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Recent Advances in Statistical Modeling and Simulations with Applications, 2nd...
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Recent Advances in Statistical Modeling and Simulations with Applications, 2nd Edition

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: 28 February 2026 | Viewed by 1608

Special Issue Editor

Dr. Stelios Zimeras

E-Mail Website
Guest Editor
Department of Statistics and Actuarial-Financial Mathematics, University of the Aegean, 83200 Karlovassi, Greece
Interests: big data; machine learning; neural networks; image analysis; medical imaging; Bayesian statistics; applied statistics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Every application is the result of a simulation process, which involves the use of advanced statistical techniques and is one of the most important aspects of data processing and analysis. The main purpose of statistical modeling is to simulate natural complex phenomena—both for analysis and to predict future processes. Therefore, the objective of any simulation is to identify the optimal or satisfactory solution to a problem through the operation of a real system. Often, failure to meet the above objectives is due to the complexity of the problem subjected to dig data processes.

Developing, supporting, and using simulation models requires statistical models in the form of statistical distributions. The important role of statistics is evident in simulations of reality, which are more realistic when the various variables and parameters are stochastic in nature. Statistical techniques are widely used to evaluate and predict variables, especially those used for big data, examples of which include medical images or general images, such as machine learning and neural networks.

Topics of interest for this Special Issue include, but are not limited to, the following:

  • Big data;
  • Machine learning;
  • Neural networks;
  • Image analysis;
  • Medical imaging;
  • Bayesian statistics;
  • Applied statistics;
  • Medical statistics;
  • Ecology;
  • Environmental sciences.

Dr. Stelios Zimeras
Guest Editor

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 100 words) can be sent to the Editorial Office for announcement on this website.

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. Axioms is an international peer-reviewed open access monthly 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 2400 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

  • big data
  • machine learning
  • neural networks
  • image analysis
  • medical imaging
  • Bayesian statistics
  • applied statistics

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (3 papers)

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Research

24 pages, 1700 KiB  
Article
Pearson and Deviance Residual-Based Control Charts for the Inverse Gaussian Ridge Regression Process: Simulation and an Application to Air Quality Monitoring
by Muhammad Amin, Samra Rani and Sadiah M. A. Aljeddani
Axioms 2025, 14(6), 455; https://doi.org/10.3390/axioms14060455 - 9 Jun 2025
Viewed by 51
Abstract
In manufacturing and service industries, monitoring processes with correlated input variables and inverse Gaussian (IG)-distributed quality characteristics is challenging due to the limitations of maximum likelihood estimator (MLE)-based control charts. When input variables exhibit multicollinearity, traditional MLE-based inverse Gaussian regression model (IGRM) control [...] Read more.
In manufacturing and service industries, monitoring processes with correlated input variables and inverse Gaussian (IG)-distributed quality characteristics is challenging due to the limitations of maximum likelihood estimator (MLE)-based control charts. When input variables exhibit multicollinearity, traditional MLE-based inverse Gaussian regression model (IGRM) control charts become unreliable. This study introduces novel Shewhart control charts using Pearson and deviance residuals based on the inverse Gaussian ridge regression (IGRR) model to address this issue. The proposed IGRR-based charts effectively handle multicollinearity, offering a robust alternative for process monitoring. Their performance is evaluated through Monte Carlo simulations using average run length (ARL) as the main criteria, demonstrating that Pearson residual-based IGRR charts outperform deviance residual-based charts and MLE-based methods, particularly under high multicollinearity. A real-world application to a Pakistan air quality dataset confirms their superior sensitivity in detecting pollution spikes, enabling timely environmental negotiations. These findings establish Pearson residual-based IGRR control charts as a practical and reliable tool for monitoring complex processes with correlated variables. Full article
(This article belongs to the Special Issue Recent Advances in Statistical Modeling and Simulations with Applications, 2nd Edition)
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31 pages, 1059 KiB  
Article
Bayesian and Non-Bayesian for Generalized Kavya–Manoharan Exponential Distribution Based on Progressive-Stress ALT Under Generalized Progressive Hybrid Censoring Scheme
by Ehab M. Almetwally, Osama M. Khaled, Hisham M. Almongy and Haroon M. Barakat
Axioms 2025, 14(6), 410; https://doi.org/10.3390/axioms14060410 - 28 May 2025
Viewed by 205
Abstract
Accelerated life tests are vital in reliability studies, especially as new technologies create highly reliable products to meet market demand and competition. Progressive stress accelerated life test (PSALT) allows continual stress adjustments. For reliability and survival analysis in accelerated life studies, generalized progressive [...] Read more.
Accelerated life tests are vital in reliability studies, especially as new technologies create highly reliable products to meet market demand and competition. Progressive stress accelerated life test (PSALT) allows continual stress adjustments. For reliability and survival analysis in accelerated life studies, generalized progressive hybrid censoring (GPHC) is very important. The research on GPHC in PSALT models is lacking despite its growing importance. Binomial elimination and generalized progressive hybrid censoring augment PSALT in this investigation. This research examines PSALT under the Generalized Kavya–Manoharan exponential distribution based on the GPHC scheme. Using gamma prior, maximum likelihood, and Bayesian techniques, estimate model parameters. Squared error and entropy loss functions yield Bayesian estimators using informational priors in simulation and non-informative priors in application. Various censoring schemes are calculated using Monte Carlo simulation. The methodology is demonstrated using two real-world accelerated life test data sets. Full article
(This article belongs to the Special Issue Recent Advances in Statistical Modeling and Simulations with Applications, 2nd Edition)
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23 pages, 469 KiB  
Article
Variational Bayesian Estimation of Quantile Nonlinear Dynamic Latent Variable Models with Possible Nonignorable Missingness
by Mulati Tuerde and Ahmadjan Muhammadhaji
Axioms 2024, 13(12), 849; https://doi.org/10.3390/axioms13120849 - 3 Dec 2024
Viewed by 776
Abstract
Our study presents an innovative variational Bayesian parameter estimation method for the Quantile Nonlinear Dynamic Latent Variable Model (QNDLVM), particularly when dealing with missing data and nonparametric priors. This method addresses the computational inefficiencies associated with the traditional Markov chain Monte Carlo (MCMC) [...] Read more.
Our study presents an innovative variational Bayesian parameter estimation method for the Quantile Nonlinear Dynamic Latent Variable Model (QNDLVM), particularly when dealing with missing data and nonparametric priors. This method addresses the computational inefficiencies associated with the traditional Markov chain Monte Carlo (MCMC) approach, which struggles with large datasets and high-dimensional parameters due to its prolonged computation times, slow convergence, and substantial memory consumption. By harnessing the deterministic variational Bayesian framework, we convert the complex parameter estimation into a more manageable deterministic optimization problem. This is achieved by leveraging the hierarchical structure of the QNDLVM and the principle of efficiently optimizing approximate posterior distributions within the variational Bayesian framework. We further optimize the evidence lower bound using the coordinate ascent algorithm. To specify propensity scores for missing data manifestations and covariates, we adopt logistic and probit models, respectively, with conditionally conjugate mean field variational Bayes for logistic models. Additionally, we utilize Bayesian local influence to analyze the Ecological Momentary Assessment (EMA) dataset. Our results highlight the variational Bayesian approach’s notable accuracy and its ability to significantly alleviate computational demands, as demonstrated through simulation studies and practical applications. Full article
(This article belongs to the Special Issue Recent Advances in Statistical Modeling and Simulations with Applications, 2nd Edition)
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