Chapter 5
Direct Statistical Estimation Techniques
This chapter addresses the fundamental methods available for the estimation of an uncertainty model when samples and expertise are directly available in order to characterise the uncertain inputs, being either independent (Section 5.2) or dependent (Section 5.3). Simultaneous estimation of both the aleatory and epistemic components is discussed on the basis of classical statistical theorems (such as asymptotic theory) or Bayesian settings (Section 5.4). The importance of physical properties such as plausible bounds or dependence structures is also introduced. In Section 5.5, the use of extreme value distributions is discussed in the light of rare probability computation: the extent to which they may be physically sound is studied in connection with the underlying time process assumptions. The key concept of rarity is discussed. For readers less familiar with probability and statistical modelling, a prior refresher is available in Annex Section 10.1 and formal links to probability theory are discussed in Annex Section 10.2.
