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Mathematics
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Research Progress and Application of Bayesian Statistics
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Research Progress and Application of Bayesian Statistics

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

Deadline for manuscript submissions: closed (30 May 2024) | Viewed by 3437

Special Issue Editor

Dr. Chao Wang

E-Mail Website
Guest Editor
Faculty of Health, Social Care and Education, Kingston University, Surrey KT2 7LB, UK
Interests: Bayesian statistics; predictive modeling; causal inference; medical statistics

Special Issue Information

Dear Colleagues,

The Bayesian method provides a natural and coherent framework for statistical inference and prediction. Its usage was, however, limited in the past due to computational complexity. During the past few decades, there has been an increasing interest in Bayesian statistical modeling thanks to advances in computing capabilities and estimation methods such as Markov chain Monte Carlo (MCMC) and Integrated Nested Laplace Approximation (INLA). 

This Special Issue aims to provide a collection of papers highlighting recent advances in theories and applications using Bayesian statistics. Bayesian methods have been widely used across different disciplines, and as such, this Special Issue welcomes contributions from different fields, such as medicine, epidemiology, engineering, economics, and business. Submissions can be in the form of original research or reviews. Examples of areas of interest include but are not limited to missing data handling; variable/feature selection; time-series analysis; comparison of different estimation methods (e.g., variants of MCMC methods and INLA); comparison between Bayesian and classical methods using real-world examples; analysis of big data. 

Dr. Chao Wang
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. 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 statistics
  • Markov chain Monte Carlo
  • inference
  • prediction
  • simulation

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Published Papers (2 papers)

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Research

22 pages, 651 KiB  
Article
Optimization of Active Learning Strategies for Causal Network Structure
by Mengxin Zhang and Xiaojun Zhang
Mathematics 2024, 12(6), 880; https://doi.org/10.3390/math12060880 - 17 Mar 2024
Viewed by 1063
Abstract
Causal structure learning is one of the major fields in causal inference. Only the Markov equivalence class (MEC) can be learned from observational data; to fully orient unoriented edges, experimental data need to be introduced from external intervention experiments to improve the identifiability [...] Read more.
Causal structure learning is one of the major fields in causal inference. Only the Markov equivalence class (MEC) can be learned from observational data; to fully orient unoriented edges, experimental data need to be introduced from external intervention experiments to improve the identifiability of causal graphs. Finding suitable intervention targets is key to intervention experiments. We propose a causal structure active learning strategy based on graph structures. In the context of randomized experiments, the central nodes of the directed acyclic graph (DAG) are considered as the alternative intervention targets. In each stage of the experiment, we decompose the chain graph by removing the existing directed edges; then, each connected component is oriented separately through intervention experiments. Finally, all connected components are merged to obtain a complete causal graph. We compare our algorithm with previous work in terms of the number of intervention variables, convergence rate and model accuracy. The experimental results show that the performance of the proposed method in restoring the causal structure is comparable to that of previous works. The strategy of finding the optimal intervention target is simplified, which improves the speed of the algorithm while maintaining the accuracy. Full article
(This article belongs to the Special Issue Research Progress and Application of Bayesian Statistics)
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16 pages, 384 KiB  
Article
Assessing Multinomial Distributions with a Bayesian Approach
by Luai Al-Labadi, Petru Ciur, Milutin Dimovic and Kyuson Lim
Mathematics 2023, 11(13), 3007; https://doi.org/10.3390/math11133007 - 6 Jul 2023
Viewed by 1639
Abstract
This paper introduces a unified Bayesian approach for testing various hypotheses related to multinomial distributions. The method calculates the Kullback–Leibler divergence between two specified multinomial distributions, followed by comparing the change in distance from the prior to the posterior through the relative belief [...] Read more.
This paper introduces a unified Bayesian approach for testing various hypotheses related to multinomial distributions. The method calculates the Kullback–Leibler divergence between two specified multinomial distributions, followed by comparing the change in distance from the prior to the posterior through the relative belief ratio. A prior elicitation algorithm is used to specify the prior distributions. To demonstrate the effectiveness and practical application of this approach, it has been applied to several examples. Full article
(This article belongs to the Special Issue Research Progress and Application of Bayesian Statistics)
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