur with the same probability. The classical approach to probability is therefore not appropriate. Furthermore, to apply the frequentist approach, we must at least be able to imagine that experiments can be repeated a large number of times under nearly identical conditions. Because this is rarely possible, we are left with a final option, the Bayesian approach. In this approach, the probability is considered to be subjective and is defined as:

Definition 2.24 (Subjective probability)

A numerical value in the interval images representing an individual's degree of belief about whether or not an event will occur.

In the Bayesian approach, it is not necessary to delimit probability to outcomes of experiments that are repeatable under the same conditions. It is fully acceptable to give the probability of an event that can only happen once. It is also acceptable to talk about the probability of events that are not the outcomes of experiments, but rather are statements or propositions. This can be a statement about the value of a nonobservable parameter, often referred to as a state of nature. To avoid a too‐complicated terminology, we also use the word event for statements, saying that an event occurs when a statement is true.

The degree of belief about an event images is not arbitrary but is the analyst's best guess based on her available knowledge images about the event. The analyst's (subjective) probability of the event images , given that her knowledge is images , should therefore be expressed as

(2.3) equation

The knowledge images may come from knowledge about the physical properties of the event, earlier experience with the same type of event, expert judgment, and many other information sources. For simplicity, we often suppress images and simply write images , but we should not forget that this is a conditional probability depending on images

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