Bayesian Networks for Probabilistic Inference and Decision Analysis in Forensic Science, 2nd Edition

Chapter 9Networks for continuous models

So far events and counts and the probability of their occurrence have been discussed. These ideas may be extended to consider measurements about which there may be some uncertainty or randomness. In certain fairly general circumstances, the way in which probability is distributed over the possible values for the measurements can be represented, mathematically, by functions known as probability distributions. The most well-known distribution for measurements is that of the Normal distribution. This will be described in Section 9.1.1. Before Normal probability distributions can be discussed here, however, certain other concepts have to be introduced.

9.1 Random variables and distribution functions

The concept of a random variable [or random quantity or uncertain quantity, Lindley (1991)] needs some explanation. There has been some discussion on this earlier in Sections 1.1.9 and 2.1.2. A statistician draws conclusions about a population. This may be done by conducting an experiment or studying a population. The possible outcomes of the experiment or the study are known as the sample space . The outcomes are unknown in advance of the experiment or the study and, hence, are said to be variable. It is possible to model the uncertainty of these outcomes because of the randomness associated with them. Thus, the outcome is considered as a random ...