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Application of the Bayesian Method in Statistical Modeling, 2nd Edition
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Application of the Bayesian Method in Statistical Modeling, 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 1570

Special Issue Editor

Dr. Diana Mindrila

E-Mail Website
Guest Editor
Department of Educational Leadership, Research, and School Improvement, University of West Georgia, Carrollton, GA 30118, USA
Interests: multivariate statistics; latent variable modeling; estimation methods; latent class analysis; latent profile analysis; factor analysis; structural equation modeling; cluster analysis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Bayesian statistics is a theory in the field of statistics based on the Bayesian interpretation of probability, where probability expresses a degree of belief in an event. Bayesian statistical methods use Bayes’ theorem to compute and update probabilities after obtaining new data. Named after Thomas Bayes, Bayes’ theorem (1973) describes the conditional probability of an event based on data as well as prior information or beliefs about the event or conditions related to the event. This approach differs from other interpretations of probability, such as the frequentist interpretation, which views probability as the limit of the relative frequency of an event after many trials. During much of the 20th century, many statisticians viewed Bayesian methods unfavourably due primarily to practical considerations. Bayesian methods required much computation to complete, and the most widely used methods during the century relied on the frequentist interpretation. However, with the advent of powerful computers and new algorithms, such as Markov chain Monte Carlo, Bayesian methods have seen increasing use within statistics in the 21st century.

This Special Issue aims to raise awareness of the availability and applicability of Bayesian analyses. It includes a collection of theoretical and applied studies using Bayesian statistics and provides information on statistical software that allows the use of Bayesian estimation methods.

Dr. Diana Mindrila
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 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-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

  • Bayesian analysis
  • Bayesian estimation
  • statistics
  • probability

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Related Special Issue

Published Papers (2 papers)

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Research

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 529
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
(This article belongs to the Special Issue Application of the Bayesian Method in Statistical Modeling, 2nd Edition)
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18 pages, 816 KB  
Article
The Convergent Indian Buffet Process
by Ilsang Ohn
Mathematics 2025, 13(23), 3881; https://doi.org/10.3390/math13233881 - 3 Dec 2025
Viewed by 461
Abstract
We propose a new Bayesian nonparametric prior for latent feature models, called the Convergent Indian Buffet Process (CIBP). We show that under the CIBP, the number of latent features is distributed as a Poisson distribution, with the mean monotonically increasing but converging to [...] Read more.
We propose a new Bayesian nonparametric prior for latent feature models, called the Convergent Indian Buffet Process (CIBP). We show that under the CIBP, the number of latent features is distributed as a Poisson distribution, with the mean monotonically increasing but converging to a certain value as the number of objects goes to infinity. That is, the expected number of features is bounded above even when the number of objects goes to infinity, unlike the standard Indian Buffet Process, under which the expected number of features increases with the number of objects. We provide two alternative representations of the CIBP based on a hierarchical distribution and a completely random measure, which are of independent interest. The proposed CIBP is assessed on a high-dimensional sparse factor model. Full article
(This article belongs to the Special Issue Application of the Bayesian Method in Statistical Modeling, 2nd Edition)
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