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Mathematics
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Mathematical and Computational Statistics and Applications
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Mathematical and Computational Statistics and Applications

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

Deadline for manuscript submissions: 30 April 2024 | Viewed by 4484

Special Issue Editor

Dr. Jinfeng Xu

E-Mail Website
Guest Editor
Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam, Hong Kong, China
Interests: high-dimensional data analysis; nonparametric and semiparametric inference; sta-tistical genetics; survival analysis; and biostatistics

Special Issue Information

Dear Colleagues,

Mathematics is inviting submissions for a Special Issue on Mathematical and Computational Statistics and Applications. The research on innovative mathematical and computational statistics methods for complex data is beginning to develop in many fields, including medicine, biology, public health, epidemiology, engineering, finance, economics, environmental sciences, and social sciences. Mathematics aims to promote the pioneering work that provides advanced techniques and tools that can be used for statistical theory, methodology, and applications. Manuscripts that concern mathematical and computational statistics and applications in all areas of science are strongly encouraged for submission.

Dr. Jinfeng Xu
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

  • high-dimensional data
  • complex data
  • statistical genetics
  • biostatistics

Published Papers (4 papers)

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Research

14 pages, 311 KiB  
Article
Exploring Complex Survival Data through Frailty Modeling and Regularization
by Xifen Huang, Jinfeng Xu and Yunpeng Zhou
Mathematics 2023, 11(21), 4440; https://0-doi-org.brum.beds.ac.uk/10.3390/math11214440 - 26 Oct 2023
Viewed by 636
Abstract
This study addresses the analysis of complex multivariate survival data, where each individual may experience multiple events and a wide range of relevant covariates are available. We propose an advanced modeling approach that extends the classical shared frailty framework to account for within-subject [...] Read more.
This study addresses the analysis of complex multivariate survival data, where each individual may experience multiple events and a wide range of relevant covariates are available. We propose an advanced modeling approach that extends the classical shared frailty framework to account for within-subject dependence. Our model incorporates a flexible frailty distribution, encompassing well-known distributions, such as gamma, log-normal, and inverse Gaussian. To ensure accurate estimation and effective model selection, we utilize innovative regularization techniques. The proposed methodology exhibits desirable theoretical properties and has been validated through comprehensive simulation studies. Additionally, we apply the approach to real-world data from the Medical Information Mart for Intensive Care (MIMIC-III) dataset, demonstrating its practical utility in analyzing complex survival data structures. Full article
(This article belongs to the Special Issue Mathematical and Computational Statistics and Applications)
26 pages, 3129 KiB  
Article
An Alternative Model for Describing the Reliability Data: Applications, Assessment, and Goodness-of-Fit Validation Testing
by Haitham M. Yousof, Hafida Goual, Walid Emam, Yusra Tashkandy, Morad Alizadeh, M. Masoom Ali and Mohamed Ibrahim
Mathematics 2023, 11(6), 1308; https://0-doi-org.brum.beds.ac.uk/10.3390/math11061308 - 08 Mar 2023
Cited by 3 | Viewed by 1383
Abstract
We provide a new extension of the exponential distribution with an emphasis on the practical elements of the model. Six different classical estimation methods were applied and compared. The main test was evaluated on complete data using four sets of data. Additionally, four [...] Read more.
We provide a new extension of the exponential distribution with an emphasis on the practical elements of the model. Six different classical estimation methods were applied and compared. The main test was evaluated on complete data using four sets of data. Additionally, four applications and the derivation of the new Nikulin statistic test for the new probability model under the censored situation are described. Both tests were evaluated through simulation experiments on complete data and on artificial and censored data. In addition, a set of simulation experiments were presented, which were used and employed to evaluate the original statistical test and the new modified statistical test based on statistical controls in the evaluation processes. Full article
(This article belongs to the Special Issue Mathematical and Computational Statistics and Applications)
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28 pages, 861 KiB  
Article
Utility of Particle Swarm Optimization in Statistical Population Reconstruction
by Sergey S. Berg
Mathematics 2023, 11(4), 827; https://0-doi-org.brum.beds.ac.uk/10.3390/math11040827 - 06 Feb 2023
Cited by 2 | Viewed by 759
Abstract
Statistical population reconstruction models based on maximum likelihood and minimum chi-square objective functions provide a robust and versatile approach to estimating the demographic dynamics of harvested populations of wildlife. These models employ numerical optimization techniques to determine which set of model parameters best [...] Read more.
Statistical population reconstruction models based on maximum likelihood and minimum chi-square objective functions provide a robust and versatile approach to estimating the demographic dynamics of harvested populations of wildlife. These models employ numerical optimization techniques to determine which set of model parameters best describes observed age-at-harvest, catch-effort, and other auxiliary field data. Although numerous optimization methods have been used in the past, the benefits of using particle swarm optimization (PSO) have yet to be explored. Using a harvested population of North American river otter (Lontra canadensis) in Indiana as a case study, we investigated the performance of population reconstruction using particle swarm optimization, spectral projected gradient (SPG), Nelder–Mead, and Broyden–Fletcher–Goldfarb–Shanno (BFGS) methods. We used Monte Carlo studies to simulate populations under a wide range of conditions to compare the relative performance of population reconstruction models using each of the four optimization methods. We found that using particle swarm optimization consistently and significantly improved model stability and precision when compared with other numerical optimization methods that may be used in statistical population reconstruction. Given that these models are frequently used to guide management decisions and set harvest limits, we encourage management agencies to adopt this more precise method of estimating model parameters and corresponding population abundance. These results illustrate the benefits of using particle swarm optimization, caution against relying on the results of population reconstruction based on optimization methods that are highly dependent on initial conditions, and reinforce the need to ensure model convergence to a global rather than a local maximum. Full article
(This article belongs to the Special Issue Mathematical and Computational Statistics and Applications)
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13 pages, 397 KiB  
Article
Spatially Weighted Bayesian Classification of Spatio-Temporal Areal Data Based on Gaussian-Hidden Markov Models
by Kęstutis Dučinskas, Marta Karaliutė and Laura Šaltytė-Vaisiauskė
Mathematics 2023, 11(2), 347; https://0-doi-org.brum.beds.ac.uk/10.3390/math11020347 - 09 Jan 2023
Cited by 1 | Viewed by 1105
Abstract
This article is concerned with an original approach to generative classification of spatiotemporal areal (or lattice) data based on implementation of spatial weighting to Hidden Markov Models (HMMs). In the framework of this approach data model at each areal unit is specified by [...] Read more.
This article is concerned with an original approach to generative classification of spatiotemporal areal (or lattice) data based on implementation of spatial weighting to Hidden Markov Models (HMMs). In the framework of this approach data model at each areal unit is specified by conditionally independent Gaussian observations and first-order Markov chain for labels and call it local HMM. The proposed classification is based on modification of conventional HMM by the implementation of spatially weighted estimators of local HMMs parameters. We focus on classification rules based on Bayes discriminant function (BDF) with plugged in the spatially weighted parameter estimators obtained from the labeled training sample. For each local HMM, the estimators of regression coefficients and variances and two types of transition probabilities are used in two levels (higher and lower) of spatial weighting. The average accuracy rate (ACC) and balanced accuracy rate (BAC), computed from confusion matrices evaluated from a test sample, are used as performance measures of classifiers. The proposed methodology is illustrated for simulated data and for real dataset, i.e., annual death rate data collected by the Institute of Hygiene of the Republic of Lithuania from the 60 municipalities in the period from 2001 to 2019. Critical comparison of proposed classifiers is done. The experimental results showed that classifiers based on HMM with higher level of spatial weighting in majority cases have advantage in spatial–temporal consistency and classification accuracy over one with lower level of spatial weighting. Full article
(This article belongs to the Special Issue Mathematical and Computational Statistics and Applications)
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