Bayesian Networks: Parameter and Structure Learning with Their Real-World Applications for Decision Making

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "D1: Probability and Statistics".

Deadline for manuscript submissions: 1 April 2026 | Viewed by 2134

Special Issue Editor


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Guest Editor
Venice School of Management—Department of Management, Ca' Foscari University of Venice, 30121 Venice, Italy
Interests: additive Bayesian networks and Bayesian hierarchical models applied to epidemiological studies; choice of suitable priors; statistical data analysis; regression models; forecasting methods

Special Issue Information

Dear Colleagues,

I am pleased to warmly welcome invite you to contribute to this Special Issue of Mathematics, centering on "Bayesian Networks: Parameter and Structure Learning with Their Real-World Applications for Decision Making". The primary aim of this Special Issue is to feature advanced research and innovative advancements in the dynamic field of Bayesian Networks. It underscores the increasing significance of parameter learning and model fitting as pivotal components and presents practical applications for decision making.

Within this Special Issue, we will delve into an extensive array of subjects, including but not limited to additive and dynamic Bayesian Networks. The emphasis will be on the choice of the prior distribution for parameter learning, different score functions for model fitting, the related factorization of the joint probability and their application of real-world case studies for decision making.

My objective is to unite a varied range of interdisciplinary perspectives, cultivating enriching discussions and collaborations among researchers from both academia and industry.

I extend a warm invitation to researchers to share their latest findings and insights in this Special Issue, pushing the boundaries of our comprehension in this captivating domain. For readers, I trust that this Special Issue will prove to be an invaluable resource regarding the latest developments in Bayesian Networks and their applications.

I am enthusiastic about your contributions and engagement in this intellectual journey!

Dr. Marta Pittavino
Guest Editor

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Keywords

  • additive Bayesian networks
  • dynamic Bayesian networks
  • decision sciences
  • choice of the prior distribution
  • factorization of the joint probability
  • score functions

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Published Papers (3 papers)

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Research

19 pages, 7441 KB  
Article
All for One or One for All? A Comparative Study of Grouped Data in Mixed-Effects Additive Bayesian Networks
by Magali Champion, Matteo Delucchi and Reinhard Furrer
Mathematics 2025, 13(22), 3649; https://doi.org/10.3390/math13223649 - 14 Nov 2025
Viewed by 370
Abstract
Additive Bayesian networks (ABNs) provide a flexible framework for modeling complex multivariate dependencies among variables of different distributions, including Gaussian, Poisson, binomial, and multinomial. This versatility makes ABNs particularly attractive in clinical research, where heterogeneous data are frequently collected across distinct groups. However, [...] Read more.
Additive Bayesian networks (ABNs) provide a flexible framework for modeling complex multivariate dependencies among variables of different distributions, including Gaussian, Poisson, binomial, and multinomial. This versatility makes ABNs particularly attractive in clinical research, where heterogeneous data are frequently collected across distinct groups. However, standard applications either pool all data together, ignoring group-specific variability, or estimate separate models for each group, which may suffer from limited sample sizes. In this work, we extend ABNs to a mixed-effect framework that accounts for group structure through partial pooling, and we evaluate its performance in a large-scale simulation study. We compare three strategies—partial pooling, complete pooling, and no pooling—cross a wide range of network sizes, sparsity levels, group configurations, and sample sizes. Performance is assessed in terms of structural accuracy, parameter estimation accuracy, and predictive performance. Our results demonstrate that partial pooling consistently yields superior structural and parametric accuracy while maintaining robust predictive performance across all evaluated settings for grouped data structures. These findings highlight the potential of mixed-effect ABNs as a versatile approach for learning probabilistic graphical models from grouped data with diverse distributions in real-world applications. Full article
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17 pages, 829 KB  
Article
vulneraR: An R Package for Uncertainty Analysis in Coastal Vulnerability Studies
by Federico Mattia Stefanini, Sid Ambrosini and Felice D′Alessandro
Mathematics 2025, 13(22), 3603; https://doi.org/10.3390/math13223603 - 10 Nov 2025
Viewed by 219
Abstract
Coastal vulnerability describes the susceptibility of a system to adverse effects from natural hazards. It is typically evaluated using spatial data on geographical attributes and is often synthesized using tools such as a Coastal Vulnerability Index (CVI). However, the literature highlights that there [...] Read more.
Coastal vulnerability describes the susceptibility of a system to adverse effects from natural hazards. It is typically evaluated using spatial data on geographical attributes and is often synthesized using tools such as a Coastal Vulnerability Index (CVI). However, the literature highlights that there is no universal method for assessing vulnerability, emphasizing the importance of site-specific adaptations. A key challenge in coastal risk management is dealing with the inherent uncertainty of environmental variables and their future dynamics. Incorporating this uncertainty is essential for producing reliable assessments and informed decision-making. In this paper, we present an R package that facilitates the implementation of probabilistic graphical models explicitly incorporating epistemic uncertainty. This approach allows for vulnerability assessments even in situations where data availability is limited. The proposed methodology aims to deliver a more flexible and transparent framework for vulnerability analysis under uncertainty, providing valuable support to local policymakers, in particular during the early phases of intervention planning and technology selection for coastal mitigation strategies. Full article
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13 pages, 743 KB  
Article
Bayesian Network Applications in Decision Support Systems
by Ron S. Kenett
Mathematics 2025, 13(21), 3484; https://doi.org/10.3390/math13213484 - 1 Nov 2025
Cited by 1 | Viewed by 585
Abstract
Decision support systems are designed to provide decision makers with a view of the present and the future under alternative scenarios. A decision support system is different from a dashboard application representing current conditions and trends using a set of indicators and descriptive [...] Read more.
Decision support systems are designed to provide decision makers with a view of the present and the future under alternative scenarios. A decision support system is different from a dashboard application representing current conditions and trends using a set of indicators and descriptive statistics. This paper focuses on decision support systems implementing Bayesian networks, with three case studies presenting applications in different areas. The first case study is about the integration of mobility data available from Google with hospitalization data related to COVID-19. This data from the pandemic era provides an impact assessment of non-pharmaceutical interventions such as the closure of airports. A second case study is from a website usability assessment with data from web surfing characteristics. A third application is a conflict resolution politography application where economic, demographic, and other types of data are analyzed to create a data-driven narrative for decision makers and researchers. These three different examples show how Bayesian networks are used in different contexts to support decision support systems. The paper is about decision support systems and Bayesian networks, with examples of implementation. It begins with an introduction to general decision support systems, then case studies, and concludes with a section describing future research pathways. Full article
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