Rosa F. Ropero

Groundwater quality assessment using data clustering based on hybrid Bayesian networks

Bayesian networks (BNs) have become a standard in the field of Artificial Intelligence as a means of dealing with uncertainty and risk modelling. In recent years, there has been particular interest in the simultaneous use of continuous and discrete domains, obviating the need for discretization, using so-called hybrid BNs. In these hybrid environments, Mixtures of Truncated Exponentials (MTEs) provide a suitable solution for working without any restriction. The objective of this study is the assessment of groundwater quality through the design and application of a probabilistic clustering, based on hybrid Bayesian networks with MTEs. Firstly, the results obtained allows the differentiation of three groups of sampling points, indicating three different classes of groundwater quality. Secondly, the probability that a sampling point belongs to each cluster allows the uncertainty in the clusters to be assessed, as well as the risks associated in terms of water quality management. The methodology developed could be applied to other fields in environmental sciences.

Regression using hybrid Bayesian networks: Modelling landscape–socioeconomy relationships

Abstract Modelling environmental systems becomes a challenge when dealing directly with continuous and discrete data simultaneously. The aim in regression is to give a prediction of a response variable given the value of some feature variables. Multiple linear regression models, commonly used in environmental science, have a number of limitations: (1) all feature variables must be instantiated to obtain a prediction, and (2) the inclusion of categorical variables usually yields more complicated models. Hybrid Bayesian networks are an appropriate approach to solve regression problems without such limitations, and they also provide additional advantages. This methodology is applied to modelling landscape–socioeconomy relationships for different types of data (continuous, discrete or hybrid). Three models relating socioeconomy and landscape are proposed, and two scenarios of socioeconomic change are introduced in each one to obtain a prediction. This proposal can be easily applied to other areas in environmental modelling.

Modelling uncertainty in social-natural interactions

Socio-ecological systems can be represented as a complex network of causal interactions. Modelling such systems requires methodologies that are able to take uncertainty into account. Due to their probabilistic nature, Bayesian networks are a powerful tool for representing complex systems where interactions between variables are subject to uncertainty. In this paper, we study the interactions between social and natural subsystems (land use and water flow components) using hybrid Bayesian networks based on the Mixture of Truncated Exponentials model. This study aims to provide a new methodology to model systemic change in a socio-ecological context. Two endogenous changes - agricultural intensification and the maintenance of traditional cropland - are proposed. Intensification of the agricultural practices leads to a rise in the rate of immigration to the area, as well as to greater water losses through evaporation. By contrast, maintenance of traditional cropland hardly changes the social structure, while increasing evapotranspiration rates and improving the control over runoff water. These results indicate that hybrid Bayesian networks are an excellent tool for modelling social-natural interactions. Uncertainty has to be taken into account in Socio-ecological system modelling.Socio-ecological system is modelled by hybrid BNs.Extreme-values probabilities are provided as a new tool to assess systemic change.Hybrid BNs can represent complex systems under conditions of uncertainty.

Continuous Bayesian networks for the estimation of species richness

We propose a new methodology based on continuous Bayesian networks for assessing species richness. Specifically, we applied a restricted structure Bayesian network, known as tree augmented naive Bayes (TAN), regarding a set of environmental continuous predictors. First, we analysed the relationships between the response variable (called the terrestrial vertebrate species richness) and a set of environmental predictors. Second, the learnt model was used to estimate the species richness in Andalusia (Spain) and the results were depicted on a map. In addition to this, the TAN model was compared to three other methods commonly used for regression in terms of their root mean squared error. The experimental results showed that the TAN model not only was competitive from the point of view of accuracy but also managed to deal with the species richness–environment relationship, which is complex from the ecological point of view. The results highlight that landscape heterogeneity, topographical and social variables had a direct relationship with species richness while climatic variables showed more complicated relationships with the response.

Using a New Tool to Visualize Environmental Data for Bayesian Network Modelling

This paper presents the software Omnigram Explorer, a visualization tool developed for interactive exploration of relations between variables in a complex system. Its objective is to help users gain an initial knowledge of their data and the relationships between variables. As an example, we apply it to the water reservoir data for Andalusia, Spain. Two Bayesian networks are learned using causal discovery, both with and without the information gleaned from this exploration process, and compared in terms of the Logarithmic loss and causal structure. Even though they show the same predictive accuracy, the initial exploration with Omnigram Explorer supported the use of prior information to achieve a more informative causal structure.

Redes bayesianas: una herramienta probabilística en los modelos de distribución de especies

Ropero, R.F., Aguilera, P.A., Fernandez, A., Rumi, R. 2014. Bayesian networks: a probabilistic tool for species distribution models. Ecosistemas 23(1):54-60. Doi.: 10.7818/ECOS.2014.23-1.08 Bayesian networks are multivariate probabilistic models able to deal with uncertainty. They have been hardly applied in species distribution models, and have mainly focused on discrete variables without taking advantage of their potentiality. In this paper, Bayesian networks are presented as a tool to solve different problems in species distribution models such as classification, characterization and regression. Their ability to deal with discrete and continuous data simultaneously, the variety of problems that can be solved, and the flexibility in the model structure, make them an appropriate tool in species distribution models and Macroecology.

Learning and inference methodologies for hybrid dynamic Bayesian networks: a case study for a water reservoir system in Andalusia, Spain

AbstractTime series analysis requires powerful and robust tools; at the same time the tools must be intuitive for users. Bayesian networks have been widely applied in static problem modelling, but, in some knowledge areas, Dynamic Bayesian networks are hardly known. Such is the case in the environmental sciences, where the application of static Bayesian networks in water resources research is notable, while fewer than five papers have been found in the literature for the dynamic extension. The aim of this paper is to show how Dynamic Bayesian networks can be applied in environmental sciences by means of a case study in water reservoir system management. Two approaches are applied and compared for model learning, and another two for inference. Despite slight differences in terms of model complexity and computational time, both approaches for model learning provide similar results. In the case of inference methods, again, there were slight differences in computational time, but the selection of one approach over the other is based on the prediction needed: If the aim is just to go one step forward, both Window and Roll out approaches are similar, when we need to go more than one step forward; the most appropriate will be Roll out.

Dynamic OOBNs applied to water management in dams

Bayesian networks (BNs) are a mature technology now widely used for modelling complex domains requiring decision making under certainty, such as environmental modelling. Object-oriented BNs (OOBNs) have been proposed to help manage the modelling complexity through structured decomposition, abstraction and encapsulation. OOBNs have been applied previously to water catchment management, but without explicit spatial modelling. In this paper, we present a novel schema that captures the spatial relationships between connected dams, as well as the temporal dynamics of the catchment over successive seasons. This is validated on an abstracted 5 dam example, with results presented for two representative cases.

Estimation of Species Richness Using Bayesian Networks

We propose a new methodology based on continuous Bayesian networks for assessing species richness. Specifically, we applied a restricted structure Bayesian network, known as tree augmented naive Bayes, regarding a set of environmental continuous predictors. Firstly, we analyzed the relationships between the response variable called the terrestrial vertebrate species richness and a set of environmental predictors. Secondly, the learnt model was used to estimate the species richness in Andalusia Spain and the results were depicted on a map. The model managed to deal with the species richness - environment relationship, which is complex from the ecological point of view. The results highlight that landscape heterogeneity, topographical and social variables had a direct relationship with species richness while climatic variables showed more complicated relationships with the response.

Soft Clustering Based on Hybrid Bayesian Networks in Socioecological Cartography

The interactions between nature and society need new tools capable of dealing with the inherent complexity and heterogeneity of the territory. Traditional clustering methodologies have been applied to solve this problem. Although these return adequate results, soft clustering based on hybrid Bayesian networks, returns more detailed results. Moreover their probabilistic nature delivers additional advantages. The main contribution of this paper, is to apply this tool to obtain the socioecological cartography of a Mediterranean watershed. The results are compared to a traditional agglomerative clustering.