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Axioms
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Applications of Bayesian Methods in Statistical Analysis
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Applications of Bayesian Methods in Statistical Analysis

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

Deadline for manuscript submissions: 30 November 2025 | Viewed by 5499

Special Issue Editors

Dr. Yanqing Zhang

E-Mail Website
Guest Editor
School of Mathematics and Statistics, Yunnan University, Kunming, China
Interests: Bayesian analysis; tensor regression; missing data
Prof. Dr. Puying Zhao

E-Mail Website
Guest Editor
School of Mathematics and Statistics, Yunnan University, Kunming, China
Interests: sampling statistics

Special Issue Information

Dear Colleagues,

The Bayesian method and its applications play an important role in many branches of statistics. This Special Issue, "Applications of Bayesian Methods in Statistical Analysis", aims to explore the cutting-edge applications of Bayesian statistics across various domains, including but not limited to machine learning, bioinformatics, environmental science, and social sciences. This Special Issue encompasses theoretical advancements, computational innovations, and practical applications of Bayesian methods.  This Special Issue aims to provide a comprehensive collection of articles that demonstrate the versatility and power of Bayesian methods in solving complex problems, enhancing decision-making processes, and contributing to the advancement of scientific research. It will seek to bridge the gap between theoretical developments in Bayesian statistics and their practical applications in various domains. Moreover, it will highlight the interdisciplinary nature of Bayesian statistics and encourage the exploration of new areas where these methods can be applied. Therefore, this Special Issue is designed to usefully supplement the existing literature on Bayesian statistics and its applications by filling gaps, highlighting new research directions, and showcasing practical implementations.

Dr. Yanqing Zhang
Prof. Dr. Puying Zhao
Guest Editors

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

  • Bayesian inference
  • variational Bayesian method
  • machine learning
  • Markov Chain Monte Carlo (MCMC) methods
  • applications in Bayesian methods
  • Bayesian prior
  • hierarchical model
  • parameter estimation
  • interval estimation
  • related topics about Bayesian method

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

Published Papers (5 papers)

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Research

33 pages, 4186 KiB  
Article
A New Bivariate Survival Model: The Marshall-Olkin Bivariate Exponentiated Lomax Distribution with Modeling Bivariate Football Scoring Data
by Sulafah M. S. Binhimd, Zakiah I. Kalantan, Abeer A. EL-Helbawy, Gannat R. AL-Dayian, Ahlam A. M. Mahmoud, Reda M. Refaey and Mervat K. Abd Elaal
Axioms 2024, 13(11), 775; https://doi.org/10.3390/axioms13110775 - 8 Nov 2024
Viewed by 1052
Abstract
This paper focuses on applying the Marshall-Olkin approach to generate a new bivariate distribution. The distribution is called the bivariate exponentiated Lomax distribution, and its marginal distribution is the exponentiated Lomax distribution. Numerous attributes are examined, including the joint reliability and hazard functions, [...] Read more.
This paper focuses on applying the Marshall-Olkin approach to generate a new bivariate distribution. The distribution is called the bivariate exponentiated Lomax distribution, and its marginal distribution is the exponentiated Lomax distribution. Numerous attributes are examined, including the joint reliability and hazard functions, the bivariate probability density function, and its marginals. The joint probability density function and joint cumulative distribution function can be stated analytically. Different contour plots of the joint probability density function and joint reliability and hazard rate functions of the bivariate exponentiated Lomax distribution are given. The unknown parameters and reliability and hazard rate functions of the bivariate exponentiated Lomax distribution are estimated using the maximum likelihood method. Also, the Bayesian technique is applied to derive the Bayes estimators and reliability and hazard rate functions of the bivariate exponentiated Lomax distribution. In addition, maximum likelihood and Bayesian two-sample prediction are considered to predict a future observation from a future sample of the bivariate exponentiated Lomax distribution. A simulation study is presented to investigate the theoretical findings derived in this paper and to evaluate the performance of the maximum likelihood and Bayes estimates and predictors. Furthermore, the real data set used in this paper comprises the scoring times from 42 American Football League matches that took place over three consecutive independent weekends in 1986. The results of utilizing the real data set approve the practicality and flexibility of the bivariate exponentiated Lomax distribution in real-world situations, and the bivariate exponentiated Lomax distribution is suitable for modeling this bivariate data set. Full article
(This article belongs to the Special Issue Applications of Bayesian Methods in Statistical Analysis)
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24 pages, 499 KiB  
Article
Constrained Bayesian Method for Testing Equi-Correlation Coefficient
by Kartlos Kachiashvili and Ashis SenGupta
Axioms 2024, 13(10), 722; https://doi.org/10.3390/axioms13100722 - 17 Oct 2024
Viewed by 617
Abstract
The problem of testing the equi-correlation coefficient of a standard symmetric multivariate normal distribution is considered. Constrained Bayesian and classical Bayes methods, using the maximum likelihood estimation and Stein’s approach, are examined. For the investigation of the obtained theoretical results and choosing the [...] Read more.
The problem of testing the equi-correlation coefficient of a standard symmetric multivariate normal distribution is considered. Constrained Bayesian and classical Bayes methods, using the maximum likelihood estimation and Stein’s approach, are examined. For the investigation of the obtained theoretical results and choosing the best among them, different practical examples are analyzed. The simulation results showed that the constrained Bayesian method (CBM) using Stein’s approach has the advantage of making decisions with higher reliability for testing hypotheses concerning the equi-correlation coefficient than the Bayes method. Also, the use of this approach with the probability distribution of linear combinations of chi-square random variables gives better results compared to that of using the integrated probability distributions in terms of providing both the necessary precisions as well as convenience of implementation in practice. Recommendations towards the use of the proposed methods for solving practical problems are given. Full article
(This article belongs to the Special Issue Applications of Bayesian Methods in Statistical Analysis)
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24 pages, 607 KiB  
Article
Bivariate Length-Biased Exponential Distribution under Progressive Type-II Censoring: Incorporating Random Removal and Applications to Industrial and Computer Science Data
by Aisha Fayomi, Ehab M. Almetwally and Maha E. Qura
Axioms 2024, 13(10), 664; https://doi.org/10.3390/axioms13100664 - 26 Sep 2024
Viewed by 837
Abstract
In this paper, we address the analysis of bivariate lifetime data from a length-biased exponential distribution observed under Type II progressive censoring with random removals, where the number of units removed at each failure time follows a binomial distribution. We derive the likelihood [...] Read more.
In this paper, we address the analysis of bivariate lifetime data from a length-biased exponential distribution observed under Type II progressive censoring with random removals, where the number of units removed at each failure time follows a binomial distribution. We derive the likelihood function for the progressive Type II censoring scheme with random removals and apply it to the bivariate length-biased exponential distribution. The parameters of the proposed model are estimated using both likelihood and Bayesian methods for point and interval estimators, including asymptotic confidence intervals and bootstrap confidence intervals. We also employ different loss functions to construct Bayesian estimators. Additionally, a simulation study is conducted to compare the performance of censoring schemes. The effectiveness of the proposed methodology is demonstrated through the analysis of two real datasets from the industrial and computer science domains, providing valuable insights for illustrative purposes. Full article
(This article belongs to the Special Issue Applications of Bayesian Methods in Statistical Analysis)
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17 pages, 1026 KiB  
Article
Research on Change Point Detection during Periods of Sharp Fluctuations in Stock Prices–Based on Bayes Method β-ARCH Models
by Fenglin Tian, Yong Wang, Qi Qin and Boping Tian
Axioms 2024, 13(9), 643; https://doi.org/10.3390/axioms13090643 - 19 Sep 2024
Viewed by 1366
Abstract
In periods of dramatic stock price volatility, the identification of change points in stock price time series is important for analyzing the structural changes in financial market data, as well as for risk prevention and control in the financial market. As their residuals [...] Read more.
In periods of dramatic stock price volatility, the identification of change points in stock price time series is important for analyzing the structural changes in financial market data, as well as for risk prevention and control in the financial market. As their residuals follow a generalized error distribution, the problem of estimating the change point parameters of the β-ARCH model is solved by combining the Kalman filtering method and the Bayes method innovatively, and we give a method for parameter estimation of the Bayes factors for the occurrences of change points, the expected values of the change point positions, and the variance of the change points. By detecting the change points of the price of eight stocks with a high number of limit up and limit down changes occurring in the observation period, the following conclusions are obtained: (1) Change point detection using the β-ARCH model based on the Bayes method is effective. (2) For different values of β, this research study finds that based on the classical ARCH model (i.e., β=1) of the change point parameter, the results are relatively optimal. (3) The accuracy of change point detection can be improved by correcting stock short-term effects by using the Kalman filtering method. Full article
(This article belongs to the Special Issue Applications of Bayesian Methods in Statistical Analysis)
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15 pages, 273 KiB  
Article
On Bivariate Distributions with Singular Part
by Carles M. Cuadras
Axioms 2024, 13(7), 433; https://doi.org/10.3390/axioms13070433 - 27 Jun 2024
Cited by 1 | Viewed by 816
Abstract
There are many families of bivariate distributions with given marginals. Most families, such as the Farlie–Gumbel–Morgenstern (FGM) and the Ali–Mikhail–Haq (AMH), are absolutely continuous, with an ordinary probability density. In contrast, there are few families with a singular part or a positive mass [...] Read more.
There are many families of bivariate distributions with given marginals. Most families, such as the Farlie–Gumbel–Morgenstern (FGM) and the Ali–Mikhail–Haq (AMH), are absolutely continuous, with an ordinary probability density. In contrast, there are few families with a singular part or a positive mass on a curve. We define a general condition useful to detect the singular part of a distribution. By continuous extension of the bivariate diagonal expansion, we define and study a wide family containing these singular distributions, obtain the probability density, and find the canonical correlations and functions. The set of canonical correlations is described by a continuous function rather than a countable sequence. An application to statistical inference is given. Full article
(This article belongs to the Special Issue Applications of Bayesian Methods in Statistical Analysis)
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