Good practice in Bayesian network modelling

Abstract

Bayesian networks (BNs) are increasingly being used to model environmental systems, in order to: integrate multiple issues and system components; utilise information from different sources; and handle missing data and uncertainty. BNs also have a modular architecture that facilitates iterative model development. For a model to be of value in generating and sharing knowledge or providing decision support, it must be built using good modelling practice. This paper provides guidelines to developing and evaluating Bayesian network models of environmental systems, and presents a case study habitat suitability model for juvenile Astacopsis gouldi, the giant freshwater crayfish of Tasmania. The guidelines entail clearly defining the model objectives and scope, and using a conceptual model of the system to form the structure of the BN, which should be parsimonious yet capture all key components and processes. After the states and conditional probabilities of all variables are defined, the BN should be assessed by a suite of quantitative and qualitative forms of model evaluation. All the assumptions, uncertainties, descriptions and reasoning for each node and linkage, data and information sources, and evaluation results must be clearly documented. Following these standards will enable the modelling process and the model itself to be transparent, credible and robust, within its given limitations.

Introduction

Bayesian networks (BNs) represent systems as a network of interactions between variables from primary cause to final outcome, with all cause–effect assumptions made explicit. BNs are often considered suitable for modelling environmental systems due to their ability to integrate multiple issues, interactions and outcomes and investigate tradeoffs. Furthermore, they are apt for utilising data and knowledge from different sources and handling missing data. BNs readily incorporate and explicitly represent uncertain information, and this uncertainty is propagated through to and expressed in the model outputs. BNs are based on a relatively simple causal graphical structure, meaning they can be built without highly technical modelling skills and be understood by non-technical users and stakeholders. This is a very valuable feature of BNs, particularly in the context of natural resource management which benefits from interdisciplinary and participatory processes (Voinov and Bousquet, 2010).

In BNs, variables are represented by nodes, which are linked by arcs that symbolise dependent relationships between variables. The strength of these relationships is defined in the Conditional Probability Tables (CPTs) attached to each node. CPTs specify the degree of belief (expressed as probabilities) that the node will be in a particular state given the states of the parent nodes (the nodes that directly affect that node). Evidence is entered into the BN by substituting the a priori beliefs of one or more nodes with observation or scenario values. Through belief propagation using Bayes' Theorem, the a priori probabilities of the other nodes are updated. This belief propagation enables BNs to be used for diagnostic (‘bottom–up’ reasoning) or explanatory purposes (‘top–down’ reasoning) (Castelletti and Soncini-Sessa, 2007). Therefore unlike black-box models, such as neural networks (Chen et al., 2008), BN users can interrogate the reasoning behind the model outputs as interactions between variables are clearly displayed, providing transparency to users and promoting system learning. BNs can be used for classification and prediction of states or events even when data is partial or uncertain (Newton, 2010), which is a huge advantage over many other traditional statistical models that rely on large amounts of empirical data to be built (Marcot et al., 2006).

There is an enormous scope for the possible applications of BNs in natural resources management including species or community models (Marcot et al., 2001; Borsuk et al., 2006), management models (Bromley et al., 2004; Lynam et al., 2010; Nash and Hannah, 2011), integrated models (Ticehurst et al., 2007; Kragt et al., 2011) social models (Ticehurst et al., 2011), and risk assessment models (Pollino and Hart, 2005; Pollino et al., 2007b). The limitations of BNs include their inability to readily represent feedback loops and dynamic relationships (Uusitalo, 2007). However some software packages can handle dynamic models by representing each time slice with a separate network (Kjærulff, 1995) and there has also been some progress in the development of spatial BNs (Smith et al., 2007). The case study presented later in this paper is a spatial BN linked to GIS to model habitat suitability for an endangered species. More details about the advantages and limitations of BNs in environmental modelling can be found in Castelletti and Soncini-Sessa (2007) and Uusitalo (2007). Commonly used BN software platforms include Hugin Expert (Hugin, www.hugin.com), Netica (Norsys Software Corp., www.norsys.com), Analytica (Lumina Decision Systems, www.lumina.com), GeNIe and SMILE (University of Pittsburgh, genie.sis.pitt.edu), BUGS (MRC and Imperial College, www.mrc-bsu.cam.ac.uk/bugs) and BayesiaLab (Bayesia Ltd., www.bayesia.com).

Modelling can be a useful approach to understanding and supporting decisions on environmental systems. However, for a model to be of value, good practice in its construction, testing and application is essential, as is awareness of the purposes, capabilities and limitations of the modelling approach. Without this, there is a risk of the model user misinterpreting or misusing model outputs, and drawing invalid conclusions (Jakeman et al., 2006). Poor modelling practice reduces the credibility of the model and can lead to the model capabilities being ‘oversold’, potentially causing poor decisions to be made based on models, or where model transparency and testing has not been completed, users mistrusting models and their outputs (Refsgaard and Henriksen, 2004). Models that are not properly evaluated also risk being discredited. Consequently, guidelines for good modelling practice that create standards to help ensure the development and application of credible and purposeful models are essential.

Several authors have developed modelling guidelines (Refsgaard and Henriksen, 2004; Jakeman et al., 2006; Crout et al., 2008), where the key components for good practice include:

• Clearly defining model purpose and the assumptions underlying the model

• Thorough evaluation of the model and its results

• Transparent reporting of the whole modelling process, including its formulation, parameterisation, implementation and evaluation

Good modelling practice will result in better understanding of the development and application of models, benefitting not only the modelling community but also model users.

The objective of this paper is to introduce a good practice framework for developing and evaluating BN models of environmental systems. BN modelling protocols have been published by Cain (2001) and Marcot et al. (2006). Cain (2001) provided guidelines to using BNs for supporting planning and management of natural resources, with a large emphasis on facilitating stakeholder consultation. In the context of natural resources management, stakeholder consultation is seen as essential to ensuring that the management plan is followed through and implemented (Cain, 2001). Marcot et al. (2006) developed guidelines for Bayesian networks applied to wildlife and ecological assessment, with the steps to developing and updating the BNs described at three model levels: alpha, beta and gamma. The alpha-level model is the initial functioning BN, suitable only for internal use and review. The BN is considered a beta-level model after formal peer review and revision is conducted. The gamma-level or final application model, is created by further testing, calibrating, validating and updating the beta-level model (Marcot et al., 2006). This paper presents an updated set of guidelines relevant to the wide scope of possible applications of the modelling approach.

The development and evaluation process of BNs is explored following the generic guidelines for good modelling practice outlined by Jakeman et al. (2006) and demonstrated by Welsh (2008), Robson et al. (2008) and Blocken and Gualtieri (2012). It is envisaged that adhering to the guidelines will enhance the quality and value of BNs in generating and sharing knowledge on environmental systems and providing advice on their management. Good practice in BN modelling is discussed, followed by a case study BN that models the habitat suitability of an endangered invertebrate species, Astacopsis gouldi.