Modern exact algorithms for structure learning in Bayesian networks first compute an exact local score of every candidate parent set, and then find a network structure by combinatorial optimization so as to maximize the global score. This approach assumes that each local score can be computed fast, which can be problematic when the scarcity of the data calls for structured local models or when there are both continuous and discrete variables, for these cases have lacked efficient-to-compute local scores. To address this challenge, we introduce a local score that is based on a class of classification and regression trees. We show that under modest restrictions on the possible branchings in the tree structure, it is feasible to find a structure that maximizes a Bayes score in a range of moderate-size problem instances. In particular, this enables global optimization of the Bayesian network structure, including the local structure. In addition, we introduce a related model class that extends ordinary conditional probability tables to continuous variables by employing an adaptive discretization approach. The two model classes are compared empirically by learning Bayesian networks from benchmark real-world and synthetic data sets. We discuss the relative strengths of the model classes in terms of their structure learning capability, predictive performance, and running time.

Introduction

Bayesian networks (BNs) compose a multivariate distribution as a product of univariate conditional probability distributions (CPDs). The potential complexity of the local CPDs, together with the global acyclicity constraint of the BN structure, make the task of learning BNs from data challenging in many ways. Even if we assume that the available data contain neither unobserved variables nor missing entries—like we will do throughout this article—there often remain the following three concerns: (i) Statistical efficiency: the data may be scarce, rendering simple tabular parameterizations of the CPDs, such as the conditional probability tables (CPTs), statistically inefficient. (ii) Heterogeneous variables: so-called hybrid BNs contain both discrete and continuous variables, again ruling out the most convenient and standard parameterizations of CPDs. (iii) Computational efficiency: the most natural formulations of the learning problem are computationally hard. This limits both the dimensions of the data and the complexity of the CPDs in relation to what can be solved under useful quality guarantees. Each of these issues (i–iii) has been addressed in the literature, as we will describe in the next paragraphs. The present authors are, however, not aware of any prior work that would simultaneously address all the three concerns.

1. Introduction

2. Quantification of influence diagram (ID) for complex systems using matrix-based Bayesian network (MBN)

3. Proxy objective function for optimizing ID that has multiple strategically relevant decision variables

4. Multi-objective optimization using proxy objective function

5. Numerical examples

6. Conclusions

Acknowledgement

References

Abstract

For optimal design and maintenance of complex systems such as civil infrastructure systems or networks, the optimization problem should take into account the system-level performance, multiple objectives, and the uncertainties in various factors such as external hazards and system properties. Influence Diagram (ID), a graphical probabilistic model for decision-making, can facilitate modeling and inference of such complex problems. The optimal decision rule for ID is defined as the probability distributions of decision variables that minimize (or maximize) the sum of the expected values of utility variables. However, in a discrete ID, the interdependency between component events that arises from the definition of the system event, results in the exponential order of complexity in both quantifying and optimizing ID as the number of components increases. In order to address this issue, this paper employs the recently proposed matrix-based Bayesian network (MBN) to quantify ID for large-scale complex systems. To reduce the complexity of optimization to polynomial order, a proxy measure is also introduced for the expected values of utilities. The mathematical condition that makes the optimization problems employing proxy objective functions equivalent to the exact ones is derived so as to promote its applications to a wide class of problems. Moreover, the proposed proxy measure allows the analytical evaluation of a set of non-dominated solutions in which the weighted sum of multiple objective values is optimized. By using the strategies developed to compensate the errors by the approximation as well as the weighted sum formulation, the proposed methodology can identify even a larger set of non-dominated solutions than the exact objective function of weighted sum. Four numerical examples demonstrate the accuracy and efficiency of the proposed methodology.

Introduction

In various efforts to construct, operate, and maintain real-world complex systems such as civil infrastructures and their networks, it is crucial to identify optimal decision-making strategies especially when budgets are limited. When dealing with such systems, the optimization should be able to take into account not only the performance of individual components but also the system-level performance. However, mathematical formulations for the system-level optimization are not straightforward in general. In addition, for large-scale systems, multiple random variables (r.v.’s) are introduced to represent both external factors (e.g. natural or man-made hazards and deterioration-inducing environment) and internal factors (e.g. material or geometric properties of components and system), for which a high-dimensional joint probability distribution needs to be constructed. Probabilistic graphical models (PGMs) can be employed to this end, which can translate realworld causal relationships into mathematical representations [1,2].

Bayesian network (BN) is one of the most widely used PGMs, which facilitates the modeling of causal relationships between r.v.’s as a joint probability distribution by use of nodes and directed arrows (Fig. 1(a)). On the other hand, Influence Diagram (ID) is an extension of BN for the purpose of decision-making in which two additional types of variables are introduced, namely, decision and utility variables (Fig. 1(b)). As the terms imply, decision variables represent the decision alternatives while utility variables quantify the utilities of each instance of interest. The optimal decision rule for an ID is defined as the probability mass functions (PMFs) of decision variables that minimize (or maximize) the sum of the expectations of utility variables. Discrete BN and ID in which all r.v.’s are discrete, allow us to develop inference algorithms that are flexible and widely applicable.

1- Introduction

2- Modeling of a radial MMG system oriented to performance sharing

3- A BN-based reliability evaluation method for the radial MMG systems

4- The system modeling and BN parameter modeling

5- Case study

6- Conclusion

References

Abstract

The multi-microgrid (MMG) system is studied as a rudiment of the smart grid, and the radial MMG system is regarded as the comprehensive and typical one. The reliability evaluation of MMG systems are widely discussed to ensure its reliable and steady operation. The power balance between supply and demand is the core criterion for the reliability evaluation of MMG systems, which will be broken by unexpected events or inherent limits, such as the failure of equipment and the insufficient transmission capacity of distribution network (DN). In existing research, few have established a reliability model considering partial failure and imperfect repair of the equipment, and the DN transmission capacity usually is ignored. In this study, we abstract the radial MMG system as a performance-sharing system and present a Bayesian-network-based (BN-based) unified modeling method for performance and reliability to solve the deficiencies in existing research. First, the operation of radial MMG systems is analyzed to establish an abstract model to simplify the problem. Afterwards, the executive program of the BN-based reliability evaluation method is given. Further, the system modeling and the BN parameter modeling are introduced. Finally, a radial MMG system including 9 microgrids (MGs) is studied as a case, the variation of the system reliability index in grid-connected and island modes is analyzed. The results show that the method supports the reliability evaluation and analysis of radial MMG systems considering unexpected events and inherent limits.

Introduction

The concept of an MMG is developed on the EU’s “More Microgrid” program proposed in 2006 (Xu et al., 2018), which forms at the medium-voltage (MV) level, and consists of several low-voltage (LV) MGs and distributed generation (DG) units connected to adjacent MV feeders (Gil & Lopes, 2007). With the popularization of renewable energy power generation, an increasing number of neighboring MGs interconnected to the DN will form a multilevel (and high-voltage) radial MMG system in a wide area (Madureira et al., 2011), which is more typical representative of the future grid. The radial MMG systems are regarded as the rudiment of the smart grid, which have the complex architecture, energy dispatch and failure modes. Compared to traditional power systems, the reliability evaluation of MMG systems is more difficult due to its more complex structure and operating modes. MG is an independently operating unit in an MMG system, and there are many reliability evaluation methods of MG. The typical characteristics of the MG, such as uncertainties, energy storage, and multiple operating modes, are taken into account in existing methods (Bae & Kim, 2008; Bai, Miao, Zhang, & Bai, 2015; Conti, Nicolosi, & Rizzo, 2012; Conti, Rizzo, El-Saadany, Essam, & Atwa, 2014; Costa & Matos, 2009; Moslehi & Kumar, 2010); which are the foundation of MMG reliability evaluation. The MMG reliability evaluation method has the following development trend: first, it only focused on the power balance between supply and demand, for example, Nikmehr and Najafi-Ravadanegh (2015, 2016) optimized power dispatch of an MMG system constructed by three interconnected MGs and evaluated the satisfaction of loads demands. However, equipment failure and maintenance will affect system reliability seriously, which is gradually taken into account in the latter methods. In general, the equipment has some intermediate states in addition to the states of “normal” and “failure”. For example, in a DG consisting of multiple diesel units, if one unit fails while the others generate power properly, the system is in the state of derating operation, which is an intermediate state. This state, which was ignored completely in the existing reliability model of the MMG, is called partial failure.

I- Introduction

II- Preliminaries and Notation

III- Design of Scoring Function

IV- Structure Learning

V- Experimental Results

VI- CONCLUSIONS AND FUTURE WORKS

References

Abstract

Bayesian network utilizes graphical model to describe dependencies among variables in probabilistic way, it is one of the most important model for uncertainty processing in Artificial Intelligence. Incremental learning of Bayesian networks has been received more attentions in recent years, in this paper a novel method is proposed to learn Bayesian network from incremental data. In this method, a novel incremental scoring function is designed to adaptively adjust the tendency of matching new and old data in the process of incremental learning. We propose an improved adaptive incremental structure learning algorithm for Bayesian network. Theoretical analysis and experimental results both demonstrate the proposed method outperforms other state-ofthe-art methods.

INTRODUCTION

With the coming of big data era, the statistical machine learning for probabilistic graphical model has attracted extensive attention in recent years. Bayesian network is one of the most typical probabilistic graphical models which is a fundamental model for uncertainty processing in Artificial Intelligence [1]. Learning Bayesian networks from data is NP-hard problem and still one of the most challenges in machine learning [2]. The incremental learning of Bayesian networks is an area that has gained more importance in recent years, in this case, data records are received sequentially, and Bayesian network is constructed incrementally [3]. In this paper, we propose a score-based adaptive algorithm to learn Bayesian network in the presence of concept drift. We design a scoring function which makes the learning process adaptively regulate the searching strategy for each local structure of Bayesian network, then we propose an adaptive parameter learning method based on Lagrange multiplier, we also provide an improved structure learning method. The remainder of this paper is organized as follows: Section II provides the preliminaries and notations of the incremental learning of Bayesian network, and the novel scoring function is proposed in Section III. Section IV offers learning method. Section V offers the experimental results and comparisons of the proposed method. Finally, conclusions are summarized in Section VI.

The abundance of event data in current software configuration management systems makes it possible to discover software process models automatically by using actual observed behavior. However, traditional process mining algorithms cannot be applied to event logs recorded in software configuration management (SCM) systems, such as SVN, because of missing activity attributes. To address this problem, a software process activity classifier is proposed to build event-activity mapping relationships from software development event streams, revealing activity attributes and associating the activity to the original SVN log. The proposed approach extracts activity from the SVN log based on semantic features and introduces a novel technique based on a naive Bayes approach to associate event activities dynamically. The approach has been applied to two real-world software development process logs, ArgoUML and jEdit, consisting of more than 80,000 events, covering development information from 1998 to 2015. With the application of our approach to such data, activities can be extracted from event logs and a classifier can be constructed for adding activity attributes to new events. The results of the classification are evaluated in terms of precision rate, recall rate, and the F-measure. Overall, two real-world software development process logs are used to validate the method, and the experimental results show that the approach can mine software process activities from SVN log events automatically and in real-time.

Introduction

Nowadays, it is widely accepted that the quality of software is not only related to the product, but to the organization and to the production process that is carried out [1]–[3]. Software process modeling helps to create process descriptions that correspond to processes actually performed during software development or maintenance. Process models can be used to visualize tacit knowledge, roles, and information flows in the processes, identifying points for improvement and optimization [4], [5]. However, with the deepening of research on software development, problems associated with traditional subjective modeling methods have become apparent. These arise because the task of designing a software process model is complex and error prone, and because the life cycle of the model is short, individuals are not sensitive to differences between actual processes and the process model, and there are increasing requirements for process engineers, all while the software process is still evolving [6]–[8]. As software systems become more and more complex, the establishment of a sound process model is becoming more like ‘‘an art rather than a science’’ [9].

1. Introduction

2. Intuitionistic Fuzzy Reasoning

3. Dynamic Bayesian network

4. Intuitionistic Fuzzy Dynamic Bayesian Network

5. Case study

6. Conclusions

Acknowledgement

References

The period of terminating situation in air combat is time-varying and full of information with uncertainty. In order to process the fuzzy information in time series and assess the situation effectively, Intuitionistic Fuzzy Dynamic Bayesian Network (IFDBN) is built. In this model, intuitionistic fuzzy reasoning engine is embedded into dynamic Bayesian Network as a virtual node. Besides, a new method to convert the intuitionistic fuzzy reasoning output into probability which can be input into dynamic Bayesian Network as virtual evidence is proposed. On these bases, the detailed intuitionistic fuzzy reasoning algorithms are formulated and the dynamic Bayesian Network information transferring mode is analyzed. Finally, a case study for terminating situation assessment in air combat is given to prove the feasibility of the proposed model.

Introduction

At the core of nonlinear reasoning techniques is Bayesian Network (BN), which is widely used because of its information processing system and strong reasoning ability. However, terminating situation has special features and differences from situation in conventional mode. On one hand, the combat in the period of terminating situation is full of fuzzy information and data which always appear in huge volume2 . On the other hand, terminating situation is in rapid time series, which requires the method to consider the factor of time. Therefore, using the traditional knowledge representation and reasoning ability of BN cannot meet the demand of terminating situation assessment. In order to describe the situation in time-varying state, the improvement of dynamic Bayesian Network has aroused wide concerns, and many academic achievements have been done. Chai et al. Reference 3 analyze the causal relationship between different elements in Bayesian Network under continuous time slices and incorporates time series factor into BN, which maintains the robust of model.

For decomposable score-based structure learning of Bayesian networks, existing approaches first compute a collection of candidate parent sets for each variable and then optimize over this collection by choosing one parent set for each variable without creating directed cycles while maximizing the total score. We target the task of constructing the collection of candidate parent sets when the score of choice is the Bayesian Information Criterion (BIC). We provide new non-trivial results that can be used to prune the search space of candidate parent sets of each node. We analyze how these new results relate to previous ideas in the literature both theoretically and empirically. We show in experiments with UCI data sets that gains can be significant. Since the new pruning rules are easy to implement and have low computational costs, they can be promptly integrated into all state-of-the-art methods for structure learning of Bayesian networks.

Introduction

A Bayesian network [1] is a well-known probabilistic graphical model with applications in a variety of fields. It is composed of (i) an acyclic directed graph (DAG) where each node is associated to a random variable and arcs represent dependencies between the variables entailing the Markov condition: every variable is conditionally independent of its non-descendant variables given its parents; and (ii) a set of conditional probability mass functions defined for each variable given its parents in the graph. Their graphical nature makes Bayesian networks excellent models for representing the complex probabilistic relationships existing in many real problems ranging from bioinformatics to law, from image processing to economic risk analysis. Learning the structure (that is, the graph) of a Bayesian network from complete data is an NP-hard task [2]. We are interested in score-based learning, namely finding the structure which maximizes a score that depends on the data [3]. A typical first step of methods for this purpose is to build a list of suitable candidate parent sets for each one of the n variables of the domain. Later an optimization is run to find one element from each such list in a way that maximizes the total score and does not create directed cycles. This work concerns pruning ideas in order to build those lists. The problem is unlikely to admit a polynomial-time (in n) algorithm, since it is proven to be LOGSNP-hard [4]. Because of that, usually one forces a maximum in-degree (number of parents per node) k and then simply computes the score of all parent sets that contain up to k parents. A worth-mention exception is the greedy search of the K2 algorithm [5]. A high in-degree implies a large search space for the optimization and thus increases the possibility of finding better structures. On the other hand, it requires higher computational time, since there are Θ(nk) candidate parent sets for a bound of k if an exhaustive search is performed. Our contribution is to provide new rules for pruning sub-optimal parent sets when dealing with the Bayesian Information Criterion score [6], one of the most used score functions in the literature. We devise new theoretical bounds that can be used in conjunction with currently published ones [7]. The new results provide tighter bounds on the maximum number of parents of each variable in the optimal graph, as well as new pruning techniques that can be used to skip large portions of the search space without any loss of optimality. Moreover, the bounds can be efficiently computed and are easy to implement, so they can be promptly integrated into existing software for learning Bayesian networks and imply immediate computational gains. The paper is divided as follows. Section 2 presents the problem, some background and notation. Section 3 describes the existing results in the literature, and Section 4 contains the theoretical developments for the new bounds and pruning rules. Section 5 shows empirical results comparing the new results against previous ones, and finally some conclusions are given in Section 6.

In this paper we present a stochastic model for predicting the propagation of train delays based on Bayesian networks. This method can efficiently represent and compute the complex stochastic inference between random variables. Moreover, it allows updating the probability distributions and reducing the uncertainty of future train delays in real time under the assumption that more information continuously becomes available from the monitoring system. The dynamics of a train delay over time and space is presented as a stochastic process that describes the evolution of the time-dependent random variable. This approach is further extended by modelling the interdependence between trains that share the same infrastructure or have a scheduled passenger transfer. The model is applied on a set of historical traffic realisation data from the part of a busy corridor in Sweden. We present the results and analyse the accuracy of predictions as well as the evolution of probability distributions of event delays over time. The presented method is important for making better predictions for train traffic, that are not only based on static, offline collected data, but are able to positively include the dynamic characteristics of the continuously changing delays.

Introduction

Accurate prediction of train delays (deviations from timetable) is an important requirement for proactive and anticipative realtime control of railway traffic. Traffic controllers need to predict the arrival times of the trains within (or heading towards) their area in order to control the feasibility of timetable realisation. Similarly, the transport controllers on behalf of train operating companies may use the predictions to estimate the feasibility of planned passenger transfers, as well as rolling-stock and crew circulation plans. Valid estimates of arrival and departure times are therefore important for preventing or reducing delay propagation, managing connections, and providing reliable passenger information. The difficulty for predicting the train event times comes from the uncertainty and unpredictability of process times in railway traffic. The models for real-time traffic control have so far mostly focused on overcoming the great combinatorial complexity of train rescheduling (Corman et al., 2014b; Meng and Zhou, 2014; Törnquist and Persson, 2007), delay management (Dollevoet et al., 2014) and rolling-stock and crew rescheduling (Nielsen et al., 2012; Potthoff et al., 2010). The developed approaches are able to solve complex instances in real-time, however they typically assume perfect deterministic knowledge of the input traffic state and subsequent traffic evolution. In recent years, the uncertainty of train event times has been recognised as one of the major obstacles for computing feasible and implementable solutions for rescheduling problems in railway traffic (Corman and Meng, 2014; Quaglietta et al., 2013). The uncertainty of an event is usually represented by the probability distribution of its realisation. However, most of the existing approaches assume fixed probability distributions for train delays and do not consider the effect that real-time information on train positions and delays may have on (the parameters of) the corresponding distributions. In order to create realistic online tools for real-time traffic management, the dynamics of uncertainty of delays needs to be considered. When new information about train positions and delays becomes available, the uncertainty for predicting subsequent events is typically reduced. The main objective of this paper is to examine the effect that the prediction horizon and incoming information about a running train may have on the predictability of subsequent arrival and departure times of all trains. In other words, we try to give an answer to the question: how does the probability distribution of delay of an event change over time?

In pharmacovigilance, reported cases are considered suspected adverse drug reactions (ADR). Health authorities have thus adopted structured causality assessment methods, allowing the evaluation of the likelihood that a drug was the causal agent of an adverse reaction. The aim of this work was to develop and validate a new causality assessment support system used in a regional pharmacovigilance centre. A Bayesian network was developed, for which the structure was defined by experts while the parameters were learnt from 593 completely filled ADR reports evaluated by the Portuguese Northern Pharmacovigilance Centre medical expert between 2000 and 2012. Precision, recall and time to causality assessment (TTA) was evaluated, according to the WHO causality assessment guidelines, in a retrospective cohort of 466 reports (April–September 2014) and a prospective cohort of 1041 reports (January–December 2015). Additionally, a simplified assessment matrix was derived from the model, enabling its preliminary direct use by notifiers. Results show that the network was able to easily identify the higher levels of causality (recall above 80%), although struggling to assess reports with a lower level of causality. Nonetheless, the median (Q1:Q3) TTA was 4 (2:8) days using the network and 8 (5:14) days using global introspection, meaning the network allowed a faster time to assessment, which has a procedural deadline of 30 days, improving daily activities in the centre. The matrix expressed similar validity, allowing an immediate feedback to the notifiers, which may result in better future engagement of patients and health professionals in the pharmacovigilance system.

Introduction

In pharmacovigilance, most of the reported cases are considered as suspected adverse drug reactions (ADR). Health professionals and consumers are asked to report episodes they believe are related with drug intake, but in most of the cases ADR are not particular for each drug and a drug rechallenge (i.e. the suspected drug was reintroduced into the patient’s therapy, or the patient has taken the same suspected drug before) rarely occurs. To solve this difficulty, health authorities have adopted structured and harmonized causality assessment methods, in order to classify the ADR reports with one of the causality degrees proposed by the Uppsala Monitoring Centre (WHO-UMC) causality assessment system [1]. Apart from ADR identification, where innovative methods have been proposed [2], causality assessment is an essential tool in the pharmacovigilance system, as it helps the riskbenefit evaluation of commercialized medicines, and is part of the signal detection (being a signal a “reported information on a possible causal relationship between an adverse event and a drug, the relationship being unknown or incompletely documented previously” [1]) performed by health authorities. The Portuguese Pharmacovigilance System has adopted the method of Global Introspection [3], since its creation. During this process, an expert (or a group of experts) expresses judgement about possible drug causation, considering all available data in the ADR report. The decision is based on the expert knowledge and experience, and uses no standardized tools. Although this is the method most widely used [4], it has some limitations related to its reproducibility and validity [5–7]. Besides, this method is closely linked with the medical expert availability which not always allows meeting legal deadlines. Causality assessment can also be done through validated algorithms such as the Naranjo [8], Jones [9] or Karch-Lasagna [10] algorithms. Although these algorithms have better agreement rates than Global Introspection, they also have the disadvantage of not being flexible and, consequently, it is not possible to include more causal factors to be evaluated at the same time [4]. Moreover, in our experience, some real cases evaluated by more than one algorithm may give rise to different degrees of causality. Guidelines such as the ones used for causality assessment are several times hard to interpret and to apply, even by experienced practicioners. Furthermore, they often result in simple rules or association measures, making their application in decision support somewhat limited, especially in the context of guidelines that are to be computer-interpreted for decision support systems [11].

1- Introduction

2- Big data and social media mining

3- Bayesian networks: An introduction

4- Data integration methodology of social media with survey data

5- CaseStudy: the airport passengers datasets

6- Application of the big data integration methodology

7- Discussion and conclusions

References

Abstract

In recent years, the growing availability of huge amounts of information, generated in every sector at high speed and in a wide variety of forms and formats, is unprecedented. The ability to harness big data is an opportunity to obtain more accurate analyses and to improve decision-making in industry, government and many other organizations. However, handling big data may be challenging and proper data integration is a key dimension in achieving high information quality. In this paper, we propose a novel approach to data integration that calibrates online generated big data with interview based customer survey data. A common issue of customer surveys is that responses are often overly positive, making it difficult to identify areas of weaknesses in organizations. On the other hand, online reviews are often overly negative, hampering an accurate evaluation of areas of excellence. The proposed methodology calibrates the levels of unbalanced responses in different data sources via resampling and performs data integration using Bayesian Networks to propagate the new re-balanced information. In this paper we show, with a case study example, how the novel data integration approach allows businesses and organizations to get a bias corrected appraisal of the level of satisfaction of their customers. The application is based on the integration of online data of review blogs and customer satisfaction surveys from the San Francisco airport. We illustrate how this integration enhances the information quality of the data analytic work in four of InfoQ dimensions, namely, Data Structure, Data Integration, Temporal Relevance and Chronology of Data and Goal.

Introduction

The growing availability of abundant masses of data in every sector, including business, government and health care, is posing new analytic and statistical challenges. This data may come from different sources such as posts in social media sites, digital pictures and videos, cell phone GPS, purchase transaction records and signal sensors used to gather climate information, to name a few. This is called Big Data and is characterized by high volume, variety and gathering velocity. Large quantities of information, mostly unstructured, are generated by social media, every minute. On the web, billions of individuals around the globe simultaneously produce, share and consume content generated by the user themselves. Through social media people express their opinions and sentiments towards specific topics, products and services, and the analysis of this information (called social media mining or sentiment analysis) may be key to organizations and businesses to monitor the satisfaction of their customers or to plan business initiatives or design new products and services. In recent years, advances in the literature of big data analysis have been significant. Amongst recent contributions to sentiment analysis, Stander, Dalla Valle, and Cortina Borja (2016a) and Stander, Dalla Valle, Eales, Baldino, and Cortina Borja (2016b), extracted Facebook data to analyze sentiment scores and voting patterns about the June 2016 EU referendum in the UK. Zhang, Fuehres, and Gloor (2011) used sentiment analysis techniques to predict stock market indicators using Twitter data. Asur and Huberman (2010) predicted box-office movie revenues, performing an analysis of sentiments from comments posted on social media.

As human development and urbanization expand across the landscape, increasing numbers of streams are threatened with impairment from disturbance and stresses associated with land use changes. In this investigation, a Bayesian Network (BN) with an expert-informed model structure was developed to predict stream vulnerability to urbanization across a range of biophysical conditions. Primary factors affecting vulnerability were stream buffers, colonization connectivity, agriculture, watershed area, and sand/gravel aquifers. On a scale from 0 to 100 (lowest to highest probability), BN model vulnerability scores ranged from a minimum of 20 to a maximum of 87.5 across the 23,554 stream catchments in our statewide study area. Catchment vulnerability scores were linked with predictions of land development suitability from a second BN model in order to map the locations of streams at risk of impairment from projected future urbanization in two large watersheds in Maine, USA. Our BN synthesis identified 5% of the streams that are at risk based on two assessment criteria: (1) their catchments have projected future impervious cover (IC) levels greater than 6% and (2) the stream catchments have predicted vulnerability scores in the highest quartile of the BN model probability distribution. These at-risk streams represent priority targets for proactive monitoring, management, and conservation efforts to avoid future degradation and expensive restoration costs. This study laid the conceptual groundwork for using BN spatial models to identify streams that are not only vulnerable to urbanization, but are also located in catchments classified with a high probability of development suitability and future urbanization.

Introduction

An undeveloped forested watershed can tolerate only a limited amount of urbanization and human development activity before symptoms of stress and degradation begin to appear in downstream aquatic ecosystems. However, the response of streams to anthropogenic land use changes can vary as a function of watershed biophysical conditions that influence resistance or resilience properties of the coupled catchment and stream system (Alberti and Marzluff 2004; McCluney et al., 2014; Utz et al., 2016). In general, one would expect the streams at highest risk of impairment from development to be those with watershed characteristics that confer low resistance or high vulnerability to changing land use conditions or urbanization. Here, resistance refers to the ability of an ecosystem to resist change and to maintain structure and function despite increased exposure to stressors (Pearsons and Li 1992; Vieira, Clements, Guevara, & Jacobs, 2004). Conversely, vulnerability describes the sensitivity of a system to a stress and the degree to which the system will experience harm due to exposure to a stressor or perturbation (Besaw et al., 2009; Turner et al., 2003). Resilience describes the ability of a system to recover from disturbance or stress. Under authority of the federal Clean Water Act (CWA) and state water quality standards, the U.S. Environmental Protection Agency (US EPA) and state regulatory agencies endeavor to sustain healthy aquatic resources and to restore the chemical, physical, and biological integrity of waters that have been impaired by urbanization, non-point pollution, or other stressors. In Maine, the Department of Environmental Protection (Maine DEP) monitors the health of streams and determines if they attain water quality standards and criteria associated with four state-defined statutory classes (Courtemanch, Davies, & Laverty, 1989; Danielson et al., 2012; Davies, Drummond, Courtemanch, Tsomides, & Danielson, 2016). If a stream does not attain water quality standards or criteria associated with its designated class, then it may be listed as impaired in the CWA 303(d) inventory of impaired waters (Maine DEP, 2012a). Unfortunately, the economic cost of restoring impaired streams can be substantial − as one example, ongoing restoration of the impaired Long Creek ecosystem in Portland, Maine is projected to cost $14 million (FB Environmental Associates 2009).