Epistemic vs. Aleatory uncertainty

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Panagiotis Vounatsos - s182563

Abstract

Uncertainty is embedded in many aspects of a project, program and portfolio management. It is present in decision making for project integration and complexity, scope management, schedule management, cost management and risk management as this is mentioned in PMI standards as well as in risk management given in AXELOS project management standards.

Uncertainty derives from not knowing for sure if a statement is true or false. More specifically, it is the absence of information and if put more scientifically, it is the difference between the amount of information required to perform a task and the amount of information already possessed^[1]. Uncertainty is considered crucial to be identified and mitigated as it can contribute to severe consequences to the aforementioned aspects of a project, program or portfolio. Depending on the level of the uncertainty and the consequence it may result in jeopardizing the outcome of an action or even of the whole project. It is worth mentioning that uncertainty is not only a part of the project management but also a part of the technical implementation of a project.

The capability to quantify the impact of uncertainty in the decision context is critical. Uncertainty can be divided in several categories but the most dominant ones in uncertainty theory are epistemic and aleatory uncertainty^[2]. Epistemic uncertainty derives from the lack of knowledge of a parameter, phenomenon or process, while aleatory uncertainty refers to uncertainty caused by probabilistic variations in a random event^[3]. Each of these two different types of uncertainty has its own unique set of characteristics that separates it from the other and can be quantified through different methods. Some of these methods include simulation, statistical analysis or measurements^[4]. There is still ongoing research for increasing the accuracy of a result and include more parameters in calculating an outcome.

What is Uncertainty

Different definitions have been given for uncertainty in project management, but their common denominator is “not knowing for sure”. There is information that are known to be true and other known to be false, but for a large portion of information there is not knowledge whether they are true or false, and therefore they are mentioned as uncertain^[1]. According to Lindley^[5] uncertainty can be considered as subjective between individuals and this is attributed to the fact that the set of information obtained from an individual can be different from another. Two facts that apply are: a) the degree of uncertainty between individuals may also differ, meaning that one person may think that an event is more likely to happen that another person, b) The number of uncertain information is vastly greater than the number of information each individual is sure that are true or false^[5]. The two aforementioned facts deeply affect decision making by taking into consideration that uncertainty creates the contingency for occurrence of risky events may lead to potential damage or loss.

Epistemic vs. Aleatory uncertainty

Uncertainty is categorized into two types: Epistemic uncertainty (also known as systematic uncertainty or reducible uncertainty) and aleatory uncertainty (also known as statistical uncertainty or irreducible uncertainty)^[6].

• Epistemic Uncertainty: derives its name from the Greek word “επιστήμη” (episteme) which can be roughly translated as knowledge. Therefore, epistemic uncertainty is presumed to derive from the lack of knowledge of information regarding the phenomena that dictate how a system should behave, ultimately affecting the outcome of an event^[2][6].
• Aleatory Uncertainty: derives its name from the Latin word “alea” which is translated as “the roll of the dice”. Therefore, aleatory uncertainty can be defined as the internal randomness of a phenomena^[2].

Key features of Epistemic and Aleatory Uncertainty

Key features characterizing pure epistemic and pure aleatory uncertainty are distinguished according to judgement and decision making.

Representation

Epistemic uncertainty targets single cases (or statements), while aleatory uncertainty focuses on a range of possible outcomes that can derive from the repetition of an experiment or situation. Robinson et al. (2006) as cited in Fox and Ülkümen (2011)^[7], have carried out an experiment asking children to predict the color of a toy building block (orange or green) that would be drawn from a bag containing only these two colors. The result presented that when the children were asked before the experimenter has drawn a block, then they chose both colors as a possible outcome. If the children were asked to predict after the experimented has drawn a block, then they usually made one choice based on their best guess on the already determined colour. This experiment suggests that when the likelihood of a single event or a group of events are calculated, then this may prime epistemic and aleatory representation, respectively.

Focus of Prediction

When purely epistemic uncertainty is assessed, it generally leads to the evaluation of events that will be true or false. In contrast, when purely aleatory uncertainty is assessed, it leads to the evaluation of trend of each event on continuous unit interval. According to that, small changes in evidence strength have a big effect on pure epistemic events leading them towards extreme values (yes or no, true or false), compared to judgement of events that include aleatory uncertainty^[7]. An example is that if there is high confidence that a project idea is slightly costlier than another, then the probability that the first project is more expensive than a second one is judged as 1. However, if there is confidence that a project is a marginally more innovative than another, then it can be supposed that the probability it will create more value (money) than the other is less than 1, probably 0.6 or 0.7.

Probability interpretation

The interpretation of pure aleatory uncertainty is carried out as an extentional measure of relative frequency, while the interpretation of pure epistemic uncertainty is conducted as an intentional measure of confidence. In this manner, using relative frequency may trigger more aleatory thinking than drawing out probability numbers. Several studies indicate that the error contained in judging that the occurrence of a combined probable and improbable event is more likely to happen than an improbable event alone, occurs less often when judging relative frequencies than single event probabilities^[7].

Attribution of uncertainty

Unpredictable outcomes that are treated as stochastic (e.g the result from the roll of a dice) relate to aleatory uncertainty. Events or outcomes that occur due to missing information or expertise (e.g. giving the correct answer to an exam), or inefficiency of an aleatory uncertainty model (e.g. the assumptions made for forecasting energy demand are valid) is associated with epistemic uncertainty^[7].Ellsebergs’ paradox provides a very good illustration on decision making under epistemic and aleatory uncertainty. Consider two urns filled with green and yellow balls, and a bet in which someone must choose an urn and guess the color of the ball that will be picked out of it. The first urn contains 10 green balls and 10 yellow balls. Choosing from this urn has a known probability and therefore pure aleatory uncertainty. The second urn contains 20 balls in total but without the known amount of green and yellow balls. Choosing from this urn presents mixed epistemic and aleatory uncertainty. The aleatory uncertainty derives from the randomness of the draw while the epistemic uncertainty derives from the unknown composition. Let’s presume that the decision maker must choose from the first urn with known probability, after the experimenter draws a ball but before the color is revealed. The event has turned from pure aleatory uncertainty, to epistemic uncertainty of lack of knowledge.

Information search

From the attribution feature, epistemic uncertainty is attributed to missing information or expertise. Therefore, it can be reduced by searching for knowledge that will allow to predict its outcome with greater accuracy. On the contrary, the determined relative frequency of possible outcomes for aleatory uncertainty cannot be further reduced^[7].Let’s assume an example where a program manager has to choose between a set of projects, each project sometimes contributes to the programs benefits and outputs, and sometimes does not. An epistemic mindset suggests that one would alter the choices exploring the combination of projects (type, size, domain, complexity etc.) that govern the sequence for success contributing to the benefits. An aleatory mindset would find which of the project size and complexity is more often successful and run only projects of this size and complexity every time.

Linguistic Markers

Hutchins as cited in Fox and Ülkümen (2011)^[7] has identified that natural languages reflect the intuitive distinguish of cognitive concepts from individuals. The fact that epistemic and aleatory uncertainty had been incorporated in natural language was anticipated and empirically validated (Teigen and Fox, Üklümen and Malle as cited in Fox and Ülkümen (2011)^[7]). These authors presented that there are phrases that express epistemic uncertainty (e.g. “I am 70% sure that…”) and aleatory uncertainty (e.g. “I think there is a 75% change that…”).

The following table (Table 1) summarizes the key features of pure aleatory and epistemic uncertainty.

Whereas epistemic uncertainty can be reduced by acquiring knowledge and information on the system, aleatory uncertainty cannot be reduced in this way, and for this reason is often called as irreducible uncertainty.

Causes of epistemic and aleatory uncertainty

Different causes of uncertainty can be recognized as given by Armacosta and Pet-Edwards, and Zimmermann cited in Zio and Pedroni ^[6].

1. Lack of information (or knowledge). The main cause of uncertainty is the lack of information or knowledge regarding the systems or events under investigation. Lack of information can either be categorized as a lack of a precise probabilistic value for an event (quantitative nature), or as lack of knowledge as how to analyze mathematically the known probabilistic values for an event (qualitative nature). Lack of knowledge also affects the detail of the mathematical method used to analyze the probabilistic values of an event. This situation is called approximation, and it occurs when there is not enough information or reason to describe the event in a high level of detail, and therefore lower detail level is used. An example for approximation is when a project manager searches and takes into consideration several parameters to calculate the project’s cost. But to what extent is it needed to calculate the value of some low-cost equipment down to two decimals, if the total cost exceeds several million cost units?

1. Abundance of information (or knowledge). In principle, humans are incapable of simultaneously assimilating and elaborating many pieces of information (or data), and that leads to uncertainty from abundance of information. Due to the explained human nature, when there is overwhelming information, attention is only given to pieces of information considered as the most important, while others are neglected. For example, this uncertainty occurs when there are different models for the analyst to choose among, in order to analyze an event.

1. Conflicting nature of pieces of information/data. This uncertainty occurs when some pieces of information give contradicting knowledge, and it cannot be reduced by increasing the amount of information. This conflict can derive from the facts a) that information is affected by unidentified from the analyst errors, or b) that information is irrelevant to the event analyzed, or c) the model used to analyze the system is incorrect.

1. Measurement errors. Uncertainty is created by errors in the measurement of a physical quantity and occur either due to an error of the measurement taker, or due to insufficient accuracy of the used instrument.

1. Linguistic ambiguity. All languages and communication forms can be structured in a way that can be differently interpreted depending on the analysis context. This cause of uncertainty is included in the “lack of information” category, because it can be reduced by clarifying the context.

1. Subjectivity of analyst opinions. This uncertainty emanates from the subjective interpretation of information by the analyst, depending on their personal experience, competence and cultural background. The uncertainty deriving from this cause, can be reduced by taking into consideration the opinion of several different experts.

Uncertainty in Management

In this subsection, details are going to be given regarding where is uncertainty met in program, project and portfolio management.

Epistemic vs. Aleatory uncertainty

Distinguishing between epistemic and aleatory uncertainty

In this subsection the distinction between epistemic and aleatory uncertainty is going to be given.

Differences of the properties for each uncertainty type are going to be given

An risk management example is going to be provided in order to better distinguish the difference between epistemic and aleatory uncertainty

Quantification of epistemic uncertainty

In this subsection, methods and models for quantifying epistemic uncertainty are going to be briefly mentioned and in certain cases further analysed

References

1. ↑ ^{1.0 1.1} G. Grote, Management of Uncertainty - Theory and application in the design of systems and organizations, London: Springer, 2009.
2. ↑ ^{2.0 2.1 2.2} A. D. Kiureghiana and O. Ditlevsen, "Aleatory or epistemic? Does it matter?," Structural Safety, vol. 31, no. 2, p. 105–112, March 2009.
3. ↑ S. Basu, "Chapter 2: Evaluation of Hazard and Risk Analysis," in Plant Hazard Analysis and Safety Instrumentation Systems, London, Elsevier, 2017, p. 152.
4. ↑ T. Aven and E. Zio, "Some considerations on the treatment of uncertainties in risk assessment for practical decision making," Reliability Engineering & System Safety, vol. 96, no. 1, pp. 64-74, 2011.
5. ↑ ^{5.0 5.1} D. V. Lindley, "Uncertainty," in Understanding Uncertainty, New Jersey, John Wiley & Sons, Inc., 2006, pp. 1-2.
6. ↑ ^{6.0 6.1 6.2} E. Zio and N. Pedroni, "Causes of uncertainty," in Uncertainty characterization in risk analysis for decision-making practice, number 2012-07 of the Cahiers de la Sécurité Industrielle, Toulouse, France, Foundation for an Industrial Safety Culture, 2012, pp. 8-9.
7. ↑ ^{7.0 7.1 7.2 7.3 7.4 7.5 7.6} C. R. Fox and G. Ülkümen, "Chapter 1: Distinguishing Two Dimensions of Uncertainty," in Perspectives on Thinking, Judging, and Decision Making, Oslo, Universitetsforlaget, 2011, pp. 22-28.