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Keywords:

  • Bayesian Networks;
  • Elicitation;
  • GIS;
  • Integration

Abstract

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. METHODS FOR INTEGRATING GISs AND BNs
  5. CASE STUDIES
  6. DISCUSSION
  7. EDITOR'S NOTE
  8. Acknowledgements
  9. REFERENCES

Bayesian networks (BNs) are becoming increasingly common in problems with spatial aspects. The degree of spatial involvement may range from spatial mapping of BN outputs based on nodes in the BN that explicitly involve geographic features, to integration of different networks based on geographic information. In these situations, it is useful to consider how geographic information systems (GISs) could be used to enhance the conceptualization, quantification, and prediction of BNs. Here, we discuss some techniques that may be used to integrate GIS and BN models, with reference to some recent literature which illustrate these approaches. We then reflect on 2 case studies based on our own experience. The first involves the integration of GIS and a BN to assess the scientific factors associated with initiation of Lyngbya majuscula, a cyanobacterium that occurs in coastal waterways around the world. The 2nd case study involves the use of GISs as an aid for eliciting spatially informed expert opinion and expressing this information as prior distributions for a Bayesian model and as input into a BN. Elicitator, the prototype software package we developed for achieving this, is also briefly described. Whereas the 1st case study demonstrates a GIS-data driven specification of conditional probability tables for BNs with complete geographical coverage for all the data layers involved, the 2nd illustrates a situation in which we do not have complete coverage and we are forced to extrapolate based on expert judgement. Integr Environ Assess Manag 2012; 8: 473–479. © SETAC


INTRODUCTION

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. METHODS FOR INTEGRATING GISs AND BNs
  5. CASE STUDIES
  6. DISCUSSION
  7. EDITOR'S NOTE
  8. Acknowledgements
  9. REFERENCES

Bayesian networks (BNs) are now a popular tool for modeling complex systems, pervading environmental, genetic, medical, financial, educational, and social science literature (Korb and Nicholson 2010). They typically comprise a conceptual map of factors (nodes) related to an outcome of interest, and the interactions and links between these factors (Pearl 1988; Korb and Nicholson 2010). These nodes may represent discrete or continuous variables. Typically, for ease of computation and interpretation, each continuous node may be discretized, so that each node in the BN has a set of mutually exclusive states (e.g., low, medium, or high; on or off) (Uusitalo 2007). The relationship of this node to other nodes is then quantified through a conditional probability table (CPT) which describes the probability of each state conditional on the factors that affect that node (Jensen and Nielsen 2007).

This provides a highly flexible modeling structure as a basis for introducing different types of complexity. These probabilities can be derived from quite diverse sources, including observed or experimental data, statistical or simulation models, published literature or reports, and elicited expert opinion (Uusitalo 2007). Additional information can be attached to the nodes, including aspects of uncertainty, cost or benefit assessments, or other weighting factors. Extensions of the basic BN include object-oriented networks (OOBNs) that facilitate the creation and combination of subnetworks, and their dynamic counterparts (DOOBNs) that describe temporal or spatial characteristics (Korb and Nicholson 2010).

Often, the structure of a BN is developed in consultation with experts, and then each CPT is populated using empirical data where it is available. Otherwise, expert judgement is used (Marcot et al. 2001). Alternatively, a BN can be generated and quantified based on the data set itself (Pearl 1988). A completed BN represents a rich synthesis of information and can reveal many useful insights: the overall probability of the outcome of interest given the network structure and its quantification, the robustness or sensitivity of this probability to changes in network parameters and evidence, factors that have most influence on the outcome probability, and optimal decisions based on various scenarios (Uusitalo 2007). More generally, the act of constructing a BN often generates improved understanding and agreement on a complex issue, identifies issues for which additional information is required or investment should be focused, and consolidates data and data sources (Uusitalo 2007; Johnson, Fielding, et al. 2010). Moreover, it can act as an adaptive data integration and information tool, because node probabilities can be updated as more information becomes available (Johnson, Mengersen, et al. 2010).

The focus of this article is on those BNs that include geographic information. These can take a number of forms. For example, particular nodes of the BN may be spatially or geographically described, or the output of the BN itself can have a spatial interpretation. Alternatively, a BN can be used to describe uncertainty of geographic information. In other words, as geographic information systems (GISs) can inform BNs, so can BNs inform GISs due to their ability to model uncertainty.

For the underlying theory and more detailed information on BN modeling and quantification, please refer to Jensen and Nielsen (2007), Koller and Friedman (2009), and Korb and Nicholson (2010).

METHODS FOR INTEGRATING GISs AND BNs

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. METHODS FOR INTEGRATING GISs AND BNs
  5. CASE STUDIES
  6. DISCUSSION
  7. EDITOR'S NOTE
  8. Acknowledgements
  9. REFERENCES

We consider GISs in both simple and complex interactions with BNs. Initially, we look at examples of simple interactions, such as input to and/or output from a BN. Thereafter, we look at more complex interactions, such as a BN modeling the uncertainty in a GIS map, and finally GIS and BN interplay within a larger, more complex environment.

The examples have therefore been ordered in the following 4 broad ways in which GIS and BNs have been integrated in published literature: 1) GIS input to BN; 2) GIS input to, and output from BN; 3) BN and GIS complex interactions, and 4) BN and GIS within a larger framework. Figure 1 provides a schematic representation of the 4 categories, which are discussed in more detail below.

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Figure 1. Conceptual integration of Bayesian network (BN) and geographical information system (GIS): 1) GIS input to BN, 2) GIS input to, and output from BN, 3) BN and GIS complex interactions, and 4) BNs and GIS within a larger framework.

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GIS input to BN

The 1st method refers to the situation in which GIS layers are explicitly used as inputs for particular BN nodes. An example of this approach is given by Dlamini (2010) in the context of modeling the key factors that influence the occurrence of wildfires in Swaziland.

Dlamini (2010) used a BN to integrate the biotic, abiotic, and human factors for predicting the likelihood of wildfire activity in Swaziland. All 13 nodes in the BN were spatially quantified with information supplied chiefly from Moderate Resolution Imaging Spectroradiometer (MODIS), the Surveyor General's Office Digital Elevation Model (DEM), and weather stations of Swaziland Meteorological Services. These nodes included fire activity, land cover, elevation, temperature, distance to settlements, and road density. The nodes were geospatially integrated using GIS ArcView and then input to the BN.

Dlamini (2010) found the BN to have a high predictive accuracy. Furthermore, by identifying the key variables influencing the occurrence of wildfires, the BN would be a useful tool in the development of wildfire management strategies.

GIS input to, and output from BN

An extension to the approach described above is to use the capabilities of GIS to not only quantify the spatial nodes, but also to visualize the output of a spatially dependent BN. This can be done by computing the output for each location as input to the GIS environment to represent the outcomes in spatially explicit maps, which amounts to using a BN for spatial prediction. There are several relevant examples in the literature. We will briefly discuss 3 illustrations of this approach: in the context of spatial risk assessment of avalanches (Grêt-Regamey and Straub 2006), for assessing threats to koalas in urban environments (Pullar and Phan 2007), and for dunnart habitat suitability modeling (Smith et al. 2007).

Grêt-Regamey and Straub (2006) linked an application program interface (API) in Hugin Expert (2008), provided in the form of a library, to the Visual Basic (VB) programming language and then called this library using the VB platform available in the ArcGIS environment. The modeling framework thus comprised the quantification of the BN root nodes using spatially explicit data sets, the propagation of evidence for each cell in the study area through the BN, using Hugin (Hugin Expert 2008), and then the BN output for each cell, which in this case was the annual risk expressed in monetary terms. These output values were provided in the ArcGIS environment and could be immediately drawn in maps.

Pullar and Phan (2007) chose a BN as a modeling framework due to significant gaps in available data. The BN structure was constructed on the basis of expert interviews to suggest an overall model for koala occurrence given threats and habitat. Surveys of experts on CPT entries were then averaged. The outcome node for koala occurrence comprised actual presences from a koala sightings database, supplemented by “pseudo-absences,” which were generated in areas beyond koala sightings, based on expert knowledge. Spatial factors mapped to a common grid size comprised habitat quality inferred from site-scale observations on vegetation and terrain, disturbance inferred from urban density and dog presence, and koala occurrence. The outcome probability (koala presence likely, possible, or unlikely) was then determined for each square in the grid, based on this mixture of observational data where available or else imputed via Bayesian learning, and subsequently mapped.

Smith et al. (2007) developed a BN that linked GIS variables to habitat suitability of the endangered Julia Creek dunnart (Sminthopsis douglasi). The authors used expert knowledge, supported by field data, to determine a set of GIS variables which were considered to be proxies for key environmental variables, which were, in turn, believed to influence habitat variables that were believed to influence dunnart habitat suitability. The BN CPTs were used to quantify the relationship between each set of variables (GIS, environmental, habitat, outcome of habitat suitability). As in the approaches described above, the BN model was then applied in a GIS to map the outcome probabilities.

BN and GIS complex interactions

The 3rd integration approach uses BNs to combine layers of information from a GIS for each pixel or area to account for uncertainty. Stassopoulou et al. (1998) gave an early example of the use of this method for combining spatial information derived from satellite images, topographic maps, geological maps, and so forth in an environmental decision support context. The usual expert rule-based approach defines a sequence of logical rules, such as “IF precipitation is high and terrain is hilly THEN outcome is low,” “ELSE IF …,” and so forth. These authors recognized that the straightforward way of combining information from layers of the GIS does not take into account the uncertainty of the sources of information or the rules for combining the information. They chose to also investigate a BN for probabilistic reasoning, embedded within a GIS, to account for uncertainty in labeling. They applied the network to a number of sites using GIS data, and compared the method with the results obtained using GIS data with reasoning in the form of the expert rule-based approach. A total of 53 sites were included in the study, of which 39 were used for training and 14 sites for testing the system. The results of each method were compared with the expert's classification based on field data. Significantly lower accuracy was found when reasoning with an expert rule-based approach than with networks. Moreover, they found that by incorporating uncertainty in the GIS labeling, it could be shown that the correct conclusion was directly influenced by the confidence of the assignment, and it also indicated how probable alternative labels were.

A more recent example of this approach is given by Aitkenhead and Aalders (2009) in land cover prediction. Aitkenhead and Aalders (2009) describe and demonstrate the development of what they call an “objective” BN, that is, for which both the network structure and its quantification are derived from data. They illustrate the use of evolutionary algorithms in creating optimal or near-optimal objective BN network structures, and contrast the data-driven or so-called “results-oriented” BNs obtained in this manner with the “methods-oriented” BNs obtained by more standard means. In their application, spatial data for 9 variables were used. These data sets were obtained from digital maps generated from aerial photographs as part of the Land Cover for Scotland (LCS88) project, major soil classes obtained from the Soil Survey for Scotland, and additional published climatic variables. A BN using forestry and land cover was created using BN modeling software, Netica (Norsys Software 2010). Another BN using the 9 variables was created by the evolutionary method using Microsoft Visual Basic. The approaches were compared with respect to flexibility, predictive accuracy of the optimized system, and ease of use. The evolved model was less flexible in terms of data input, equivalent to the Netica model in terms of accuracy and less easy to use, because it currently has no graphical user interface. The authors concluded that the evolutionary approach is better for larger BNs or for cases in which the structure of the network is unknown.

BNs and GIS within a larger framework

The 4th and final approach is the use of a BN to model one factor and GIS to model another factor in a larger descriptive system. Wilmot et al. (2000) detailed the integration of information in this manner for the purpose of health risk assessment. The objective was to locate potential sources of Legionnaires' disease by modeling the aerosols released by cooling towers in the vicinity of an infected person's location. An application was created consisting of a BN to model the uncertainty of aerosols released from cooling towers, a GIS to create a wind dispersion model, and a GIS to model the spatial location of at risk populations in the vicinity of cooling towers. Furthermore, the spatial representation of the likely sources of contamination and vulnerable communities in their proximity, enabled targeted and timely inspections of cooling towers by environmental health officers.

Kocabas and Dragicevic (2007) applied this approach in the quite different context of land use change. These authors consider a more advanced GIS cellular automata model within a GIS that consists of BN and Influence Diagram (ID) submodels. The multiple GIS layers provide inputs to both the BN and ID submodels. Conditional probabilities for the BN submodel were obtained from historical data. The model was argued to be dynamic, considerate of spatial complexity, helpful for clear definition of transition rules, able to detect spatiotemporal drivers and generate various scenarios of land use change, and in general a useful “less black-box” tool for complex modeling and planning.

CASE STUDIES

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. METHODS FOR INTEGRATING GISs AND BNs
  5. CASE STUDIES
  6. DISCUSSION
  7. EDITOR'S NOTE
  8. Acknowledgements
  9. REFERENCES

The literature described above provides a rich context for description of 2 case studies in which we have integrated GIS with BNs in different ways. The case studies were selected in order to give complementary insight or extensions to the approaches described in the previous section.

Linking BNs via GIS

Johnson, Fielding, et al. (2010) describe the process of constructing a BN to describe the various scientific factors, and their interrelationships, associated with the initiation of harmful algal bloom of Lyngbya majuscula in Moreton Bay, Queensland, Australia. This “science” BN illustrated in Figure 2a was constructed on the basis of quite diverse information with input from a multidisciplinary science panel convened by the Healthy Waterways Partnership in Brisbane. In combination with a number of environmental variables, the combined nutrients (Fe, N, and P) were identified as a major factor in the initiation of Lyngbya. In order to convert the BN to an effective management tool, the probability of a Lyngbya bloom was assessed for the potential point and diffuse nutrient sources in the Bay catchment area (Figure 2c), via a GIS-based nutrient hazard map which is shown in Figure 2b (Johnson et al. 2009). The hazard map provided a spatial representation of a hazard rating (on a scale of 1 to 4) for each specified nutrient of concern in the science BN. This hazard rating was obtained for each unique land parcel by combining separate hazard ratings on 5 GIS layers relating to acid sulfate soils, soil type, groundwater pH, land use, and vegetation before and after clearing. The 6 new layers were superimposed on each other, and the hazard values were added to produce a merged layer for each nutrient. The values in this merged layer were then weighted by a factor relating to proximity to waterways (Pointon et al. 2008).

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Figure 2. The 3 components of the integrated Bayesian network (BN) describing the initiation of Lyngbya in Moreton Bay, Australia. (a) Lyngbya Science BN (Johnson Fielding et al. 2010), (b) Nutrient Hazard GIS map (Pointon et al. 2008), and (c) section of the Lyngbya management visual network. Extract of the Management Network for Mellum Creek Subcatchment, a visual representation of the subcatchment, shows point and diffuse sources of nutrients. The inset shows the complete Management Network (Johnson Fielding et al. 2010)

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The integrated model, depicted in Figure 2, facilitated an assessment of the relative hazard of the nutrients of concern in the catchment. The management network (Figure 2c) visually represented nutrient contributions of point sources to the catchment. Management actions and possible land use changes in the catchment resulted in corresponding changes in the GIS Hazard map. This generated new hazard ratings which were then applied to the CPT of the available nutrients node in the Scientific BN. The evidence was propagated through the BN to update the probability of a Lyngbya bloom initiating (Johnson et al. 2009). For example, Figure 3 depicts a theoretical scenario used in this study where a suggested change in land use from natural vegetation to agriculture is applied to the catchment area. This change translated into an increase in the probability of a Lyngbya bloom initiation from 25.11% to 31.34%, which is a 25% increase relative to the starting probability of a Lyngbya bloom. This integrated model therefore provides a mechanism for evaluating the impact of site-specific or general changes in management practice, such as general improvement to sewage treatment plants or local conversion of forest to horticulture.

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Figure 3. Process representation of the integrated Bayesian network describing the initiation of Lyngbya in Moreton Bay, Australia.

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Eliciting expert information

The second case study involves the use of GIS, together with a statistical package, dynamic graphs and a database, as an aid for eliciting spatially informed expert opinion to help model the relationship between GIS input variables and an outcome. For many habitat modeling studies, GIS is a common platform for both sourcing and integrating information to a common spatial scale on input variables describing habitat factors, such as slope, aspect, vegetation, and geology. In Murray et al. (2009), expert knowledge elicited about habitat preferences of the brush-tailed rock-wallaby was combined with field data that was limited due to resource constraints and poor accessibility of the steep terrain inhabited by the species. In this case, there were 27 major environmental strata defined by geology, remnant vegetation and land use, as well as 3 continuous measurements for slope, elevation and aspect.

Experts may view these habitat factors within a GIS, then, using the tool Elicitator, provide their estimate of the probability of presence at sites with known values of these habitat factors (Murray et al. 2009). GIS therefore provides a useful platform for visualization, indeed facilitating elicitation, because field ecologists are familiar with thinking about species presence and absence within a spatial context (Denham and Mengersen 2007; Low Choy et al. 2009). This process has been formalised through a prototype software package, Elicitator, which outputs this information as prior distributions on regression parameters suitable for input to a Bayesian model (James et al. 2010). This approach can be used to inform CPTs in a BN, particularly in situations where a child node has several parent nodes, or the relationship between child and parents is too complicated to elicit directly from an expert. For instance ecological applications of BNs typically involve nodes for presence given habitat or environmental factors (e.g., the outcome node for Smith et al. 2007 or the interim bottom current climate node in Hamilton et al. 2007). Consider a child node with 3 parent nodes each comprising just 4 categories. The underlying CPT comprises 43 = 64 cells. Instead of asking experts to estimate the probability of presence for each and every one of these cells, representing different combinations of values of the parent nodes, this tool helps the modeler ask experts a fewer number of questions, and then constructs an underlying model. CPTs can then be populated using predictions from the model at fixed values of the input variables.

The tool enabled elicitation of a CPT of any dimension (e.g., 729 cells for 6 variables each at 3 levels) by asking experts just 30 questions about their estimated probability of presence for 30 different habitat combinations. An example series of questions started by providing the context “Consider 100 sites with volcanic geology, open forest as remnant vegetation, and mapped as forested land use, with slope of 10%, elevation at 300 m above sea level, and a northerly aspect.” Bounds were then elicited to help avoid expert biases (see Low Choy et al. 2010 for details), starting with: “What is the most number of sites (in this region) that you would expect to be occupied by brush-tailed rock-wallabies? What is the least number?” After some intermediate questions, the final question would be “What is your best estimate of the number of sites occupied?”

Expert assessments across several sites are analyzed to find the underlying expert conceptual model on the effects of each habitat factor on probability of presence. This is achieved by applying beta regression to expert estimates elicited with uncertainty (James et al. 2010; Low Choy et al. 2010). This case study illustrates a new approach which extrapolates a feasible number of expert elicitations, via regression, to populate a conditional probability table. This new method uses modeling to populate a key CPT due to the complex relationship between the multiple parent nodes and the child node of interest. It uses GIS variables as input, but these can be combined differently using different models.

DISCUSSION

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. METHODS FOR INTEGRATING GISs AND BNs
  5. CASE STUDIES
  6. DISCUSSION
  7. EDITOR'S NOTE
  8. Acknowledgements
  9. REFERENCES

The focus of this article is on discussing a range of ways in which GIS and BNs have been integrated and introducing some extensions to these approaches. Furthermore, many aspects and extensions of both GIS and BN modeling are not covered explicitly in this article. One such aspect is the range of search methods for determining BN structure, which can include spatial factors. The methods of integration and extension are discussed with reference to a number of case studies that suitably illustrate them. The review of these case studies does not constitute a definitive review of the current literature on BN and GIS integration. The references were chosen for their relevance to each of the 4 approaches being demonstrated. More recent studies on the interplay between BN and GIS can be found in Li et al. (2010) and Stelzenmüller et al. (2010).

There are obvious advantages of using GIS to facilitate input of information into geographically dependent nodes of a BN, and to represent the outputs of such a BN through a map. Moreover, visualization is an obvious benefit that facilitates communication, both within the modeling team and with data providers, but also with stakeholders. As illustrated in the second case study, these visualization benefits also reduce cognitive biases in expert elicitation, by providing a spatial setting when asking otherwise abstract questions.

A hidden benefit of using GIS in conjunction with BNs is that this helps to manage the ecological and spatial scale of inputs and outputs. When several input variables are obtained from an integrated GIS, this confers many benefits such as consistency of scale and streamlining of the input variables, including omission of spatially spurious “slivers” resulting from overlaying unintegrated layers from fragmented landscapes. Moreover, BNs are spatially “neutral” or “implicit,” in that the variance reflected in CPTs is derived from subject, spatial or temporal variability (often a mix if expert judgement is involved). Explicit linking of GIS data generation and elicitation procedures to BNs makes the spatial variance explicit and aids in visualizing the joint probability distribution, which integrates all the factors in the BN.

EDITOR'S NOTE

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. METHODS FOR INTEGRATING GISs AND BNs
  5. CASE STUDIES
  6. DISCUSSION
  7. EDITOR'S NOTE
  8. Acknowledgements
  9. REFERENCES

This paper represents 1 of 7 review and case study articles generated as a result of a workshop entitled “Scenario and decision analysis in environmental management using Bayesian Belief Networks” (1-2 October 2009, Oslo, Norway) hosted by the Norwegian Institute for Nature Research (NINA) and the Strategic Institute Project “Nature 2020 + ” and funded by the Research Council of Norway. The main aim of the workshop was to compare Bayesian network applications to different environmental and resource management problems from around the world, identifying common modeling strategies and questions for further research.

Acknowledgements

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. METHODS FOR INTEGRATING GISs AND BNs
  5. CASE STUDIES
  6. DISCUSSION
  7. EDITOR'S NOTE
  8. Acknowledgements
  9. REFERENCES

We thank the Australian Academy of Science International Linkage Program and the International Bayesian Belief workshop, sponsored by the Norwegian Institute for Nature Research (NINA) and the Norwegian Institute for Water Research (NIVA), for their financial support. We also thank 3 anonymous reviewers for their constructive comments, which have led to substantial improvements in the manuscript.

REFERENCES

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. METHODS FOR INTEGRATING GISs AND BNs
  5. CASE STUDIES
  6. DISCUSSION
  7. EDITOR'S NOTE
  8. Acknowledgements
  9. REFERENCES
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