You’re headed for Melbourne, Australia, in November and are unsure how to pack because you do not know what the weather is like there at that time of year. For simplicity, let’s focus on the daily high temperature. You do not know the mean high temperature for Melbourne in November. This is a parameter, a constant, with a true and factual value. That you do not know this fact makes the situation one of knowledge uncertainty. A true value exists and you do not know it. You are uncertain about a fact.
Suppose you learn from the Bureau of Meteorology, Australia, that this value is 21.9°C (71°F). The uncertainty has been removed. Now a new prob- lem emerges. Even though you know the average temperature is 21.9°C, you have no way of knowing what the high temperature will be on any given day. In fact, you wisely expect the high temperature to vary from day to day.
Using our very loose definition at the start of this chapter, you say you are not sure what the temperature will be on any given day, so that must be uncertainty as well. And in a very general sense it is. However, and this is an important however, this value is uncertain for a very specific, common, and recurring reason; there is variability in the universe.
This variability is usually separated out from other causes of uncertainty in order to preserve the distinction in its cause for reasons that will soon be apparent. Hence, we’d say you are no longer uncertain about the mean high temperature, but you still do not know the high temperature on any given day because of natural variability. The temperature varies from day to day due to variation in the complex system that produces a high temperature each day. For a more formal distinction of these two concepts, we introduce the terms epistemic and aleatory uncertainty.
Epistemic uncertainty is the uncertainty attributed to a lack of knowledge on the part of the observer. It is reducible in principle, although it may be dif- ficult or expensive to do so. Epistemic uncertainty, what was described in the previous example as knowledge uncertainty, arises from incomplete theory and incomplete understanding of a system, modeling limitations, or limited data. Epistemic uncertainty has also been called internal, functional, subjec- tive, reducible, or model form uncertainty. Knowledge uncertainty is another easier to remember and perhaps more descriptive term used to describe this kind of uncertainty that is used throughout this book when we refer specifi- cally to epistemic uncertainty.
Some generic examples of knowledge uncertainty include: lack of experi- mental data to characterize new materials and processes, poor understand- ing of the linkages between inputs and outputs in a system, and thinking one value is greater than another but being unsure of that. More obvious examples include dated, missing, vague, or conflicting information; incor- rect methods; faulty models; measurement errors; incorrect assumptions; and the like. Knowledge uncertainty is, quite simply, not knowing. The most
NATIONAL RESEARCH COUNCIL (2009)
Uncertainty: Lack or incompleteness of information. Quantitative uncertainty analysis attempts to analyze and describe the degree to which a calculated value may differ from the true value; it sometimes uses probability distributions. Uncertainty depends on the quality, quantity, and relevance of data and on the reli- ability and relevance of models and assumptions.
Variability: Refers to true differences in attributes due to heteroge- neity or diversity. Variability is usually not reducible by further measurement or study, although it can be better characterized.
common example may be not knowing a parameter or value we are interested in for model building or decision-making purposes.
Aleatory uncertainty is uncertainty that deals with the inherent variabil- ity in the physical world. Variability is often attributed to a random process that produces natural variability of a quantity over time and space or among members of a population. It can arise because of natural, unpredictable varia- tion in the performance of the system under study. It is, in principle, irre- ducible. In other words, the variability cannot be altered by obtaining more information, although one’s characterization of that variability might change given additional information. For example, a larger database will provide a more precise estimate of the standard deviation, but it does not reduce vari- ability in the population. Aleatory uncertainty is sometimes called variabil- ity, irreducible uncertainty, stochastic uncertainty, and random uncertain. The term adopted for usage in this book when we refer specifically to aleatory uncertainty is natural variability.
Some generic examples of natural variability include: variation in the weight of potato chips in an eight-ounce bag, variation in the response of an ecosystem to a change in the physical environment, and variation in mean hourly traffic counts from day to day. There is also variability in any attribute of a population.
Knowledge uncertainty and natural variability are terms used by the National Research Council (2009). It will be convenient to use the term uncertainty to encompass both of these ideas, so that is the convention adopted in this book. However, this is by no means the usual convention, and the reader is advised to always clarify, when possible, and to try to care- fully discern, when it is not, what the user of these terms means from the context of their usage.
To complicate matters, reality is often messy. Returning to our Melbourne example, we can see that at the outset we are dealing with both knowledge uncertainty and natural variability. It takes experience for a risk assessor to be
AN IMPORTANT DISTINCTION
Natural variability cannot be reduced with more or better information. Knowledge uncertainty can be reduced with more and better information through such means as research, data collection, better modeling and measurement, filling gaps in information and updating out-of-date information, and correcting faulty assumptions.
able to comfortably label the reasons why a value may be unknown. It is not always possible and not always important to be able to separate knowledge uncertainty and natural variability. In general, the most important reasons for separating the effects of the two in a risk assessment are to select an appropri- ate tool for addressing them and to understand that simply devoting more resources to the risk assessment effort may reduce knowledge uncertainty, but it will not reduce variability. The only way to change the variability produced by a system is to change the system itself. This will not eliminate variability; it will produce a new form of, presumably, more favorable variability in the altered system. Risk assessment can reduce uncertainty. Risk management measures can alter variability.