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Mathematics
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Advanced Statistical Application for Realistic Problems
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Advanced Statistical Application for Realistic Problems

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

Deadline for manuscript submissions: closed (1 October 2024) | Viewed by 3242

Special Issue Editor

Dr. Diogo Francisco Rossoni

E-Mail Website
Guest Editor
Department of Statistics, Biostatistics Postgraduate Program (PBE), State University of Maringá, Maringá, Av. Colombo, 5790, Maringá 87020-900, Brazil
Interests: probability; statistics; spatial statistics; geostatistics; applied mathematics; fractional calculus
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In recent decades, both statistics and spatial statistics have witnessed remarkable advancements, largely attributed to the integration of computational techniques. These techniques not only offer insights into the mechanics and rationale behind existing statistical methods but also demonstrate their practical application to real-world challenges. A notable example is the fusion of machine learning with geostatistics, equipping us with innovative tools to explore and predict in earth sciences and delve into spatial processes.

Aligned with this trajectory, this Special Issue aims to curate a selection of articles that showcase the relevance of theoretical and computational statistics across diverse scientific disciplines. This encompasses areas like spatial processes in earth sciences, survival analysis in life sciences, reliability analysis in engineering, algorithmic developments in computer science, and modern challenges addressed through machine learning, among others.

Dr. Diogo Francisco Rossoni
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

  • computational techniques
  • geostatistics and spatial statistics
  • advanced and predictive analytics
  • data-driven insights
  • applied statistics
  • algorithm development
  • data-driven insights
  • forecasting and uncertainty

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Published Papers (2 papers)

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Research

29 pages, 9774 KiB  
Article
High-Resolution Spatiotemporal Forecasting with Missing Observations Including an Application to Daily Particulate Matter 2.5 Concentrations in Jakarta Province, Indonesia
by I Gede Nyoman Mindra Jaya and Henk Folmer
Mathematics 2024, 12(18), 2899; https://doi.org/10.3390/math12182899 - 17 Sep 2024
Viewed by 1334
Abstract
Accurate forecasting of high-resolution particulate matter 2.5 (PM2.5) levels is essential for the development of public health policy. However, datasets used for this purpose often contain missing observations. This study presents a two-stage approach to handle this problem. The first stage [...] Read more.
Accurate forecasting of high-resolution particulate matter 2.5 (PM2.5) levels is essential for the development of public health policy. However, datasets used for this purpose often contain missing observations. This study presents a two-stage approach to handle this problem. The first stage is a multivariate spatial time series (MSTS) model, used to generate forecasts for the sampled spatial units and to impute missing observations. The MSTS model utilizes the similarities between the temporal patterns of the time series of the spatial units to impute the missing data across space. The second stage is the high-resolution prediction model, which generates predictions that cover the entire study domain. The second stage faces the big N problem giving rise to complex memory and computational problems. As a solution to the big N problem, we propose a Gaussian Markov random field (GMRF) for innovations with the Matérn covariance matrix obtained from the corresponding Gaussian field (GF) matrix by means of the stochastic partial differential equation (SPDE) method and the finite element method (FEM). For inference, we propose Bayesian statistics and integrated nested Laplace approximation (INLA) in the R-INLA package. The above approach is demonstrated using daily data collected from 13 PM2.5 monitoring stations in Jakarta Province, Indonesia, for 1 January–31 December 2022. The first stage of the model generates PM2.5 forecasts for the 13 monitoring stations for the period 1–31 January 2023, imputing missing data by means of the MSTS model. To capture temporal trends in the PM2.5 concentrations, the model applies a first-order autoregressive process and a seasonal process. The second stage involves creating a high-resolution map for the period 1–31 January 2023, for sampled and non-sampled spatiotemporal units. It uses the MSTS-generated PM2.5 predictions for the sampled spatiotemporal units and observations of the covariate’s altitude, population density, and rainfall for sampled and non-samples spatiotemporal units. For the spatially correlated random effects, we apply a first-order random walk process. The validation of out-of-sample forecasts indicates a strong model fit with low mean squared error (0.001), mean absolute error (0.037), and mean absolute percentage error (0.041), and a high R² value (0.855). The analysis reveals that altitude and precipitation negatively impact PM2.5 concentrations, while population density has a positive effect. Specifically, a one-meter increase in altitude is linked to a 7.8% decrease in PM2.5, while a one-person increase in population density leads to a 7.0% rise in PM2.5. Additionally, a one-millimeter increase in rainfall corresponds to a 3.9% decrease in PM2.5. The paper makes a valuable contribution to the field of forecasting high-resolution PM2.5 levels, which is essential for providing detailed, accurate information for public health policy. The approach presents a new and innovative method for addressing the problem of missing data and high-resolution forecasting. Full article
(This article belongs to the Special Issue Advanced Statistical Application for Realistic Problems)
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21 pages, 3753 KiB  
Article
Laplace-Logistic Unit Distribution with Application in Dynamic and Regression Analysis
by Vladica S. Stojanović, Tanja Jovanović Spasojević and Mihailo Jovanović
Mathematics 2024, 12(14), 2282; https://doi.org/10.3390/math12142282 - 22 Jul 2024
Cited by 4 | Viewed by 1323
Abstract
This manuscript presents a new two-parameter unit stochastic distribution, obtained by transforming the Laplace distribution, using a generalized logistic map, into a unit interval. The distribution thus obtained is named the Laplace-logistic unit (abbreviated LLU) distribution, and its basic stochastic properties are examined [...] Read more.
This manuscript presents a new two-parameter unit stochastic distribution, obtained by transforming the Laplace distribution, using a generalized logistic map, into a unit interval. The distribution thus obtained is named the Laplace-logistic unit (abbreviated LLU) distribution, and its basic stochastic properties are examined in detail. Also, the procedure for estimating parameters based on quantiles is provided, along with the asymptotic properties of the obtained estimates and the appropriate numerical simulation study. Finally, the application of the LLU distribution in dynamic and regression analysis of real-world data with accentuated “peaks” and “fat” tails is also discussed. Full article
(This article belongs to the Special Issue Advanced Statistical Application for Realistic Problems)
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