Uncertainty: any departure from the unachievable ideal of complete deterministic knowledge of the system. From the risk assessors point of view, uncertainty is best thought of as a two dimensional concept, including the i) Location, and ii) Level of uncertainty.

Location of uncertainty: refers to the aspect of the risk assessment model that is characterized by uncertainty. All of the widely used approaches to risk assessment rely on methodologies that can be considered models - that is, abstractions of the real world issues under consideration. » Read more  For example, Risk is often modeled as a function of a system that includes probability and consequence subsystems. The group of cause-effect relationships encompassed by a particular risk problem is referred to as the system model for the particular risk. The location dimension refers to where uncertainty manifests itself within the configuration of the system model.

Example 1. Location of uncertainty

Consider a map of the world that was drawn by a European cartographer in the 15^th century. Such a map would probably contain a fairly accurate description of the geography of Europe. Because the trade of spices and other goods between Europe and Asia was well established at that time, one might expect that those portions of the map depicting China, India, central Asia and the middle-east were also fairly accurate. However, as Columbus only ventured to America in 1492, the portions of the map depicting the American continent would likely be quite inaccurate (if they existed at all). Thus, it would be possible to point to the American continent as a “location” in the model that is subject to large uncertainty. In this case, the model in question is a map of the world, and all locations are geographic components of the map.

Generic model locations: The description of the model locations will vary according to the assessment method (model) that is in use. Nonetheless, it is possible to identify certain categories of locations that apply to most models. These are:

• Context » Read more  refers to the choice of the boundaries of the system to be modeled. This location is of great importance, as the choice of the boundaries of the system determines what part of the real world is considered inside the system (and therefore the model), and what part of the real world is left out. The choice of the system boundaries is often referred to as the “problem framing”, “problem definition” or “issue framing”. Different stakeholders have different perceptions of what constitutes a risk, which risks should be assessed, and how much risk is acceptable. This is a frequent cause for controversy in the regulatory debate. </more>
• Model structure » Read more  refers to the variables, parameters and relationships that are used to describe (model) a given phenomenon. Model structure uncertainty is thus uncertainty about the form of the model that describes the phenomena included within the boundaries of the system. Here one could think of the shape of dose-response functions, or the additivity vs. the multiplicativity of risk factors. In situations where the system being studied involves the interaction of several complex phenomena, different groups of researchers may have different interpretations of what the dominant relationships in the system are, and which variables and parameters characterize these relationships. Uncertainty about the structure of the system implies that any one of many model formulations might be a plausible, although partial, representation of the system. Thus, researchers with competing interpretations of the system may be equally right, or equally wrong.</more>
• Inputs » Read more  refers to the data describing the system. Uncertainty about system data can be generated by insufficient data of poor quality data. Measurements can never exactly represent the “true” value of that which is being measured. Uncertainty in data can be due to sampling error, inaccuracy, imprecision in the measurements, conflicting data or simply lacking measurements. </more>
• Parameters  » Read more 
  
  The following types of parameters can be found:
  • Exact parameters (e.g. π and e);
  • Fixed parameters, (e.g. the gravitational constant g); and
  • A priori chosen or calibrated parameters.

The uncertainty on exact and fixed parameters can generally be considered as negligible within the analysis. However, the extrapolation of parameter values from a priori experience does lead to parameter uncertainty, as past circumstances are rarely identical to current and future circumstances. Similarly, because calibrated parameters must be determined by calibration using historical data series and sufficient calibration data may not be available and/or errors may be present in the data that is available, calibrated parameters are also subject to parameter uncertainty. </more>

• Model outcome (result) » Read more 
  
  This is the uncertainty caused by the accumulation of uncertainties from all of the above locations (context, model, inputs, and parameters). These uncertainties are propagated throughout the model and are reflected in the resulting estimates of the outcomes of interest (model result). It is sometimes called prediction error, since it is the discrepancy between the true value of an outcome and the model’s predicted value.  </more>

Level of uncertainty: refers to the degree to which the object of study is uncertain, from the point of view of the decision maker.  A continuum of different levels of uncertainty includes:

• Determinism » Read more  refers tothe situation in which everything is known exactly and with absolute certainty, an ideal that is never achieved in policy relevant sciences due to the complexity of the problems dealt with. On the scale of levels of uncertainty, it is at the end of the scale where there is no uncertainty whatsoever. </more>
• Statistical uncertainty » Read more describes the situation where there exist solid grounds for the assignment of a discrete probability to each of a well-defined set of outcomes. Potential outcomes can be identified as a finite set of discrete outcomes, or a single continuous range of outcomes. In situations of statistical uncertainty, analysts possessing knowledge of the form of the distribution (normal, lognormal, exponential, etc…) and its properties (s, m, etc…) can describe the probability with which any of the potential outcomes will occur. </more>
• Scenario uncertainty » Read more  describes the state where all of the possible outcomes are known, but where it is acknowledged that there exists no credible basis for the assignment of probability distributions to these outcomes. This can be due to the fact that the mechanisms leading to the potential outcomes are not well understood and it is, therefore, not possible to formulate the probability of any one particular outcome occurring.

Example 2: scenario uncertainty

Consider the case antimicrobials and antibiotics in animal feedstuff. Antibiotics are probably the single most important discovery in the history of medicine. They have saved millions of lives by killing bacteria that cause diseases in humans and animals. Beginning in the 1940s, low levels of antibiotics began to be added to animal feedstuff as it was observed that this practice could increase the growth rate of the animals, increase the efficiency of food conversion by the animals, as well as have other benefits such as improved egg production in laying hens, increased litter size in sows and increased milk yield in dairy cows. Over the years, concerns developed over the potential for bacteria to develop resistance to the antibiotics. It was feared that the widespread use of the antibiotics would lead to the development of resistant bacterial strains, and that these antibiotics would therefore no longer be effective in the treatment of disease in humans. The scientific evidence available indicated that the development of bacterial resistance could take place, but how quickly and to what extent this could occur remain unknown to this day. The question of whether the short-term benefits outweigh the potential long-term risks is still being debated. In this case, the scenario is clear but the probability of its occurrence is unknown. The uncertainty here is of a level greater than statistical uncertainty, and is referred to as scenario uncertainty.</more>

• Recognized ignorance » Read more  describes the state where there exist neither grounds for the assignment of probabilities, nor even the basis for defining the complete set of potential outcomes. It is a state where fundamental uncertainty about the mechanisms and functional relationships being studied has been identified, and where the scientific basis for developing scenarios is weak. In some cases ignorance may be lessened by conducting further research, which implies that it might be possible to somehow achieve a better understanding. However, in cases where the functional relationships are very complicated and/or the number of parameters is very large, or in some cases where the relationships are inherently unidentifiable, due to e.g. chaotic properties in the system that make predictions impossible, neither research nor development can resolve the ignorance. </more>
• Total ignorance » Read more  is the other extreme from determinism on the scale of uncertainty, which implies a deep level of uncertainty, to the extent that it is not even know that knowledge is lacking.

Example 3: ignorance

Consider the case of mad cow disease (also known as BSE) in Britain. Following the diagnosis of the first cases of BSE in 1986, it was noticed that the pathological characteristics of the new disease closely resembled scrapie, a contagious disease common in the UK sheep population. Health authorities soon observed that contaminated feed was the principle cause of BSE in cattle. However, the question remained: contaminated by what? There was no scientific evidence that eating sheep meat from scrapie-infected animals could pose a health risk, and health authorities could not be sure that the agent that caused BSE had in fact derived from scrapie. Moreover, there was no scientific evidence indicating that BSE could subsequently be transmitted to humans in the form of Creutzfeldt-Jakob disease (CJD), and it was a big surprise when, in 1995, it was discovered that this could happen.

The notion of ignorance is illustrated by considering the uncertainty characterizing an assessment of the potential costs associated to BSE, performed at the time of the discovery of BSE in 1986. No historical data on BSE was available and scientific understanding of how the disease is contracted was limited. The extent of the public outcry that would eventually occur remained unknown, as did the extent of the loss of exports and the drop in domestic demand that ensued. Data on the relationship between BSE and CJD would not become available for another 10 years. Furthermore, at the time there was not even a credible basis to claim that all of the potential ramifications or costs (outcomes) of the BSE crisis had been thought of. The uncertainty characterizing this situation is a good example of ignorance.