ABSTRACT
Risk is conventionally understood to be related to the concepts of uncertainty and probability
(Chap ter 1), becau se risk is derive d from a sen se that the future is imper fectly or inco mpletely
known. Uncertainty concerning the future may be due to inherent randomness (e.g., quantum
indeterminacy), effective limits on knowledge of future conditions even in deterministic
systems (chaotic systems or simply the limits of data collection and analysis), or simple lack
of knowledge (ignorance). The concept of probability and the related concepts of uncertainty,
variability, likelihood, error, credibility, etc. are sources of confusion and controversy, which
lead to linguistic uncertainty. Most environmental scientists are aware of two schools of
statistics with different concepts of probability: Frequentist and Bayesian. Many are not
aware that there are other approaches such as information-based statistics (Burnham and
Anderson 1998, 2001) or evidence-based statistics (Taper and Lele 2004), or that many
statisticians consider their field to be in need of a conceptual revolution (Gigerenzer et al.
1989; Salsburg 2001; Royall 2004). This chapter will avoid most of these issues by sticking to
approaches that are in reasonably common use. Those who are uncertain about probability
should consult Hacking’s (2001) marvelously clear text. Those who want specifics about how
quantitative methods are used in risk assessment might consult a text on quantitative methods
in risk assessment such as Vose (2000), Burgman (2005), andWarren-Hicks andMoore (1998).
We speak of risks and analyze probabilities because we wish to predict the future but realize
that we cannot know the future. This is due to variability and uncertainty and to unquantified
or unacknowledged factors.
