Lesson 2 - Understanding Uncertainty
This is the first of a number of Lessons in this Unit in which we discuss some fundamental concepts regarding probabilistic simulation. Because these Lessons are not “hands-on” (we won’t be looking at GoldSim), you may be tempted to skip these. DON’T!! Only after you are comfortable with these concepts can we start to discuss how these are implemented in GoldSim.
The first thing we need to discuss regarding probabilistic simulation is what we mean when we say something is “uncertain”. When quantifying the uncertainty in a system, there are two fundamental causes of uncertainty that it is important to distinguish between:
- that due to inherent (temporal) randomness; and
- that due to ignorance or lack of knowledge.
These are sometimes referred to as aleatory and epistemic uncertainty, respectively.
Note: "Aleatory" is from the Latin alea, referring to a die or a game of chance. "Epistemic" is from the Greek episteme, referring to science or knowledge.
Remembering this specific terminology is not important. What is important, however, is understanding conceptually how these two kinds of uncertainty are different.
Aleatory uncertainty results from the fact that given our present state of understanding and technology, many phenomena simply cannot be predicted deterministically, and hence the parameters representing them are treated as inherently variable (random or noisy) over time such that their behavior can only be described statistically. Examples include the flow rate in a river, the price of a stock, or the temperature at a particular location.
Other parameters are not considered inherently variable over time (e.g., they may actually have a single constant value), but cannot be specified precisely due to epistemic uncertainty: we lack precise information or knowledge (e.g., measurements) to specify their value with certainty. Examples include the strength of a particular material, the height of a mountain, or the efficacy of a new drug.
A fundamental difference between these two types of uncertainty is that epistemic uncertainty (i.e., resulting from lack of information) can theoretically be reduced by studying (e.g., observing or measuring) the parameter or system. That is, since the uncertainty is due to a lack of knowledge, theoretically that knowledge could be improved by carrying out experiments or collecting data (i.e., making more observations). Aleatory uncertainty, on the other hand, is inherently irreducible. If the parameter itself is inherently variable, studying the parameter further (e.g., making more observations) will certainly not do anything to change that variability. Why is this important? As we will discuss later (in Lesson 10), one of the key purposes of probabilistic simulation modeling is not just to make predictions, but to identify those parameters that are contributing the most to the uncertainty in results. If the uncertainty in the results is due primarily to epistemic parameters, we know that we could (at least theoretically) reduce our uncertainty in our results by obtaining more information about those parameters.
It should be noted that parameters that have both kinds of uncertainty are not uncommon in simulation models. For example, in considering the flow rate in a river, we know that it will be temporally variable (inherently random in time so it can only be described statistically), but in the absence of adequate data, we will have uncertainty about the statistical measures (e.g., mean, standard deviation) describing that variability. By taking measurements, we can reduce our uncertainty in these statistical measures (i.e., what is the mean flow rate?), but we will not be able to reduce the inherent variability in the flow.
When building models we should always try to explicitly distinguish random variability from ignorance/lack of knowledge. We will discuss this further in the next Lesson.