SPSG #9: A Practical Guide to Theoretical Probability

This Risk Analysis methodology chapter is the applied version of the philosophical discussion of probability presented in Chapter 2. It also fixes the flaws in the Redbook paradigm discussed in Chapter 4, resulting in the Guillotine paradigm. It begins with a discussion of characterizing uncertainty when there are both statistical and theoretical probabilities involved. While a theoretical probability does not need to be quantified when it is the only probability involved or when there is no decision at stake, giving it the same epistemic standing as a statistical one is unavoidable when both matter. However, that does not mean a theoretical probability can be used as if it were a statistical probability. A theoretical probability is perhaps true always or perhaps false always; is it not true sometimes and false at other times. The discussion then turns to the problem of assigning probabilities to alternative theories. Declaring that all sum to one is a simple matter, but deciding the probability of each theory is not. Since theoretical probabilities are subjective, depending on the opinions of those who have one (that usually means experts) is in some way is inevitable. However, instead of asking experts to assign probabilities to theories directly, there are advantage to garnering opinion in the form of evidential weights, where each alternative theory is evaluated more or less independently. Although formal weight-of-the-evidence schemes have been developed for many regulatory purposes, they are not usually thought of as quantitative exercises. However, it has been done and could be done better. It is also argued that WoE analysis and dose-response modeling need to be more tightly integrated, especially when the judgment that there is a causal relationship becomes more likely than not. First, the shape of the dose-response relationship may influence the judgment that there is a causal relationship. Second, the last vestiges of causal uncertainty may not matter if the estimated risks are too low to matter or high enough to be a concern even if they are only probable.