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Keywords = Bayesian decision theory

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17 pages, 498 KB  
Article
Bayesian Chance-Constrained Planning Under Limited Sampling for Sectional Warping
by Daniel López-Rodríguez, Jorge Jordán-Núñez, Bàrbara Micó-Vicent and Antonio Belda
AppliedMath 2026, 6(4), 55; https://doi.org/10.3390/appliedmath6040055 - 2 Apr 2026
Viewed by 145
Abstract
Sectional warping requires selecting a final operating length when only a small sample of residual cone masses can be measured. This paper proposes a Bayesian chance-constrained planning rule that combines a conjugate log-space model with fast posterior predictive simulation of the population minimum [...] Read more.
Sectional warping requires selecting a final operating length when only a small sample of residual cone masses can be measured. This paper proposes a Bayesian chance-constrained planning rule that combines a conjugate log-space model with fast posterior predictive simulation of the population minimum to recommend a risk-limited band length. The method provides a transparent risk parameter, efficient computation, and direct comparison with heuristic, bootstrap, distribution-free, and tail-model baselines. In an industrial-like synthetic study, the Bayesian policy reduced the mean remainder relative to a tuned sample-minimum rule while maintaining controlled shortage risk, and the results clarify why fully distribution-free guarantees are impractical under typical sampling budgets. Full article
(This article belongs to the Section Probabilistic & Statistical Mathematics)
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17 pages, 22749 KB  
Article
Identification and Application of Carbonate Reservoir Based on Bayesian Model
by Bei Wang, Xixiang Liu, Yong Hu, Lianjin Zhang, Ruiduo Zhang, Liang Wang, Xin Dai and Jie Tian
Processes 2026, 14(6), 955; https://doi.org/10.3390/pr14060955 - 17 Mar 2026
Viewed by 295
Abstract
Aiming at the challenges in accurately identifying complex pore-space types, significant scale variations, and overlapping log responses in carbonate reservoirs, this study takes the Jurassic Da’anzhai Member in the central Sichuan Basin as the research object. By integrating core observations, cast thin sections, [...] Read more.
Aiming at the challenges in accurately identifying complex pore-space types, significant scale variations, and overlapping log responses in carbonate reservoirs, this study takes the Jurassic Da’anzhai Member in the central Sichuan Basin as the research object. By integrating core observations, cast thin sections, scanning electron microscopy, and well log data, the genetic types and log response characteristics of pore spaces at different scales are systematically analyzed. Building on this, a multivariate distribution identification model for pore-space scales is established based on Bayesian discriminant theory. To enhance the model’s identification accuracy, Z-score normalization is introduced to eliminate dimensional differences. Nonlinear combined features, such as the ratio of the compensated acoustic log (AC) to the gamma ray log (GR) and the logarithmic difference between deep and shallow resistivity logs (RT and RI), are constructed to achieve a multidimensional coupling representation of reservoir physical properties; a class-balancing augmentation method based on Gaussian perturbation is adopted to mitigate decision bias caused by sample imbalance. The results show that the improved Bayesian model achieves F1 scores exceeding 0.80 for large-, small-, and micro-scale pore spaces, with an overall identification accuracy of 84.38%, significantly outperforming the conventional crossplot method’s accuracy of 59.38%. Validation through experiments and well log data demonstrates that the model’s identification results are consistent with core and thin-section observations, indicating that this method can effectively identify large-, small-, and micro-scale pore spaces in strongly heterogeneous carbonate reservoirs. This study provides a valuable approach for reservoir log interpretation and favorable reservoir prediction. Full article
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20 pages, 2758 KB  
Article
A Dynamic Risk Assessment System for Expressway Lane-Changing: Integrating Bayesian Networks and Markov Chains Under High-Density Traffic
by Quantao Yang and Peikun Li
Systems 2026, 14(3), 306; https://doi.org/10.3390/systems14030306 - 15 Mar 2026
Viewed by 276
Abstract
In high-density expressway environments, lane-changing (LC) maneuvers act as stochastic perturbations that compromise the hydrodynamic stability of traffic flow, leading to safety hazards and operational delays. While existing literature has extensively modeled crash severity in static complex environments (e.g., tunnels and mountainous terrains), [...] Read more.
In high-density expressway environments, lane-changing (LC) maneuvers act as stochastic perturbations that compromise the hydrodynamic stability of traffic flow, leading to safety hazards and operational delays. While existing literature has extensively modeled crash severity in static complex environments (e.g., tunnels and mountainous terrains), there remains a critical deficiency in quantifying the dynamic, systemic risks induced by LC maneuvers under saturation conditions. To address this gap, this study proposes a novel Systemic Risk Assessment Framework. First, a Hidden Markov Model (HMM) is employed to decode the latent state transitions of following vehicles, quantifying the systemic consequence of LC maneuvers as “operational delay” based on traffic wave theory. Second, a Bayesian Network (BN) is constructed to infer the causal probability of risk, integrating geometric proxies such as insertion angle with kinematic variables. Validated with real-world trajectory data, the model achieves high accuracy in identifying risk accumulation precursors. This research contributes to the field of transportation systems by shifting the risk paradigm from static collision prediction to dynamic system reliability analysis, offering theoretical support for Connected and Autonomous Vehicle (CAV) decision logic. Full article
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19 pages, 1182 KB  
Article
Predicting Consumer Purchase Intention for Pre-Prepared Meals Based on Random Forest and Explainable AI (SHAP): A Study in Jilin Province, China
by Xiaodan Qi, Hongyan Zhao and Xihe Yu
Foods 2026, 15(5), 896; https://doi.org/10.3390/foods15050896 - 5 Mar 2026
Viewed by 308
Abstract
The pre-prepared meal industry is a vital engine for food sector upgrading in China. This study investigates the key drivers of consumer purchasing decisions and identifies strategic pathways to support high-quality industry development. Grounded in behavioral decision theory and the stimulus–organism–response framework, we [...] Read more.
The pre-prepared meal industry is a vital engine for food sector upgrading in China. This study investigates the key drivers of consumer purchasing decisions and identifies strategic pathways to support high-quality industry development. Grounded in behavioral decision theory and the stimulus–organism–response framework, we propose two central research questions: (1) What are the dominant determinants of consumer purchase intention for pre-prepared meals? and (2) How do these determinants interact in nonlinear and asymmetric ways to shape final decisions? To address these questions, we analyzed 805 valid questionnaires collected in Jilin Province using an integrated machine learning framework. Data quality and validity were ensured through baseline balance tests, and sample imbalance was corrected using the SMOTE–Tomek algorithm. Six models, including Random Forest (RF) and XGBoost, were optimized via Gaussian process-based Bayesian optimization. The RF model achieved optimal performance on the test set, with an F1 score of 0.907, an AUC of 0.928, and a prediction accuracy of 0.876. To enhance model interpretability, Mean Decrease Impurity (MDI) was integrated with the SHAP framework. Our findings reveal that: (1) purchase decisions are predominantly willingness-driven, with behavioral tendency—especially recommendation willingness—accounting for over 72% of predictive importance; (2) rational considerations, such as convenience and channel accessibility, serve as foundational enablers; and (3) recommendation willingness exhibits a significant S-shaped nonlinear threshold, where a shift to “relatively willing” marks a critical marketing intervention window. SHAP force plot analysis further uncovers an asymmetric decision logic: high willingness can compensate for perceived product shortcomings, whereas the absence of core intention functions as a non-compensatory barrier. Theoretically, these findings synthesize machine learning outputs with classical behavioral models (e.g., the Theory of Planned Behavior and Prospect Theory) by empirically quantifying bounded rationality and nonlinear activation mechanisms. These findings suggest that enterprises should transition from traffic-centric to retention-oriented strategies by leveraging word-of-mouth and proximity-based channels. Moreover, establishing a collaborative governance system is essential to mitigate risk perception and ensure long-term industry prosperity. Full article
(This article belongs to the Section Sensory and Consumer Sciences)
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22 pages, 1345 KB  
Article
Multi-UAVs Searching and Tracking for USV Swarm: A Center-Sub-Critics Reinforcement Learning Approach
by Ye Hou, Bo Li and Xueru Miao
Drones 2026, 10(2), 123; https://doi.org/10.3390/drones10020123 - 11 Feb 2026
Viewed by 473
Abstract
This work proposes a multiple unmanned aerial vehicles (UAVs) cooperative trajectory planning scheme constructed by multi-agent reinforcement learning with hybrid critics, improving the searching and tracking efficiency and fairness when the dynamic unmanned surface vehicle (USV) swarm exceeds the number of UAVs. A [...] Read more.
This work proposes a multiple unmanned aerial vehicles (UAVs) cooperative trajectory planning scheme constructed by multi-agent reinforcement learning with hybrid critics, improving the searching and tracking efficiency and fairness when the dynamic unmanned surface vehicle (USV) swarm exceeds the number of UAVs. A confidence map of targets’ existence probability with spatio-temporal decay is first established through a local information fusion mechanism based on Bayesian update theory. It leads to a reformulation of the problem model into a communication-enhanced partially observable Markov decision process. To suppress policy variance and credibility imbalance of the multi-UAVs, a center-sub-critics deep deterministic policy gradient algorithm is then proposed, combining multiple centralized critics with decentralized critics. Meanwhile, a segmented reward function is designed to incentivize the UAV to revisit detected targets. Finally, the simulation results compared with diverse baseline algorithms demonstrate the efficacy and scalability of the proposed scheme in this paper. Full article
(This article belongs to the Section Artificial Intelligence in Drones (AID))
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24 pages, 37585 KB  
Article
Dynamic Failure Analysis of Suction Anchor Installation Operation in Marine Natural Gas Hydrate Development Using DBN-GO Method
by Kang Liu, Haojun Zhang, Haitao Xu, Fei Cao, Guoming Chen, Lei Liu and Duoya Liu
Sustainability 2026, 18(4), 1769; https://doi.org/10.3390/su18041769 - 9 Feb 2026
Viewed by 318
Abstract
Suction anchors play an important role in the exploration and development of marine natural gas hydrate (NGH). Suction anchors increase the bearing capacity and reduce tilting or sinking risk of underwater wellheads in the exploration and development process. This study proposes a dynamic [...] Read more.
Suction anchors play an important role in the exploration and development of marine natural gas hydrate (NGH). Suction anchors increase the bearing capacity and reduce tilting or sinking risk of underwater wellheads in the exploration and development process. This study proposes a dynamic failure analysis procedure for suction anchor installation based on the DBN-GO method. Firstly, a Goal-Oriented (GO) model is established by analyzing the human and equipment factor nodes in the suction anchor installation operation process. A Bayesian Network (BN) analysis model is set up by mapping the key nodes in the GO model. Then, the Cognitive Reliability and Error Analysis Method (CREAM) and the Dempster–Shafer (D-S) evidence theory are used to quantify the failure probabilities of human and equipment factor nodes in the BN model. The main risk factors are identified using Bayesian backward inference. Finally, the dynamic risk assessment of the suction anchor installation operation is conducted, considering the equipment node transition probability of the BN. Tkae the second production test of natural gas hydrates in the South China Sea as a case study. The study result shows that the failure probability of the suction anchor installation operation is 0.298%, which is at a low-risk level. Suction pump pressure control is the most critical factor leading to human errors. Among the equipment factor, the reliability of the suction pump and the ROV is the most important. Dynamic Bayesian inference shows the risk gradually increases with time. A reasonable maintenance strategy is conducive to reducing the accumulated risks caused by the time-varying degradation of equipment performance. The results could provide significant support in risk management and decision-making for the suction anchor installation operation, which will further promote the environmental sustainability, operational safety and economic feasibility of marine natural gas hydrate development. Full article
(This article belongs to the Special Issue Advanced Research on Marine and Deep Oil & Gas Development)
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19 pages, 2077 KB  
Article
Mechanisms and Simulations of Corporate Investment Decision-Making in Forestry Carbon Sequestration Under China’s Carbon Market
by Huibo Qi, Xiaowei Lu, Fei Long and Xiaoyu Zheng
Forests 2026, 17(2), 212; https://doi.org/10.3390/f17020212 - 4 Feb 2026
Viewed by 302
Abstract
Within the framework of the carbon market mechanism, corporate investments to secure forestry carbon credits play a pivotal role in mobilizing social capital for ecological construction and realizing the value of ecosystem services. This study integrates information decision theory and Bayesian network analysis [...] Read more.
Within the framework of the carbon market mechanism, corporate investments to secure forestry carbon credits play a pivotal role in mobilizing social capital for ecological construction and realizing the value of ecosystem services. This study integrates information decision theory and Bayesian network analysis to simulate corporate investment decision-making for forestry carbon sequestration within China’s carbon market. Through this approach, we explore the decision-making mechanisms behind corporate investments in forestry carbon sequestration and conduct decision simulations. The findings reveal several key insights: (1) External factors, including tax incentives, consumer preference for low-carbon products, and societal environmental awareness, exert a significant impact on the valuation of forestry carbon sequestration investments. Internally, the challenge posed by technological costs in achieving emission reductions significantly influences the evaluation of forestry carbon sequestration investments. (2) Investment value judgments are shaped by the nature of the decision-making problem, which inherently involves a synergistic relationship. (3) Corporations recognize the importance of forestry carbon sequestration in reducing the costs of emission reduction, formulating low-carbon development plans, expanding investment opportunities, and enhancing the quality of forestry carbon sequestration. (4) The collective value judgment of corporates regarding forestry carbon sequestration in terms of cost reduction for emission reduction, low-carbon development planning, investment opportunity expansion, and corporate image enhancement significantly influences their investment decisions in forestry carbon sequestration. (5) Corporate investment decisions exhibit a strong preference for market-based pricing and risk-sharing mechanisms. Consequently, enhancing the carbon information disclosure system and the carbon market trading mechanism, as well as establishing price protection and income stabilization expectations for forestry carbon sequestration, can encourage corporates to make investments in this area. This not only aids in the green, low-carbon transformation of businesses but also addresses the challenge of positive externalities associated with forestry carbon sequestration through market-oriented solutions. Full article
(This article belongs to the Special Issue Forestry Economy Sustainability and Ecosystem Governance)
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14 pages, 443 KB  
Article
A Bayesian Decision-Theoretic Optimization Model for Personalized Timing of Non-Invasive Prenatal Testing Based on Maternal BMI
by Yubu Ding, Kaixuan Ni, Xiaona Fan and Qinglun Yan
Mathematics 2026, 14(3), 437; https://doi.org/10.3390/math14030437 - 27 Jan 2026
Viewed by 470
Abstract
Non invasive prenatal testing, NIPT, is widely used for fetal aneuploidy screening, but its clinical utility depends on gestational timing and maternal characteristics. Low fetal fraction can lead to unreportable tests and increased false negative risk, while GC-content-related sequencing bias may contribute to [...] Read more.
Non invasive prenatal testing, NIPT, is widely used for fetal aneuploidy screening, but its clinical utility depends on gestational timing and maternal characteristics. Low fetal fraction can lead to unreportable tests and increased false negative risk, while GC-content-related sequencing bias may contribute to both false positive and false negative findings. We propose a Bayesian decision-theoretic optimization framework to recommend personalized NIPT timing across maternal body mass index (BMI) strata, explicitly incorporating test credibility and detection errors. We performed a retrospective analysis of de-identified NIPT records from a hospital in Guangdong Province, China, covering 1 January 2023 to 18 February 2024, including 1082 male fetus tests. Y chromosome concentration was used as a proxy for test reportability, with a 4 percent reporting threshold. Detection state proportions were empirically summarized from clinical reference information, with false positives at 10.35 percent and false negatives at 2.77 percent. A logistic regression model quantified the probability of obtaining a reportable result as a function of gestational week, maternal age, height, and weight, and the estimated probabilities were used to parameterize the Bayesian risk model. The optimized BMI-stratified schedule produced six BMI groups with recommended testing weeks ranging from 11 to 16, and the overall expected risk converged to 0.531. These results indicate a nonlinear BMI–timing relationship and suggest that a single universal testing week is suboptimal. The proposed framework provides quantitative decision support for BMI-stratified NIPT scheduling in clinical practice. Full article
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27 pages, 1619 KB  
Article
Uncertainty-Aware Multimodal Fusion and Bayesian Decision-Making for DSS
by Vesna Antoska Knights, Marija Prchkovska, Luka Krašnjak and Jasenka Gajdoš Kljusurić
AppliedMath 2026, 6(1), 16; https://doi.org/10.3390/appliedmath6010016 - 20 Jan 2026
Viewed by 811
Abstract
Uncertainty-aware decision-making increasingly relies on multimodal sensing pipelines that must fuse correlated measurements, propagate uncertainty, and trigger reliable control actions. This study develops a unified mathematical framework for multimodal data fusion and Bayesian decision-making under uncertainty. The approach integrates adaptive Covariance Intersection (aCI) [...] Read more.
Uncertainty-aware decision-making increasingly relies on multimodal sensing pipelines that must fuse correlated measurements, propagate uncertainty, and trigger reliable control actions. This study develops a unified mathematical framework for multimodal data fusion and Bayesian decision-making under uncertainty. The approach integrates adaptive Covariance Intersection (aCI) for correlation-robust sensor fusion, a Gaussian state–space backbone with Kalman filtering, heteroskedastic Bayesian regression with full posterior sampling via an affine-invariant MCMC sampler, and a Bayesian likelihood-ratio test (LRT) coupled to a risk-sensitive proportional–derivative (PD) control law. Theoretical guarantees are provided by bounding the state covariance under stability conditions, establishing convexity of the aCI weight optimization on the simplex, and deriving a Bayes-risk-optimal decision threshold for the LRT under symmetric Gaussian likelihoods. A proof-of-concept agro-environmental decision-support application is considered, where heterogeneous data streams (IoT soil sensors, meteorological stations, and drone-derived vegetation indices) are fused to generate early-warning alarms for crop stress and to adapt irrigation and fertilization inputs. The proposed pipeline reduces predictive variance and sharpens posterior credible intervals (up to 34% narrower 95% intervals and 44% lower NLL/Brier score under heteroskedastic modeling), while a Bayesian uncertainty-aware controller achieves 14.2% lower water usage and 35.5% fewer false stress alarms compared to a rule-based strategy. The framework is mathematically grounded yet domain-independent, providing a probabilistic pipeline that propagates uncertainty from raw multimodal data to operational control actions, and can be transferred beyond agriculture to robotics, signal processing, and environmental monitoring applications. Full article
(This article belongs to the Section Probabilistic & Statistical Mathematics)
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28 pages, 7162 KB  
Article
Research on Scenario Deduction of Mass Life-Threatening Incidents at Sea Based on Bayesian Network
by Qiaojie Wang, Jiacai Pan, Jun Li, Qiang Zhao, Feng Zhang, Feng Ma and Zhihui Hu
J. Mar. Sci. Eng. 2026, 14(2), 158; https://doi.org/10.3390/jmse14020158 - 11 Jan 2026
Cited by 1 | Viewed by 450
Abstract
The growth of the cruise industry and rising passenger numbers have led to an increase in cruise-related accidents, presenting challenges for mass rescue operations. It is crucial to understand the evolution of MAss Life-Threatening Incidents at Sea (MALTISs) in order to make effective [...] Read more.
The growth of the cruise industry and rising passenger numbers have led to an increase in cruise-related accidents, presenting challenges for mass rescue operations. It is crucial to understand the evolution of MAss Life-Threatening Incidents at Sea (MALTISs) in order to make effective decisions in such situations. This study, therefore, presents a scenario deduction model for MALTIS, integrating knowledge element theory, Bayesian Networks (BNs), fuzzy set theory, and improved Dempster–Shafer (DS) evidence theory. Based on knowledge element theory, this study identifies the scenario elements in typical maritime accidents. Given the large scale and complex disaster chain characteristics of MALTISs, the BN method is employed to convert the scenario elements into BN nodes, therefore constructing the MALTIS deduction model. To minimize the subjectivity associated with expert assessments, this study combines fuzzy set theory and the improved DS evidence theory to integrate the opinions of multiple experts, thereby enhancing the reliability of the model’s deduction. BN inference is then used to calculate the probabilities of various situational states, and sensitivity analysis is conducted to identify the key nodes. The Costa Concordia grounding incident serves as an empirical case study. The deduction results closely align with the actual accident evolution, and sensitivity analysis reveals five critical nodes in the event’s progression. This validates the effectiveness of the proposed scenario deduction model. These findings demonstrate that the model can effectively support emergency decision-making in MALTISs. Full article
(This article belongs to the Section Ocean Engineering)
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29 pages, 10446 KB  
Article
Safety Risk Analysis of a Construction Project on a Tropical Island
by Bo Huang, Junwu Wang, Jun Huang, Chunbao Yuan and Sijun Lv
Appl. Sci. 2026, 16(1), 271; https://doi.org/10.3390/app16010271 - 26 Dec 2025
Viewed by 422
Abstract
Construction projects on tropical islands face a high incidence of safety accidents due to complex environmental conditions, construction technologies, and varying levels of worker safety awareness. Traditional risk analysis frameworks, constrained by narrow analytical perspectives, struggle to account for the escalating uncertainties and [...] Read more.
Construction projects on tropical islands face a high incidence of safety accidents due to complex environmental conditions, construction technologies, and varying levels of worker safety awareness. Traditional risk analysis frameworks, constrained by narrow analytical perspectives, struggle to account for the escalating uncertainties and safety perturbations inherent in tropical island construction processes. To address this gap, and to improve upon both Health Safety and Environment Management System (HSE) and Bayesian Networks (BN) methods, an IHIB model for construction safety risk analysis of tropical island buildings was established. The Improve Health Safety and Environment Management System (IHSE) method constructs an indicator system from six dimensions: institutional, health, organizational, safety, environmental, and emergency response factors. The Improved Bayesian network (IBN)method, by introducing fuzzy set theory and an improved similarity aggregation method, more accurately infers the influencing factors and the most probable causal chains for construction safety on tropical islands. Taking the Sanya Haitang Bay construction project as a case study, the IHIB analysis model reveals that high temperatures and strong winds are the decisive factors influencing construction safety risks on tropical islands. The findings contribute to proactive risk prevention and mitigation, offering practical guidance for enhancing construction safety management on tropical islands. Full article
(This article belongs to the Special Issue Risk Assessment for Hazards in Infrastructures)
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26 pages, 1531 KB  
Article
Integrating Deep Learning and Complex Network Theory for Estimating Flight Delay Duration in Aviation Management
by Xiuyu Shen, Haoran Huang, Liu Liu and Jingxu Chen
Sustainability 2026, 18(1), 241; https://doi.org/10.3390/su18010241 - 25 Dec 2025
Viewed by 430
Abstract
Flight delay serves as a pivotal metric for assessing service quality in the aviation industry. Accurately estimating flight delay duration is increasingly acknowledged as a cornerstone of aviation management, with significant implications for operational efficiency, passenger satisfaction, and economic outcomes. Most existing approaches [...] Read more.
Flight delay serves as a pivotal metric for assessing service quality in the aviation industry. Accurately estimating flight delay duration is increasingly acknowledged as a cornerstone of aviation management, with significant implications for operational efficiency, passenger satisfaction, and economic outcomes. Most existing approaches often focus on single airports or airlines and overlook the complex interdependencies within the broader aviation network, limiting their applicability for system-wide planning. To address this gap, this study proposes a novel integrated framework that combines deep learning and complex network theory to predict flight arrival delay duration from a multi-airport and multi-airline perspective. Leveraging Bayesian optimization, we fine tune hyperparameters in the XGBoost algorithm to extract critical aviation network features at both node (airports) and edge (flight routes) levels. These features, which capture structural properties such as airport congestion and route criticality, are then used as inputs for a deep kernel extreme learning machine to estimate delay duration. Numerical experiment using a high-dimensional flight dataset from the U.S. Bureau of Transportation Statistics reveals that the proposed framework achieves superior accuracy, with an average delay error of 3.36 min and a 7.8% improvement over established benchmark methods. This approach fills gaps in network-level delay prediction, and the findings of this research could provide valuable insights for the aviation administration, aiding in making informed decisions on proactive measures that contribute to the sustainable development of the aviation industry. Full article
(This article belongs to the Section Sustainable Transportation)
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19 pages, 521 KB  
Article
Comparative Evidence-Based Model Choice: A Sketch of a Theory
by Prasanta S. Bandyopadhyay, Samidha Shetty and Gordon Brittan
Entropy 2026, 28(1), 13; https://doi.org/10.3390/e28010013 - 23 Dec 2025
Viewed by 510
Abstract
An extensive literature on decision theory has been developed by both subjective Bayesians and Neyman–Pearson (NP) theorists, with more recent contributions to it from evidential decision theorists. The last-mentioned, however, have often been framed from a Bayesian perspective and therefore retain a subjectivist [...] Read more.
An extensive literature on decision theory has been developed by both subjective Bayesians and Neyman–Pearson (NP) theorists, with more recent contributions to it from evidential decision theorists. The last-mentioned, however, have often been framed from a Bayesian perspective and therefore retain a subjectivist orientation. By contrast, we advance a comparative evidence-based model choice (CEMC) account of epistemic utility, which is explicitly non-subjective. On this account, competing models are assessed by the degree to which they are supported by the data and relevant background information, and evaluated comparatively in terms of their relative distances. CEMC thus provides a philosophical framework for inference that integrates the complementary epistemic goals of prediction and explanation. Our approach proceeds in two stages. First, we articulate a framework for non-subjective, non-NP-style, comparative, evidence-based model choice grounded in epistemic utility. Second, we identify statistical tools appropriate for measuring epistemic utility within this framework. We then contrast CEMC with non-comparative evidential decision-theoretic approaches, such as interval-based probability, pioneered by Henry Kyburg, which do not necessarily share the dual aims of explanation and prediction. We conclude by considering the interrelations between prediction, explanation, and model selection criteria, and by showing how these are closely connected with the central commitments of CEMC. Full article
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34 pages, 518 KB  
Review
Decision, Inference, and Information: Formal Equivalences Under Active Inference
by Patrick Sweeney, Jaime Ruiz-Serra and Michael S. Harré
Entropy 2026, 28(1), 1; https://doi.org/10.3390/e28010001 - 19 Dec 2025
Viewed by 1708
Abstract
A central challenge in artificial intelligence and cognitive science is identifying a unifying principle that governs inference, learning, and action. Active inference proposes such a principle: the minimization of variational free energy. Advocates of active inference argue that the framework subsumes classical models [...] Read more.
A central challenge in artificial intelligence and cognitive science is identifying a unifying principle that governs inference, learning, and action. Active inference proposes such a principle: the minimization of variational free energy. Advocates of active inference argue that the framework subsumes classical models of optimal behavior—including Bayesian decision theory, resource rationality, optimal control, and reinforcement learning—while also instantiating information-theoretic principles such as rate-distortion theory and maximum entropy. However, the literature outlining these conceptual links remains fragmented, limiting integration across fields. This review develops these connections systematically. We show how these major frameworks admit formal correspondences with expected free energy minimization when expressed in variational form, exposing a shared optimization principle that underlies theories of optimal decision-making and information processing. This synthesis is intended both to orient researchers from other fields who are new to active inference and to clarify foundational assumptions for those already working within the framework. Full article
27 pages, 3758 KB  
Article
Belief Entropy-Based MAGDM Algorithm Under Double Hierarchy Quantum-like Bayesian Networks and Its Application to Wastewater Reuse
by Juxiang Wang, Yaping Li, Xin Wang and Yanjun Wang
Symmetry 2025, 17(11), 2013; https://doi.org/10.3390/sym17112013 - 20 Nov 2025
Viewed by 523
Abstract
The traditional multi-attribute group decision-making (MAGDM) method easily ignores the interference effect among decision-makers (DMs), while quantum theory can effectively portray the uncertainty in the decision-making process and quantify the preference interference among DMs. The asymmetry of evaluation information in social networks can [...] Read more.
The traditional multi-attribute group decision-making (MAGDM) method easily ignores the interference effect among decision-makers (DMs), while quantum theory can effectively portray the uncertainty in the decision-making process and quantify the preference interference among DMs. The asymmetry of evaluation information in social networks can have a significant impact on decision-making. In this paper, a quantum MAGDM algorithm based on probabilistic linguistic term sets (PLTSs) and a quantum-like Bayesian network (QLBN) is proposed (PL-QLBN), utilizing quantum theory and social network concepts and introducing a novel method for calculating interference effects based on belief entropy. Firstly, a complete trust network is constructed based on the probabilistic linguistic trust transfer operator and the minimum path method. A trust aggregation method, considering interference effects, is proposed for the QLBN to determine the DM weights. Next, the attribute weights are calculated based on the entropy weight method. Then, a probabilistic linguistic MAGDM considering interference effects is proposed based on the QLBN. Finally, the feasibility and validity of the provided method are verified through Hefei City’s selection of wastewater reuse alternatives. Full article
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