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Mathematics
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Bayesian Statistical Analysis of Big Data and Complex Data
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Bayesian Statistical Analysis of Big Data and Complex Data

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

Deadline for manuscript submissions: 10 June 2025 | Viewed by 3313

Special Issue Editor

Dr. Duchwan Ryu

E-Mail Website
Guest Editor
Department of Statistics and Actuarial Science, Northern Illinois University, DeKalb, IL 60115, USA
Interests: Bayesian funcational data analysis; sequential Monte Carlo methods; longitudinal measurements; measurement error models; uncertainty quantifications

Special Issue Information

Dear Colleagues, 

Advances in technologies including communications, mobile devices, digital sensors and DNA sequencing lead to not only large amounts but also complicated structures of data and change the environment of statistical analysis. Big data can be described by the size of the data, the speed of incoming and outgoing data, the sources and types of data and the messiness and trustworthiness of data. To handle big data, lots of computing methods have been used such as cloud computing, grid computing, stream computing, granular computing, parallel computing, quantum computing, edge computing, optical computing and so on. Regarding the analysis of big data, the tremendous volume and the speed of incoming and outgoing data hinder statistical analysis. Further, the complicated structure of data with more parameters in the statistical model makes the statistical analysis even harder. Bayesian approaches have an additional burden to model the parameters with the prior distributions. To cope with the difficulties of Bayesian statistical analysis, many efficient computational methodologies are proposed and expected that encompass the dimension reduction methods, the integrated nested Laplace approximations, the hidden Markov chains, the multi-chain Markov chain Monte Carlo, the multi-stage Monte Carlo and the sequential Monte Carlo methods.

Dr. Duchwan Ryu
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

  • Bayesian approximation
  • Bayesian big data analysis
  • Bayesian dimension reduction
  • Bayesian model for complex data
  • efficient Bayesian computing

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Published Papers (2 papers)

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Research

43 pages, 8756 KiB  
Article
Bayesian Model Selection for Addressing Cold-Start Problems in Partitioned Time Series Prediction
by Jaeseong Yoo and Jihoon Moon
Mathematics 2024, 12(17), 2682; https://doi.org/10.3390/math12172682 - 28 Aug 2024
Viewed by 992
Abstract
How to effectively predict outcomes when initial time series data are limited remains unclear. This study investigated the efficiency of Bayesian model selection to address the lack of initial data for time series analysis, particularly in cold-start scenarios—a common challenge in predictive modeling. [...] Read more.
How to effectively predict outcomes when initial time series data are limited remains unclear. This study investigated the efficiency of Bayesian model selection to address the lack of initial data for time series analysis, particularly in cold-start scenarios—a common challenge in predictive modeling. We utilized a comprehensive approach that juxtaposed observational data against various candidate models through strategic partitioning. This method contrasted traditional reliance on distance measures like the L2 norm. Instead, it applied statistical tests to validate model efficacy. Notably, the introduction of an interactive visualization tool featuring a slide bar for setting significance levels marked a significant advancement over conventional p-value displays. Our results affirm that when observational data align with a candidate model, effective predictions are possible, albeit with necessary considerations of stationarity and potential structural breaks. These findings underscore the potential of Bayesian methods in predictive analytics, especially when initial data are scarce or incomplete. This research not only enhances our understanding of model selection dynamics but also sets the stage for future investigations into more refined predictive frameworks. Full article
(This article belongs to the Special Issue Bayesian Statistical Analysis of Big Data and Complex Data)
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17 pages, 3512 KiB  
Article
Bayesian Joint Modeling Analysis of Longitudinal Proportional and Survival Data
by Wenting Liu, Huiqiong Li, Anmin Tang and Zixin Cui
Mathematics 2023, 11(16), 3469; https://doi.org/10.3390/math11163469 - 10 Aug 2023
Cited by 1 | Viewed by 1637
Abstract
This paper focuses on a joint model to analyze longitudinal proportional and survival data. We utilize a logit transformation on the longitudinal proportional data and employ a partially linear mixed-effect model. With this model, we estimate the unknown function of time using the [...] Read more.
This paper focuses on a joint model to analyze longitudinal proportional and survival data. We utilize a logit transformation on the longitudinal proportional data and employ a partially linear mixed-effect model. With this model, we estimate the unknown function of time using the B-splines technique. Additionally, we introduce a centered Dirichlet process mixture model (CDPMM) to capture the random effects, allowing for a flexible distribution. The survival data are assumed using a Cox proportional hazard model, and the sharing random effects joint model is developed for the two types of data. We develop a Bayesian Lasso (BLasso) approach that combines the Gibbs sampler and the Metropolis–Hastings algorithm. The proposed method allows for the estimation of unknown parameters and the selection of significant covariates simultaneously. We evaluate the performance of our proposed methods through simulation studies and also provide an illustration of our methodologies using an example from the MA.5 research experiment. Full article
(This article belongs to the Special Issue Bayesian Statistical Analysis of Big Data and Complex Data)
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