Special Issue "Uncertainty Quantification Techniques in Statistics"

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: 31 August 2019

Special Issue Editor

Guest Editor
Prof. Dr. Jong-Min Kim

Statistics Discipline, Division of Science and Mathematics, University of Minnesota at Morris, Morris, MN 56267, USA
Website | E-Mail
Interests: artificial intelligence; blockchain; big data; cryptocurrencies; cyber security; data analytics; data mining; deep learning; electronic data interchange (EDI); e-learning; Internet security; Internet of things; mobile applications; mobile learning; neural networks; fuzzy logic; expert systems; security; sentiment analysis; support vector machines; web services and performance

Special Issue Information

Dear Colleagues,

Uncertainty Quantification (UQ) is a mainstream research topic in applied mathematics and statistics. To identify UQ problems, diverse modern techniques for large and complex data analysis have been developed in applied mathematics, computer science, and statistics.

To promote these modern data analysis methods in biology, economics, environmental studies, finance, mathematics, operational research, science, and statistics, a Special Issue of Mathematics (ISSN 2227-7390), the Science Citation Index Expanded (SCIE) Journal, will be devoted to “Uncertainty Quantification Techniques in Statistics”.

The Guest Editor for this Special Issue is Prof. Dr. Jong‐Min Kim.

Prof. Dr. Jong-Min Kim
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 monthly journal published by MDPI.

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Keywords

  • Bayesian statistics
  • Change-point detection
  • Computer model
  • Financial time series
  • Functional data analysis
  • Machine learning
  • Quality control
  • Spatial statistics

Published Papers (2 papers)

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Research

Open AccessArticle
On the Performance of Variable Selection and Classification via Rank-Based Classifier
Mathematics 2019, 7(5), 457; https://doi.org/10.3390/math7050457
Received: 26 April 2019 / Revised: 11 May 2019 / Accepted: 14 May 2019 / Published: 21 May 2019
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Abstract
In high-dimensional gene expression data analysis, the accuracy and reliability of cancer classification and selection of important genes play a very crucial role. To identify these important genes and predict future outcomes (tumor vs. non-tumor), various methods have been proposed in the literature. [...] Read more.
In high-dimensional gene expression data analysis, the accuracy and reliability of cancer classification and selection of important genes play a very crucial role. To identify these important genes and predict future outcomes (tumor vs. non-tumor), various methods have been proposed in the literature. But only few of them take into account correlation patterns and grouping effects among the genes. In this article, we propose a rank-based modification of the popular penalized logistic regression procedure based on a combination of 1 and 2 penalties capable of handling possible correlation among genes in different groups. While the 1 penalty maintains sparsity, the 2 penalty induces smoothness based on the information from the Laplacian matrix, which represents the correlation pattern among genes. We combined logistic regression with the BH-FDR (Benjamini and Hochberg false discovery rate) screening procedure and a newly developed rank-based selection method to come up with an optimal model retaining the important genes. Through simulation studies and real-world application to high-dimensional colon cancer gene expression data, we demonstrated that the proposed rank-based method outperforms such currently popular methods as lasso, adaptive lasso and elastic net when applied both to gene selection and classification. Full article
(This article belongs to the Special Issue Uncertainty Quantification Techniques in Statistics)
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Open AccessArticle
Skew-Reflected-Gompertz Information Quantifiers with Application to Sea Surface Temperature Records
Mathematics 2019, 7(5), 403; https://doi.org/10.3390/math7050403
Received: 19 March 2019 / Revised: 25 April 2019 / Accepted: 2 May 2019 / Published: 6 May 2019
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Abstract
The Skew-Reflected-Gompertz (SRG) distribution, introduced by Hosseinzadeh et al. (J. Comput. Appl. Math. (2019) 349, 132–141), produces two-piece asymmetric behavior of the Gompertz (GZ) distribution, which extends the positive to a whole dominion by an extra parameter. The SRG distribution also permits a [...] Read more.
The Skew-Reflected-Gompertz (SRG) distribution, introduced by Hosseinzadeh et al. (J. Comput. Appl. Math. (2019) 349, 132–141), produces two-piece asymmetric behavior of the Gompertz (GZ) distribution, which extends the positive to a whole dominion by an extra parameter. The SRG distribution also permits a better fit than its well-known classical competitors, namely the skew-normal and epsilon-skew-normal distributions, for data with a high presence of skewness. In this paper, we study information quantifiers such as Shannon and Rényi entropies, and Kullback–Leibler divergence in terms of exact expressions of GZ information measures. We find the asymptotic test useful to compare two SRG-distributed samples. Finally, as a real-world data example, we apply these results to South Pacific sea surface temperature records. Full article
(This article belongs to the Special Issue Uncertainty Quantification Techniques in Statistics)
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