101 This computer-intensive framework allows a random sample from the analytically intractable
distribution of the risk output to be obtained. Summary statistics that we produce from the simulated risk output Monte-Carlo sample converge to the corresponding summary statistics
from the risk output’s distribution in large enough simulations. Summary statistics about how those summary statistics change across the uncertainty about inputs, converge to an expression of
our uncertainty about the risk output’s distribution in large enough simulations.
The estimator’s specification is generally completed by referring to the Monte-Carlo simulation size below, sampling method, and randomization method. The estimators’ characteristics,
convergence properties and standard errors are examined in the Appendix section “Simulation Estimator Characteristics for the Risk Outputs”.
8.3. Variability Uncertainty
8.3.1. Contrasting Variability and Uncertainty
When we account fully for how managers make risk decisions, how we treat variability and uncertainty should differ.
“Uncertainty forces decision makers to judge how probable it is that risks will be overestimated or underestimated for every member of the exposed population, whereas
variability forces them to cope with the certainty that different individuals will be subjected to risks both above and below any reference point one chooses” National
Research Council 1994, p. 237 In National Research Council’s sense 1994 and under Codex alimentarius commission
conventions, we should reserve variability to refer to how the risk output varies, over some well- defined reference population and we should reserve uncertainty to refer to our cumulative
knowledge or lack knowledge about that variability.
Variability Sources
Variability represents the heterogeneity of the risk within a particular population. In the present application, it is linked to the variability in the exposure, i.e. the heterogeneity of the number of
cells in a serving chosen at random. Some examples of elements of variability that are considered in this model are the location to location variability of environmental contamination as inferred
102 from Gombas et al. 2003, the variability in the ability of a Listeria population to grow in a
cheese at random linked to strain to strain variability and to cheese to cheese variability, the specific ability of a population of Listeria to grow linked to variability in time and temperature
of storage, and the variability in the number of cells per serving when a portion, which varies in size, is taken from a whole wheel of soft-ripened cheese. Such heterogeneity in the exposure
leads to heterogeneity in the risk per serving: the risk per serving varies over a reference population of servings.
Uncertainty Sources
Uncertainty about how the risk per serving varies arises from our lack of perfect knowledge, and it may be related to the model used to characterize the risk, the parameters used to provide values
for the model, or both. In some cases, we can reduce uncertainty by obtaining better information, but this may not always be possible. Having uncertain results implies that one might make a less-
than-optimal risk decision because one may expect one outcome but something quite different might actually occur Thompson 2002.
Sources of uncertainty include model uncertainty, data uncertainty and estimator uncertainty. Model uncertainty includes
• how one represents, summarizes or simplifies physical phenomena;
• how one represents methods to sample information from physical phenomena;
that is, the umbrella of model uncertainty includes the basic notion of how one infers from sample to sampling population and how one extrapolates from
sampling population to reference population the population that the risk assessment is interested in; and,
• how we represent the sampling distribution for the model’s basic outputs.
Data uncertainty includes •
inference from small samples via a particular model to the sampling population from which the data come; and,
• lack of clear definition of the sampling population and lack of clear description
for how the data were sampled from that sampling population.
