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Mathematics
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Advances in Computational Statistics, Design of Experiments, and Its Applications
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Advances in Computational Statistics, Design of Experiments, and Its Applications

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

Deadline for manuscript submissions: closed (28 February 2025) | Viewed by 2366

Special Issue Editor

Dr. Stella Stylianou

E-Mail Website
Guest Editor
School of Science, RMIT University, Melbourne, VIC 3000, Australia
Interests: experimental designs; statistical modelling; factorial designs; optimal designs; computational methods

Special Issue Information

Dear Colleagues,

Computational statistics has significant applications in many research fields, and the design of experiments is a traditional and widespread method of experimentation. The combination of the design of experiments and computational statistics is fascinating. The purpose of this Special Issue is to provide a collection of high-quality manuscripts that focus on all aspects of theoretical research and novel applications of computational statistics and/or the design of experiments, especially in social sciences and engineering.

Topics of interest include but are not limited to the following: algorithms and computational methods, factorial designs DSDs, response surface methodology, orthogonal designs, Latin hypercube designs, space-filling designs, estimation methods, statistical modelling, optimal designs, and applications in social sciences and engineering.

Dr. Stella Stylianou
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

  • experimental designs
  • statistical modelling
  • factorial designs
  • optimal designs
  • computational methods

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (3 papers)

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Research

26 pages, 482 KiB  
Article
Computational Construction of Sequential Efficient Designs for the Second-Order Model
by Norah Alshammari, Stelios Georgiou and Stella Stylianou
Mathematics 2025, 13(7), 1190; https://doi.org/10.3390/math13071190 - 4 Apr 2025
Viewed by 239
Abstract
Sequential experimental designs enhance data collection efficiency by reducing resource usage and accelerating experimental objectives. This paper presents a model-driven approach to sequential Latin hypercube designs (SLHDs) tailored for second-order models. Unlike traditional model-free SLHDs, our method optimizes a conditional A-criterion to improve [...] Read more.
Sequential experimental designs enhance data collection efficiency by reducing resource usage and accelerating experimental objectives. This paper presents a model-driven approach to sequential Latin hypercube designs (SLHDs) tailored for second-order models. Unlike traditional model-free SLHDs, our method optimizes a conditional A-criterion to improve efficiency, particularly in higher dimensions. By relaxing the restriction of non-replicated points within equally spaced intervals, our approach maintains space-filling properties while allowing greater flexibility for model-specific optimization. Using Sobol sequences, the algorithm iteratively selects good points, enhancing conditional A-efficiency compared to distance minimization methods. Additional criteria, such as D-efficiency, further validate the generated design matrices, ensuring robust performance. The proposed approach demonstrates superior results, with detailed tables and graphs illustrating its advantages across applications in engineering, pharmacology, and manufacturing. Full article
(This article belongs to the Special Issue Advances in Computational Statistics, Design of Experiments, and Its Applications)
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16 pages, 494 KiB  
Article
An Upper Bound for Locating Strings with High Probability Within Consecutive Bits of Pi
by Víctor Manuel Silva-García, Manuel Alejandro Cardona-López and Rolando Flores-Carapia
Mathematics 2025, 13(2), 313; https://doi.org/10.3390/math13020313 - 19 Jan 2025
Viewed by 551
Abstract
Numerous studies on the number pi (π) explore its properties, including normality and applicability. This research, grounded in two hypotheses, proposes and proves a theorem that employs a Bernoulli experiment to demonstrate the high probability of encountering any finite bit string [...] Read more.
Numerous studies on the number pi (π) explore its properties, including normality and applicability. This research, grounded in two hypotheses, proposes and proves a theorem that employs a Bernoulli experiment to demonstrate the high probability of encountering any finite bit string within a sequence of consecutive bits in the decimal part of π. This aligns with findings related to its normality. To support the hypotheses, we present experimental evidence about the equiprobable and independent properties of bits of π, analyzing their distribution, and measuring correlations between bit strings. Additionally, from a cryptographic perspective, we evaluate the chaotic properties of two images generated using bits of π. These properties are evaluated similarly to those of encrypted images, using measures of correlation and entropy, along with two hypothesis tests to confirm the uniform distribution of bits and the absence of periodic patterns. Unlike previous works that solely examine the presence of sequences, this study provides, as a corollary, a formula to calculate an upper bound N. This bound represents the length of the sequence from π required to ensure the location of any n-bit string at least once, with an adjustable probability p that can be set arbitrarily close to one. To validate the formula, we identify sequences of up to n= 40 consecutive zeros and ones within the first N bits of π. This work has potential applications in Cryptography that use the number π for random sequence generation, offering insights into the number of bits of π required to ensure good randomness properties. Full article
(This article belongs to the Special Issue Advances in Computational Statistics, Design of Experiments, and Its Applications)
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21 pages, 619 KiB  
Article
Group Doubly Coupled Designs
by Weiping Zhou, Shigui Huang and Min Li
Mathematics 2024, 12(9), 1352; https://doi.org/10.3390/math12091352 - 29 Apr 2024
Cited by 1 | Viewed by 944
Abstract
Doubly coupled designs (DCDs) have better space-filling properties between the qualitative and quantitative factors than marginally coupled designs (MCDs) which are suitable for computer experiments with both qualitative and quantitative factors. In this paper, we propose a new class of DCDs, called group [...] Read more.
Doubly coupled designs (DCDs) have better space-filling properties between the qualitative and quantitative factors than marginally coupled designs (MCDs) which are suitable for computer experiments with both qualitative and quantitative factors. In this paper, we propose a new class of DCDs, called group doubly coupled designs (GDCDs), and provide methods for constructing two forms of GDCDs, within-group doubly coupled designs and between-group doubly coupled designs. The proposed GDCDs can accommodate more qualitative factors than DCDs, when the subdesigns for the qualitative factors are symmetric. The subdesigns of qualitative factors are not asymmetric in the existing results on DCDs, and in this paper, we construct GDCDs with symmetric and asymmetric designs for the qualitative factors, respectively. Moreover, detailed comparisons with existing MCDs show that GDCDs have better space-filling properties between qualitative and quantitative factors. Finally, the methods are particularly easy to implement. Full article
(This article belongs to the Special Issue Advances in Computational Statistics, Design of Experiments, and Its Applications)
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