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New Trends in Advanced Statistical Techniques and AI: A Multidisciplinary Approach

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A Special Issue of Mathematics (ISSN 2227-7390) belonging to the section "D1: Probability and Statistics".

Deadline for manuscript submissions: closed (20 May 2026) | Viewed by 22078

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Editors

Prof. Dr. Araceli Queiruga-Dios

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Guest Editor

Department of Applied Mathematics, School of Industrial Engineering, University of Salamanca, 37008 Salamanca, Spain
Interests: cryptography; algorithms; applied mathematics; applied and computational mathematics
Special Issues, Collections and Topics in MDPI journals

Prof. Dr. Deolinda M. L. Dias Rasteiro

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Guest Editor

Department of Mathematics and Physics, Coimbra Polytechnic—ISEC, 3045-093 Coimbra, Portugal
Interests: discrete mathematics; network optimization; advanced statistical analysis; mathematical modelling; educational technology; active learning methodologies
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Dr. María Anciones-Polo

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Guest Editor Assistant

Department of Statistics, Faculty of Medicine, Universidad de Salamanca, 37007 Salamanca, Spain
Interests: descriptive and inferential statistics; multivariate techniques; statistics education

Special Issue Information

Dear Colleagues,

Statistics are an essential part of our daily lives, underpinning research, decision making, and policy development across various disciplines. It is difficult to engage in discussions on present-day concerns and recent developments without referencing data, statistical analyses, and their corresponding results. Indeed, it is common practice to use the term "statistics" to describe the analytical processes, visual representations, and outcomes derived from diverse statistical methodologies.

This Special Issue is designed for researchers, educators, and professionals seeking to apply advanced statistical techniques in their work, particularly in conjunction with artificial intelligence (AI) to enhance analytical capabilities and derive meaningful insights. The rapid advancement of AI and statistical methodologies has significantly transformed different fields, such as healthcare, finance, engineering, and social sciences. This Special Issue aims to explore emerging trends in advanced statistical techniques and AI-based methodologies, with a particular focus on their interdisciplinary applications. It will serve as a platform for scholars to present innovative approaches, theoretical developments, and real-world applications that bridge the gap between traditional statistical methods and AI.

Topics of interest include, but are not limited to, the following:

Applications of AI and statistics in different areas such as education, engineering, healthcare, business, and social sciences;
Cutting-edge AI and machine learning (ML) models with statistical foundations;
High-dimensional data analysis and dimensionality reduction techniques;
AI-based statistical inference and optimization;
Statistical learning in big data;
Multivariate statistical analysis.

Prof. Dr. Araceli Queiruga-Dios
Prof. Dr. Deolinda M. L. Dias Rasteiro
Guest Editors

Dr. María Anciones-Polo
Guest Editor Assistant

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-anonymized peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

applications of AI and statistics in different areas such as education, engineering, healthcare, business, and social sciences
cutting-edge AI and machine learning (ML) models with statistical foundations
high-dimensional data analysis and dimensionality reduction techniques
AI-based statistical inference and optimization
statistical learning in big data
multivariate statistical analysis

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Published Papers (5 papers)

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Research

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23 pages, 1417 KB

Open AccessArticle

EPECT: An Eigenvalue-Guided Positional Encoding Classification Transformer for Cross-Subject EEG-fNIRS Decoding

by Chayut Bunterngchit, Laith H. Baniata and Sangwoo Kang

Mathematics 2026, 14(13), 2416; https://doi.org/10.3390/math14132416 - 6 Jul 2026

Viewed by 552

Abstract

Decoding mental states from non-invasive neural recordings is central to brain-computer interface research. Multimodal acquisition that combines electroencephalography (EEG) and functional near-infrared spectroscopy (fNIRS) couples the high temporal resolution of EEG with the spatial specificity of fNIRS, compensating for the individual limitations of each modality. While such hybrid systems achieve strong intra-subject performance, cross-subject generalization remains constrained by inter-individual variability in neural responses. This study introduces the Eigenvalue-Guided Positional Encoding Classification Transformer (EPECT), an architecture that integrates eigenvalue-aware multi-head self-attention with sinusoidal positional encoding to capture both the spectral structure of the learned feature representations and the temporal ordering of multimodal sequences. Stacked one-dimensional convolutions extract local patterns prior to transformer encoding, and global average pooling aggregates the final representation for classification. EPECT was evaluated on two publicly available EEG-fNIRS datasets covering motor imagery (MI), n-back, discrimination/selection response (DSR), and word generation (WG) paradigms under a cross-subject protocol. The model achieved classification accuracies of 97.3%, 96.3%, 98.1%, and 97.9% on the MI, n-back, DSR, and WG tasks, respectively. Ablation studies quantified the contribution of each architectural component, and integrated gradients analysis revealed structured modality-specific attribution patterns aligned with task-relevant cortical regions. Additional experiments with synthetic cortical perturbations demonstrate the sensitivity of EPECT to subtle activity changes, indicating potential utility for tracking neurorehabilitation outcomes in future clinical applications. Full article

(This article belongs to the Special Issue New Trends in Advanced Statistical Techniques and AI: A Multidisciplinary Approach)

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20 pages, 3963 KB

Open AccessArticle

CalcTutor: Multi-Agent LLM Grading of Handwritten Mathematics with RAG-Grounded Feedback for Adaptive Learning Support

by Le Ying Tan, Buyuan Zhu, Shiyu Hu, Ankit Mishra, Darren J. Yeo and Kang Hao Cheong

Mathematics 2026, 14(7), 1094; https://doi.org/10.3390/math14071094 - 24 Mar 2026

Viewed by 2234

Abstract

Personalized instruction remains a major bottleneck in higher education, especially in large classes where timely, individualized feedback is difficult to achieve. Existing automation typically relies on rigid rule-based pipelines or computationally heavy deep learning models, making it difficult to simultaneously achieve interpretability, instructional usability, and scalable deployment. In this study, we present CalcTutor, a generative-AI-based assessment and feedback system designed to support open-ended handwritten calculus problem solving. The system organizes instructional support through three coordinated components: (1) a multi-agent large language model (LLM) mechanism that evaluates solution processes and produces diagnostic feedback, (2) a retrieval-augmented generation (RAG) pipeline that links diagnosed difficulties to aligned instructional materials, and (3) real-time learner analytics for both students and instructors, forming an integrated instructional support workflow rather than an automated answer-checking tool. In offline evaluation and a pilot classroom deployment, the multi-agent grader achieved a weighted agreement accuracy of 0.931 and an F1-score of 0.934 on 1055 handwritten solutions. Participant feedback and workflow testing indicated that CalcTutor can be stably integrated into routine classroom use and enables students to interpret and act upon the provided feedback. These results indicate that automated assessment, diagnostic feedback, and targeted review can operate coherently within a single instructional process that supports instructor-led assessment practices. Using undergraduate calculus as an application domain for open-ended handwritten mathematical assessment, the study demonstrates the operational feasibility of a closed-loop assessment–feedback–revision workflow and provides a deployable instructional infrastructure for formative instructional support in real classroom contexts. Full article

(This article belongs to the Special Issue New Trends in Advanced Statistical Techniques and AI: A Multidisciplinary Approach)

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21 pages, 1619 KB

Open AccessArticle

Multiple Correspondence Analysis and Hierarchical Clustering of Occupational Exposure to COVID-19 Among Healthcare Workers in Castilla y León, Spain

by Verónica Carrasco-Bonal, Purificación Vicente-Galindo and Araceli Queiruga-Dios

Mathematics 2025, 13(22), 3574; https://doi.org/10.3390/math13223574 - 7 Nov 2025

Cited by 1 | Viewed by 2009

Abstract

The COVID-19 pandemic represents a major challenge for healthcare systems, particularly affecting healthcare workers (HCW) due to their higher occupational risk. A retrospective observational study was conducted using data from 239,188 diagnostic tests performed on HCW from the Castilla y León (Spain) Health Service between March 2020 and March 2022. The objective was to explore associations between categorical variables, such as geographic areas, job categories, and infection status, through Multiple Correspondence Analysis and Hierarchical Clustering. The results revealed higher infection rates among HCW in regions near Madrid and in job categories with a greater care-related workload. These findings help identify risk factors and support the development of more effective occupational hazard prevention and health interventions to reduce infection risk and improve preventive measures. Full article

(This article belongs to the Special Issue New Trends in Advanced Statistical Techniques and AI: A Multidisciplinary Approach)

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20 pages, 2757 KB

Open AccessFeature PaperArticle

AI-Driven Optimization for Efficient Public Bus Operations

by Cheng-Yu Ku, Chih-Yu Liu and Ting-Yuan Wu

Mathematics 2025, 13(20), 3249; https://doi.org/10.3390/math13203249 - 10 Oct 2025

Viewed by 2499

Abstract

Public transport bus services often experience financial inefficiencies due to high operational costs and unbalanced service allocation. To address these challenges, this study presents a machine learning-based framework aimed at optimizing financial and operational performance in public bus systems. A dataset comprising 57 routes including cost, service, and ridership data was analyzed to identify key factors correlated with net revenue. These features were integrated into multiple predictive models, among which support vector regression (SVR) with a Gaussian kernel and Bayesian optimization achieved the highest accuracy (R² = 0.99), indicating excellent generalization capability. Scenario simulations using the trained SVR model evaluated the effects of service and cost adjustments. Results showed that cutting personnel costs had the most significant effect on net income, followed by administrative and financial expenses. These findings highlight the importance of data-driven strategies such as route reallocation and workforce optimization. The proposed framework offers transit agencies a robust tool for improving efficiency and ensuring financial sustainability. Full article

(This article belongs to the Special Issue New Trends in Advanced Statistical Techniques and AI: A Multidisciplinary Approach)

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Review

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23 pages, 967 KB

Open AccessReview

A Comprehensive Review on Automated Grading Systems in STEM Using AI Techniques

by Le Ying Tan, Shiyu Hu, Darren J. Yeo and Kang Hao Cheong

Mathematics 2025, 13(17), 2828; https://doi.org/10.3390/math13172828 - 2 Sep 2025

Cited by 25 | Viewed by 13573

Abstract

This paper presents a comprehensive analysis of artificial intelligence-powered automated grading systems (AI AGSs) in STEM education, systematically examining their algorithmic foundations, mathematical modeling approaches, and quantitative evaluation methodologies. AI AGSs enhance grading efficiency by providing large-scale, instant feedback and reducing educators’ workloads. Compared to traditional manual grading, these systems improve consistency and scalability, supporting a wide range of assessment types, from programming assignments to open-ended responses. This paper provides a structured taxonomy of AI techniques including logistic regression, decision trees, support vector machines, convolutional neural networks, transformers, and generative models, analyzing their mathematical formulations and performance characteristics. It further examines critical challenges, such as user trust issues, potential biases, and students’ over-reliance on automated feedback, alongside quantitative evaluation using precision, recall, F1-score, and Cohen’s Kappa metrics. The analysis includes feature engineering strategies for diverse educational data types and prompt engineering methodologies for large language models. Lastly, we highlight emerging trends, including explainable AI and multimodal assessment systems, offering educators and researchers a mathematical foundation for understanding and implementing AI AGSs into educational practices. Full article

(This article belongs to the Special Issue New Trends in Advanced Statistical Techniques and AI: A Multidisciplinary Approach)

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