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Stats, Volume 8, Issue 3 (September 2025) – 11 articles

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17 pages, 384 KiB  
Article
The Detection Method of the Tobit Model in a Dataset
by El ouali Rahmani and Mohammed Benmoumen
Stats 2025, 8(3), 59; https://doi.org/10.3390/stats8030059 (registering DOI) - 12 Jul 2025
Abstract
This article proposes an extension of detection methods for the Tobit model by generalizing existing approaches from cases with known parameters to more realistic scenarios where the parameters are unknown. The main objective is to develop detection procedures that account for parameter uncertainty [...] Read more.
This article proposes an extension of detection methods for the Tobit model by generalizing existing approaches from cases with known parameters to more realistic scenarios where the parameters are unknown. The main objective is to develop detection procedures that account for parameter uncertainty and to analyze how this uncertainty affects the estimation process and the overall accuracy of the model. The methodology relies on maximum likelihood estimation, applied to datasets generated under different configurations of the Tobit model. A series of Monte Carlo simulations is conducted to evaluate the performance of the proposed methods. The results provide insights into the robustness of the detection procedures under varying assumptions. The study concludes with practical recommendations for improving the application of the Tobit model in fields such as econometrics, health economics, and environmental studies. Full article
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16 pages, 1288 KiB  
Article
Quantile Estimation Based on the Log-Skew-t Linear Regression Model: Statistical Aspects, Simulations, and Applications
by Raúl Alejandro Morán-Vásquez, Anlly Daniela Giraldo-Melo and Mauricio A. Mazo-Lopera
Stats 2025, 8(3), 58; https://doi.org/10.3390/stats8030058 - 11 Jul 2025
Abstract
We propose a robust linear regression model assuming a log-skew-t distribution for the response variable, with the aim of exploring the association between the covariates and the quantiles of a continuous and positive response variable under skewness and heavy tails. This model [...] Read more.
We propose a robust linear regression model assuming a log-skew-t distribution for the response variable, with the aim of exploring the association between the covariates and the quantiles of a continuous and positive response variable under skewness and heavy tails. This model includes the log-skew-normal and log-t linear regression models as special cases. Our simulation studies indicate good performance of the quantile estimation approach and its outperformance relative to the classical quantile regression model. The practical applicability of our methodology is demonstrated through an analysis of two real datasets. Full article
(This article belongs to the Special Issue Robust Statistics in Action II)
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14 pages, 16727 KiB  
Article
Well Begun Is Half Done: The Impact of Pre-Processing in MALDI Mass Spectrometry Imaging Analysis Applied to a Case Study of Thyroid Nodules
by Giulia Capitoli, Kirsten C. J. van Abeelen, Isabella Piga, Vincenzo L’Imperio, Marco S. Nobile, Daniela Besozzi and Stefania Galimberti
Stats 2025, 8(3), 57; https://doi.org/10.3390/stats8030057 - 10 Jul 2025
Abstract
The discovery of proteomic biomarkers in cancer research can be effectively performed in situ by exploiting Matrix-Assisted Laser Desorption Ionization (MALDI) Mass Spectrometry Imaging (MSI). However, due to experimental limitations, the spectra extracted by MALDI-MSI can be noisy, so pre-processing steps are generally [...] Read more.
The discovery of proteomic biomarkers in cancer research can be effectively performed in situ by exploiting Matrix-Assisted Laser Desorption Ionization (MALDI) Mass Spectrometry Imaging (MSI). However, due to experimental limitations, the spectra extracted by MALDI-MSI can be noisy, so pre-processing steps are generally needed to reduce the instrumental and analytical variability. Thus far, the importance and the effect of standard pre-processing methods, as well as their combinations and parameter settings, have not been extensively investigated in proteomics applications. In this work, we present a systematic study of 15 combinations of pre-processing steps—including baseline, smoothing, normalization, and peak alignment—for a real-data classification task on MALDI-MSI data measured from fine-needle aspirates biopsies of thyroid nodules. The influence of each combination was assessed by analyzing the feature extraction, pixel-by-pixel classification probabilities, and LASSO classification performance. Our results highlight the necessity of fine-tuning a pre-processing pipeline, especially for the reliable transfer of molecular diagnostic signatures in clinical practice. We outline some recommendations on the selection of pre-processing steps, together with filter levels and alignment methods, according to the mass-to-charge range and heterogeneity of data. Full article
(This article belongs to the Section Applied Statistics and Machine Learning Methods)
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18 pages, 359 KiB  
Article
On the Decision-Theoretic Foundations and the Asymptotic Bayes Risk of the Region of Practical Equivalence for Testing Interval Hypotheses
by Riko Kelter
Stats 2025, 8(3), 56; https://doi.org/10.3390/stats8030056 - 8 Jul 2025
Viewed by 68
Abstract
Testing interval hypotheses is of huge relevance in the biomedical and cognitive sciences; for example, in clinical trials. Frequentist approaches include the proposal of equivalence tests, which have been used to study if there is a predetermined meaningful treatment effect. In the Bayesian [...] Read more.
Testing interval hypotheses is of huge relevance in the biomedical and cognitive sciences; for example, in clinical trials. Frequentist approaches include the proposal of equivalence tests, which have been used to study if there is a predetermined meaningful treatment effect. In the Bayesian paradigm, two popular approaches exist: The first is the region of practical equivalence (ROPE), which has become increasingly popular in the cognitive sciences. The second is the Bayes factor for interval null hypotheses, which was proposed by Morey et al. One advantage of the ROPE procedure is that, in contrast to the Bayes factor, it is quite robust to the prior specification. However, while the ROPE is conceptually appealing, it lacks a clear decision-theoretic foundation like the Bayes factor. In this paper, a decision-theoretic justification for the ROPE procedure is derived for the first time, which shows that the Bayes risk of a decision rule based on the highest-posterior density interval (HPD) and the ROPE is asymptotically minimized for increasing sample size. To show this, a specific loss function is introduced. This result provides an important decision-theoretic justification for testing the interval hypothesis in the Bayesian approach based on the ROPE and HPD, in particular, when sample size is large. Full article
(This article belongs to the Section Bayesian Methods)
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24 pages, 347 KiB  
Article
Estimating the Ratio of Means in a Zero-Inflated Poisson Mixture Model
by Michael Pearce and Michael D. Perlman
Stats 2025, 8(3), 55; https://doi.org/10.3390/stats8030055 - 5 Jul 2025
Viewed by 88
Abstract
The problem of estimating the ratio of the means of a two-component Poisson mixture model is considered, when each component is subject to zero-inflation, i.e., excess zero counts. The resulting zero-inflated Poisson mixture (ZIPM) model can be viewed as a three-component Poisson mixture [...] Read more.
The problem of estimating the ratio of the means of a two-component Poisson mixture model is considered, when each component is subject to zero-inflation, i.e., excess zero counts. The resulting zero-inflated Poisson mixture (ZIPM) model can be viewed as a three-component Poisson mixture model with one degenerate component. The EM algorithm is applied to obtain frequentist estimators and their standard errors, the latter determined via an explicit expression for the observed information matrix. As an intermediate step, we derive an explicit expression for standard errors in the two-component Poisson mixture model (without zero-inflation), a new result. The ZIPM model is applied to simulated data and real ecological count data of frigatebirds on the Coral Sea Islands off the coast of Northeast Australia. Full article
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14 pages, 715 KiB  
Article
A Data-Driven Approach of DRG-Based Medical Insurance Payment Policy Formulation in China Based on an Optimization Algorithm
by Kun Ba and Biqing Huang
Stats 2025, 8(3), 54; https://doi.org/10.3390/stats8030054 - 30 Jun 2025
Viewed by 253
Abstract
The diagnosis-related group (DRG) system classifies patients into different groups in order to facilitate decisions regarding medical insurance payments. Currently, more than 600 standard DRGs exist in China. Payment details represented by DRG weights must be adjusted during decision-making. After modeling the DRG [...] Read more.
The diagnosis-related group (DRG) system classifies patients into different groups in order to facilitate decisions regarding medical insurance payments. Currently, more than 600 standard DRGs exist in China. Payment details represented by DRG weights must be adjusted during decision-making. After modeling the DRG weight-determining process as a parameter-searching and optimization-solving problem, we propose a stochastic gradient tracking algorithm (SGT) and compare it with a genetic algorithm and sequential quadratic programming. We describe diagnosis-related groups in China using several statistics based on sample data from one city. We explored the influence of the SGT hyperparameters through numerous experiments and demonstrated the robustness of the best SGT hyperparameter combination. Our stochastic gradient tracking algorithm finished the parameter search in only 3.56 min when the insurance payment rate was set at 95%, which is acceptable and desirable. As the main medical insurance payment scheme in China, DRGs require quantitative evidence for policymaking. The optimization algorithm proposed in this study shows a possible scientific decision-making method for use in the DRG system, particularly with regard to DRG weights. Full article
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14 pages, 784 KiB  
Article
Distance-Based Relevance Function for Imbalanced Regression
by Daniel Daeyoung In and Hyunjoong Kim
Stats 2025, 8(3), 53; https://doi.org/10.3390/stats8030053 - 28 Jun 2025
Viewed by 159
Abstract
Imbalanced regression poses a significant challenge in real-world prediction tasks, where rare target values are prone to overfitting during model training. To address this, prior research has employed relevance functions to quantify the rarity of target instances. However, existing functions often struggle to [...] Read more.
Imbalanced regression poses a significant challenge in real-world prediction tasks, where rare target values are prone to overfitting during model training. To address this, prior research has employed relevance functions to quantify the rarity of target instances. However, existing functions often struggle to capture the rarity across diverse target distributions. In this study, we introduce a novel Distance-based Relevance Function (DRF) that quantifies the rarity based on the distance between target values, enabling a more accurate and distribution-agnostic assessment of rare data. This general approach allows imbalanced regression techniques to be effectively applied to a broader range of distributions, including bimodal cases. We evaluate the proposed DRF using Mean Squared Error (MSE), relevance-weighted Mean Absolute Error (MAEϕ), and Symmetric Mean Absolute Percentage Error (SMAPE). Empirical studies on synthetic datasets and 18 real-world datasets demonstrate that DRF tends to improve the performance across various machine learning models, including support vector regression, neural networks, XGBoost, and random forests. These findings suggest that DRF offers a promising direction for rare target detection and broadens the applicability of imbalanced regression methods. Full article
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13 pages, 300 KiB  
Article
New Effects and Methods in Brownian Transport
by Dmitri Martila and Stefan Groote
Stats 2025, 8(3), 52; https://doi.org/10.3390/stats8030052 - 26 Jun 2025
Viewed by 203
Abstract
We consider the noise-induced transport of overdamped Brownian particles in a ratchet system driven by nonequilibrium symmetric three-level Markovian noise and additive white noise. In addition to a detailed analysis of this system, we consider a simple example that can be solved exactly, [...] Read more.
We consider the noise-induced transport of overdamped Brownian particles in a ratchet system driven by nonequilibrium symmetric three-level Markovian noise and additive white noise. In addition to a detailed analysis of this system, we consider a simple example that can be solved exactly, showing both the increase in the number of current reversals and hypersensitivity. The simplicity of the exact solution and the model itself is beneficial for comparison with experiments. Full article
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14 pages, 464 KiB  
Article
Elicitation of Priors for the Weibull Distribution
by Purvi Prajapati, James D. Stamey, David Kahle, John W. Seaman, Jr., Zachary M. Thomas and Michael Sonksen
Stats 2025, 8(3), 51; https://doi.org/10.3390/stats8030051 - 23 Jun 2025
Viewed by 187
Abstract
Bayesian methods have attracted increasing interest in the design and analysis of clinical trials. Many of these clinical trials investigate time-to-event endpoints. The Weibull distribution is often used in survival and reliability analysis to model time-to-event data. We propose a process to elicit [...] Read more.
Bayesian methods have attracted increasing interest in the design and analysis of clinical trials. Many of these clinical trials investigate time-to-event endpoints. The Weibull distribution is often used in survival and reliability analysis to model time-to-event data. We propose a process to elicit information about the parameters of the Weibull distribution for pharmaceutical applications. Our method is based on an expert’s answers to questions about the median and upper quartile of the distribution. Using the elicited information, a joint prior is constructed for the median and upper quartile of the Weibull distribution, which induces a joint prior distribution on the shape and rate parameters of the Weibull. To illustrate, we apply our elicitation methodology to a pediatric clinical trial, where information is elicited from a subject-matter expert for the control arm. Full article
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19 pages, 920 KiB  
Article
Ethicametrics: A New Interdisciplinary Science
by Fabio Zagonari
Stats 2025, 8(3), 50; https://doi.org/10.3390/stats8030050 - 22 Jun 2025
Viewed by 247
Abstract
This paper characterises Ethicametrics (EM) as a new interdisciplinary scientific research area focusing on metrics of ethics (MOE) and ethics of metrics (EOM), by providing a comprehensive methodological framework. EM is scientific: it is based on behavioural mathematical modelling to be statistically validated [...] Read more.
This paper characterises Ethicametrics (EM) as a new interdisciplinary scientific research area focusing on metrics of ethics (MOE) and ethics of metrics (EOM), by providing a comprehensive methodological framework. EM is scientific: it is based on behavioural mathematical modelling to be statistically validated and tested, with additional sensitivity analyses to favour immediate interpretations. EM is interdisciplinary: it spans from less to more traditional fields, with essential mutual improvements. EM is new: valid and invalid examples of EM (articles referring to an explicit and an implicit behavioural model, respectively) are scarce, recent, time-stable and discipline-focused, with 1 and 37 scientists, respectively. Thus, the core of EM (multi-level statistical analyses applied to behavioural mathematical models) is crucial to avoid biased MOE and EOM. Conversely, articles inside EM should study quantitatively any metrics or ethics, in any alternative context, at any analytical level, by using panel/longitudinal data. Behavioural models should be ethically explicit, possibly by evaluating ethics in terms of the consequences of actions. Ethical measures should be scientifically grounded by evaluating metrics in terms of ethical criteria coming from the relevant theological/philosophical literature. Note that behavioural models applied to science metrics can be used to deduce social consequences to be ethically evaluated. Full article
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27 pages, 2058 KiB  
Article
Mission Reliability Assessment for the Multi-Phase Data in Operational Testing
by Jianping Hao and Mochao Pei
Stats 2025, 8(3), 49; https://doi.org/10.3390/stats8030049 - 20 Jun 2025
Viewed by 186
Abstract
Traditional methods for mission reliability assessment under operational testing conditions exhibit some limitations. They include coarse modeling granularity, significant parameter estimation biases, and inadequate adaptability for handling heterogeneous test data. To address these challenges, this study establishes an assessment framework using a vehicular [...] Read more.
Traditional methods for mission reliability assessment under operational testing conditions exhibit some limitations. They include coarse modeling granularity, significant parameter estimation biases, and inadequate adaptability for handling heterogeneous test data. To address these challenges, this study establishes an assessment framework using a vehicular missile launching system (VMLS) as a case study. The framework constructs phase-specific reliability block diagrams based on mission profiles and establishes mappings between data types and evaluation models. The framework integrates the maximum entropy criterion with reliability monotonic decreasing constraints, develops a covariate-embedded Bayesian data fusion model, and proposes a multi-path weight adjustment assessment method. Simulation and physical testing demonstrate that compared with conventional methods, the proposed approach shows superior accuracy and precision in parameter estimation. It enables mission reliability assessment under practical operational testing constraints while providing methodological support to overcome the traditional assessment paradigm that overemphasizes performance verification while neglecting operational capability development. Full article
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