1.1 Uncertainty and probability
1.1.1 Probability is not about numbers, it is about coherent reasoning under uncertainty
The U.S. Federal Rule of Evidence 401 says that
‘Relevant evidence’ means evidence having any tendency to make the existence of any fact that is of consequence to the determination of the action more probable or less probable than it would be without the evidence. (Mueller and Kirkpatrick 1988, p. 33)
The term probable here means the degree of belief the fact finder entertains that a certain fact occurred. If it is not known whether the fact occurred, only a degree of belief less than certainty may be assigned to the occurrence of the fact, and there can then be discussion about the strength of this degree. Sometimes, we are satisfied with speaking loosely of ‘strong’ or ‘weak’ beliefs; sometimes, we would prefer to be more precise because we are dealing with important matters. A way to be more precise is to assign numerical values to our degrees of belief and use well-defined rules for combining them together.
People are usually not very willing to assign numbers to beliefs, especially if they are not actuaries or professional gamblers. In this book, we shall ask our readers to assign numbers, but these numbers are not important by themselves: what really matters is the fact that numbers allow us to use powerful rules of reasoning which can be implemented by computer programmes. It is not really important that the numbers ...