“This Is What We Don't Know”: Treating Epistemic Uncertainty in Bayesian Networks for Risk Assessment
Authors: Sahlin Ullrika , Helle Inari , Perepolkin Dmytro 
Published: November 2020

Abstract
Failing to communicate current knowledge limitations, that is, epistemic uncertainty, in environmental risk assessment (ERA) may have severe consequences for decision making. Bayesian networks (BNs) have gained popularity in ERA, primarily because they can combine variables from different models and integrate data and expert judgment. This paper highlights potential gaps in the treatment of uncertainty when using BNs for ERA and proposes a consistent framework (and a set of methods) for treating epistemic uncertainty to help close these gaps. The proposed framework describes the treatment of epistemic uncertainty about the model structure, parameters, expert judgment, data, management scenarios, and the assessment's output. We identify issues related to the differentiation between aleatory and epistemic uncertainty and the importance of communicating both uncertainties associated with the assessment predictions (direct uncertainty) and the strength of knowledge supporting the assessment (indirect uncertainty). Probabilities, intervals, or scenarios are expressions of direct epistemic uncertainty. The type of BN determines the treatment of parameter uncertainty: epistemic, aleatory, or predictive. Epistemic BNs are useful for probabilistic reasoning about states of the world in light of evidence. Aleatory BNs are the most relevant for ERA, but they are not sufficient to treat epistemic uncertainty alone because they do not explicitly express parameter uncertainty. For uncertainty analysis, we recommend embedding an aleatory BN into a model for parameter uncertainty. Bayesian networks do not contain information about uncertainty in the model structure, which requires several models. Statistical models (e.g., hierarchical modeling outside the BNs) are required to consider uncertainties and variability associated with data. We highlight the importance of being open about things one does not know and carefully choosing a method to precisely communicate both direct and indirect uncertainty in ERA. Integr Environ Assess Manag 2021;17:221–232. © 2020 The Authors. Integrated Environmental Assessment and Management published by Wiley Periodicals LLC on behalf of Society of Environmental Toxicology & Chemistry (SETAC)
KEY POINTS
We propose a framework for treating epistemic uncertainty that can guide assessors in communicating uncertainty due to limitations in knowledge when using Bayesian networks (BNs) for risk assessment. A BN is by itself not enough to characterize uncertainty in an assessment, and uncertainty associated with model structure, expert judgments, data, and management scenarios may require modeling external to a BN. There are several ways to characterize direct and indirect epistemic uncertainty, such as a subjective probability, an interval, an uncertainty scenario, or a list of caveats, to be combined with a BN. The users of BNs for environmental risk assessment (ERA) should distinguish between aleatory and epistemic BNs and apply expressions and methods for treating uncertainty appropriate for the given type of BN and knowledge bases of the assessment.