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Uncertainty Quantification Techniques in Statistics, Machine Learning and FinTech: 2nd...
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Uncertainty Quantification Techniques in Statistics, Machine Learning and FinTech: 2nd Edition

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

Deadline for manuscript submissions: 30 September 2026 | Viewed by 3139

Special Issue Editor

Prof. Dr. Jong-Min Kim

E-Mail Website
Guest Editor
Statistics Discipline, Division of Science and Mathematics, University of Minnesota at Morris, Morris, MN 56267, USA
Interests: probability and stochastic processes; functional data analysis; financial time series
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Uncertainty Quantification (UQ) is a mainstream research topic in applied mathematics and statistics. To identify UQ problems, diverse modern techniques for large and complex data analysis have been developed in the fields of applied mathematics, computer science, and statistics.

To promote these modern data analysis methods in biology, economics, environmental studies, finance, mathematics, operational research, science, and statistics, a Special Issue of Mathematics (ISSN 2227-7390), the Science Citation Index Expanded (SCIE) journal, will be devoted to “Uncertainty Quantification Techniques in Statistics, Machine Learning and FinTech: 2nd Edition”.

Prof. Dr. Jong-Min Kim
Guest Editor

Manuscript Submission Information

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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-blind 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

  • artificial intelligence
  • bayesian statistics
  • bioinformatics
  • biostatics
  • blockchain
  • big data
  • change-point detection
  • computer model
  • cryptocurrencies
  • cyber security
  • data analytics
  • data mining
  • deep learning
  • electronic data interchange (EDI)
  • e-Learning
  • expert systems
  • financial time series
  • functional data analysis
  • fuzzy logic
  • internet security
  • internet of things
  • machine learning
  • mobile applications
  • mobile learning
  • neural networks
  • quality control
  • security
  • sentiment analysis
  • spatial statistics
  • support vector machines
  • web services and performance

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Related Special Issue

Published Papers (3 papers)

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Research

26 pages, 3574 KB  
Article
Uncertainty Quantification of Complex Weather Dynamics Using a Novel Functional Autoregressive Model
by Ismail Shah, Muhammad Uzair, Sajid Ali and Sadiah M. Aljeddani
Mathematics 2026, 14(5), 835; https://doi.org/10.3390/math14050835 - 1 Mar 2026
Viewed by 337
Abstract
Functional time series (FTS) modeling has emerged as a powerful framework for capturing complex temporal dependencies using the functional autoregressive models FAR(p, m) and FARX(p, m, τ). These functional models characterize the evolution of functional observations [...] Read more.
Functional time series (FTS) modeling has emerged as a powerful framework for capturing complex temporal dependencies using the functional autoregressive models FAR(p, m) and FARX(p, m, τ). These functional models characterize the evolution of functional observations by incorporating ‘p’ lagged functional responses, ‘m’ truncated dimensions from functional principal component analysis (FPCA), and τ number of scalar covariates with optimal parameter selection guided by the minimization of the functional final prediction error fFPE(p, m). The aim of this study is to propose a computationally efficient FAR model that can integrate a number of functional covariates to achieve a high predictive accuracy in terms of standard out-of-sample accuracy measures. To this end, an integrated functional autoregressive model FARX(p,m,g̲,τ) is developed, where X denotes the exogenous information, this being a lagged or modeled functional profile within the FAR(p, m) framework, and ‘g̲’ represents a vector of optimal dimensions for a number of functional covariates. The theoretical contributions are twofold: first, deriving the distribution of the modified functional final prediction error, denoted as fFPEX(p,m,g̲,τ); second, using this derivation to establish formal criteria for optimal model selection. To empirically investigate the predictive performance of the proposed model, hourly temperature data from the NASA POWER project are considered, and day-ahead out-of-sample forecasts over a full annual cycle are computed. The forecasting performance of the proposed model is assessed against state-of-the-art models using different error summary metrics. The results show that functional models consistently outperform traditional time series and neural network-based approaches, with FARX(p,m,g̲,τ) achieving superior predictive accuracy compared to FAR(p, m) and FARX(p, m, τ), thereby underscoring the efficacy of incorporating functional exogenous information in FTS modeling. Full article
(This article belongs to the Special Issue Uncertainty Quantification Techniques in Statistics, Machine Learning and FinTech: 2nd Edition)
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16 pages, 324 KB  
Article
Doubly Robust Estimation of the Finite Population Distribution Function Using Nonprobability Samples
by Soonpil Kwon, Dongmin Jang and Kyu-Seong Kim
Mathematics 2025, 13(19), 3227; https://doi.org/10.3390/math13193227 - 8 Oct 2025
Viewed by 898
Abstract
The growing use of nonprobability samples in survey statistics has motivated research on methodological adjustments that address the selection bias inherent in such samples. Most studies, however, have concentrated on the estimation of the population mean. In this paper, we extend our focus [...] Read more.
The growing use of nonprobability samples in survey statistics has motivated research on methodological adjustments that address the selection bias inherent in such samples. Most studies, however, have concentrated on the estimation of the population mean. In this paper, we extend our focus to the finite population distribution function and quantiles, which are fundamental to distributional analysis and inequality measurement. Within a data integration framework that combines probability and nonprobability samples, we propose two estimators, a regression estimator and a doubly robust estimator, and discuss their asymptotic properties. Furthermore, we derive quantile estimators and construct Woodruff confidence intervals using a bootstrap method. Simulation results based on both a synthetic population and the 2023 Korean Survey of Household Finances and Living Conditions demonstrate that the proposed estimators perform stably across scenarios, supporting their applicability to the production of policy-relevant indicators. Full article
(This article belongs to the Special Issue Uncertainty Quantification Techniques in Statistics, Machine Learning and FinTech: 2nd Edition)
18 pages, 803 KB  
Article
Gaussian Process with Vine Copula-Based Context Modeling for Contextual Multi-Armed Bandits
by Jong-Min Kim
Mathematics 2025, 13(13), 2058; https://doi.org/10.3390/math13132058 - 21 Jun 2025
Cited by 1 | Viewed by 1415
Abstract
We propose a novel contextual multi-armed bandit (CMAB) framework that integrates copula-based context generation with Gaussian Process (GP) regression for reward modeling, addressing complex dependency structures and uncertainty in sequential decision-making. Context vectors are generated using Gaussian and vine copulas to capture nonlinear [...] Read more.
We propose a novel contextual multi-armed bandit (CMAB) framework that integrates copula-based context generation with Gaussian Process (GP) regression for reward modeling, addressing complex dependency structures and uncertainty in sequential decision-making. Context vectors are generated using Gaussian and vine copulas to capture nonlinear dependencies, while arm-specific reward functions are modeled via GP regression with Beta-distributed targets. We evaluate three widely used bandit policies—Thompson Sampling (TS), ε-Greedy, and Upper Confidence Bound (UCB)—on simulated environments informed by real-world datasets, including Boston Housing and Wine Quality. The Boston Housing dataset exemplifies heterogeneous decision boundaries relevant to housing-related marketing, while the Wine Quality dataset introduces sensory feature-based arm differentiation. Our empirical results indicate that the ε-Greedy policy consistently achieves the highest cumulative reward and lowest regret across multiple runs, outperforming both GP-based TS and UCB in high-dimensional, copula-structured contexts. These findings suggest that combining copula theory with GP modeling provides a robust and flexible foundation for data-driven sequential experimentation in domains characterized by complex contextual dependencies. Full article
(This article belongs to the Special Issue Uncertainty Quantification Techniques in Statistics, Machine Learning and FinTech: 2nd Edition)
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