Stats

In this study, a procedure to build Bayesian optimal designs using utility functions and exploiting existing data is proposed. The procedure is illustrated through a case study in the field of reliability, by applying a hierarchical Bayesian model and performing Markov Chain Monte Carlo simulations. Two innovative contributions are introduced: (i) the definition of specific utility functions that involve several key issues and (ii) the use of observational data. The use of observational data makes it possible to build the optimal design without additional costs for the company, while the definition of the utility functions accounts for the specific characteristics of the reliability study. Features like model residuals, i.e., discrepancies between observed and predicted response values, and the costs of the electronic component are addressed. Costs are also weighted considering the environmental impact. Satisfactory results are obtained and subsequently validated through an in-depth sensitivity analysis. Full article

The two-parameter Birnbaum–Saunders (B-S) distribution is widely applied across various fields due to its favorable statistical properties. This study aims to enhance the efficiency of modified moment estimators for the B-S distribution by systematically incorporating auxiliary non-sample information. To this end, we developed and analyzed a suite of estimation strategies, including restricted estimators, preliminary test estimators, and Stein-type shrinkage estimators. A pretest procedure was formulated to guide the decision on whether to integrate the non-sample information. The relative performance of these estimators was rigorously evaluated through an asymptotic distributional analysis, comparing their asymptotic distributional bias and risk under a sequence of local alternatives. The finite-sample properties were assessed via Monte Carlo simulation studies. The practical utility of the proposed methods is demonstrated through applications to two real-world datasets: failure times for mechanical valves and bone mineral density measurements. Both numerical results and theoretical analysis confirm that the proposed shrinkage-based techniques deliver substantial efficiency gains over conventional estimators. Full article

This study focuses on forecasting and optimizing the performance of a real-world object modelled by a multi-server queueing system that processes two types of users: primary (new) users and repeating users. The repeating users are those who succeeded in entering processing upon arrival and then decided to repeat it. These users have privilege and can enter processing when they wish once at least one device is idle. The primary user is admitted to the system only if the number of occupied devices is less than some threshold value and the quantity of repeating users residing in the system does not exceed certain thresholds. Repeating users are impatient and non-persistent. Arrivals of primary users are described by the Markovian arrival process. Processing times of primary and repeating users have distinct phase-type distributions. Utilizing the concept of the generalized phase–time distributions, the dynamics of this queueing system are formally characterized by the multidimensional Markov chain, which is examined in this paper. The ergodicity condition is derived. The relation of the key performance characteristics of the system and the thresholds defining the policy of the primary user’s admission is numerically highlighted. Optimal threshold selection is demonstrated numerically. Full article

Our new Theoretically Dynamic Regression (TDR) modeling methodology was recently applied in three types of real data modeling cases using physically based dynamic model structures with low-order linear regression static functions. Two of the modeling cases achieved the validation set modeling goal of $r_{fit,val} \ge 0.9$. However, the third case, consisting of eleven (11) type one (1) sensor glucose data sets, and thus, eleven individual models, all fail considerably short of this modeling goal and the average $r_{fit,val}$, ${\overline{r}}_{fit,val}$ = 0.68. For this case, the dynamic forms are highly complex 60 min forecast, second-order-plus-dead-time-plus-lead (SOPDTPL) structures, and the static form is a twelve (12) input first-order linear regression structure. Using these dynamic structure results, the objective is to significantly increase $r_{fit}$ for each of the eleven (11) modeling cases using the recently developed Wiener-Physically-Informed-Neural-Network (W-PINN) approach as the static modeling structure. Two W-PINN stage-two static structures are evaluated–one developed using the JMP® Pro Version 16, Artificial Neural Network (ANN) toolbox and the other developed using a novel ANN methodology coded in Python version, 3.12.3. The JMP ${\overline{r}}_{fit,val}$ = 0.74 with a maximum of 0.84. The Python ${\overline{r}}_{fit,val}$ = 0.82 with a maximum of 0.93. Incorporating bias correction, using current and past SGC residuals, the Python estimator improved the average ${\overline{r}}_{fit,val}$ from 0.82 to 0.87 with the maximum still 0.93. Full article

This article investigates the probabilistic relationship between quantum classification of Boolean functions and their Hamming distance. By integrating concepts from quantum computing, information theory, and combinatorics, we explore how Hamming distance serves as a metric for analyzing deviations in function classification. Our extensive experimental results confirm that the Hamming distance is a pivotal metric for validating nearest neighbors in the process of classifying random functions. One of the significant conclusions we arrived is that the successful classification probability decreases monotonically with the Hamming distance. However, key exceptions were found in specific classes, revealing intra-class heterogeneity. We have established that these deviations are not random but are systemic and predictable. Furthermore, we were able to quantify these irregularities, turning potential errors into manageable phenomena. The most important novelty of this work is the demarcation, for the first time to the best of our knowledge, of precise Hamming distance intervals for the classification probability. These intervals bound the possible values the probability can assume, and provide a new foundational tool for probabilistic assessment in quantum classification. Practitioners can now endorse classification results with high certainty or dismiss them with confidence. This framework can significantly enhance any quantum classification algorithm’s reliability and decision-making capability. Full article

The single-cell spatial transcriptomics (ST) data with cell type and spatial location, i.e., $(C,x,y)$ with C as cell type and $(x,y)$ as its spatial location, produced by recent biotechnologies, such as CosMx and Xenium, contain a huge amount of information about cancer tissue samples, thus have great potential for cancer research via detection of ST-Community which is defined as a collection of cells with distinct cell-type composition and similar neighboring patterns based on nearby cell-percentages. But for huge CosMx single-cell ST data, the existing clustering methods do not work well for st-community detection, and the commonly used kNN compositional data method shows lack of informative neighboring cell patterns. In this article, we propose a novel and more informative disk compositional data (DCD) method for single-cell ST data, which identifies neighboring patterns of each cell via taking into account of ST data features from recent new technologies. After initial processing single-cell ST data into the DCD matrix, an innovative DCD-TMHC computation method for st-community detection is proposed here. Extensive simulation studies and the analysis of CosMx breast cancer data, which is an example of single-cell ST dataset, clearly show that our proposed DCD-TMHC computation method is superior to other existing methods. Based on the st-communities detected for CosMx breast cancer data, the logistic regression analysis results demonstrate that the proposed DCD-TMHC computation method produces better interpretable and superior outcomes, especially in terms of assessment for different cancer categories. These suggest that our proposed novel and informative DCD-TMHC computation method here will be helpful and have an impact on future cancer research based on single-cell ST data, which can improve cancer diagnosis and monitor cancer treatment progress. Full article

This study investigates the derivation of optimal repeated measurement designs of two treatments, five periods, and n experimental units for carryover effects. The optimal designs are determined for cases where n = 0, 1 (mod 2). The adopted optimality criterion focuses on minimizing the variance of the estimated carryover effect, thereby ensuring maximum precision in parameter estimation and design efficiency. The results presented here extend and complement earlier research of Chalikias and Kounias on optimal two-treatment repeated measurement designs for a smaller number of periods, and are closely related to the more recent findings on optimal designs for direct effects. Overall, the present work contributes to the theoretical framework of optimal design methodology by providing new insights into the structure and efficiency of repeated measurement designs, particularly in the presence of carryover effects, and sets the ground for future extensions incorporating treatment–period interactions. Full article

The Rician distribution, which arises in radar, communications, and magnetic resonance imaging, is characterized by a noncentrality parameter and a scale parameter. The Rayleigh distribution is a special case of the Rician distribution with a noncentrality parameter of zero. This paper considers generalized hypothesis testing for Rayleigh and Rician distributions using Rissanen’s stochastic complexity, particularly his approximation employing Fisher information matrices. The Rayleigh distribution is a member of the exponential family, so its normalized maximum likelihood density is readily computed, and shown to asymptotically match the Fisher information approximation. Since the Rician distribution is not a member of the exponential family, its normalizing term is difficult to compute directly, so the Fisher information approximation is employed. Because the square root of the determinant of the Fisher information matrix is not integrable, we restrict the integral to a subset of its range, and separately encode the choice of subset. Full article

When determining subgroups with heterogeneous treatment effects in cancer clinical trials, the threshold of a variable that defines subgroups is often pre-determined by physicians based on their experience, and the optimality of the threshold is not well studied, particularly when the mixture cure rate model is considered. We propose a mixture cure model that allows optimal subgroups to be estimated for both the time to event for uncured subjects and the cure status. We develop a smoothed maximum likelihood method for the estimation of model parameters. An extensive simulation study shows that the proposed smoothed maximum likelihood method provides accurate estimates. Finally, the proposed mixture cure model is applied to a colon cancer study to evaluate the potential differences in the treatment effect of levamisole plus fluorouracil therapy versus levamisole alone therapy between younger and older patients. The model suggests that the difference in the treatment effect on the time to cancer recurrence for uncured patients is significant between patients younger than 67 and patients older than 67, and the younger patient group benefits more from the combined therapy than the older patient group. Full article

In the presence of multicollinearity, the ordinary least squares (OLS) estimators, aside from BLUE (best linear unbiased estimator), lose efficiency and fail to achieve minimum variance. In addition, these estimators are highly sensitive to outliers in the response direction. To overcome these limitations, robust estimation techniques are often integrated with shrinkage methods. This study proposes a new class of Kibria Ridge M-estimators specifically developed to simultaneously address multicollinearity and outlier contamination. A comprehensive Monte Carlo simulation study is conducted to evaluate the performance of the proposed and existing estimators. Based on the mean squared error criterion, the proposed Kibria Ridge M-estimators consistently outperform the traditional ridge-type estimators under varying parameter settings. Furthermore, the practical applicability and superiority of the proposed estimators are validated using the Tobacco and Anthropometric datasets. Overall, the new proposed estimators demonstrate good performance, offering robust and efficient alternatives for regression modeling in the presence of multicollinearity and outliers. Full article

In this work, we develop and investigate statistical extensions of gauge integrability and gauge summability for double sequences of functions of two real variables, formulated within the framework of deferred weighted means. We begin by establishing several fundamental limit theorems that serve to connect these generalized notions and provide a rigorous theoretical foundation. Based on these results, we establish Korovkin-type approximation theorems using the classical test function set $1,s,t,s^2+t^2$ in the Banach space $\mathcal{C}\left({[0,1]}^2\right)$. To demonstrate the applicability of the proposed framework, we further present an example involving families of positive linear operators associated with the Meyer-König and Zeller (MKZ) operators. These findings not only extend classical Korovkin-type theorems to the setting of statistical deferred gauge integrability and summability but also underscore their robustness in addressing double sequences and the approximation of two-variable functions. Full article

The asymptotic limit theorems of information and control theories, instantiated as the Rate Distortion Control Theory of bounded rationality, enable examination of stability across models of cognition based on a variety of fundamental, underlying probability distributions likely to characterize different forms of embodied ‘intelligent’ systems. Embodied cognition is inherently unstable, requiring the pairing of cognition with regulation at and across the various and varied scales and levels of organization. Like contemporary Large Language Model ‘hallucination,’ de facto ‘psychopathology’—the failure of regulation in systems of cognitive modules—is not a bug but an inherent feature of embodied cognition. What particularly emerges from this analysis, then, is the ubiquity of failure-under-stress even for ‘intelligent’ embodied cognition, where cognitive and regulatory modules are closely paired. There is still No Free Lunch, much in the classic sense of Wolpert and Macready. With some further effort, the probability models developed here can be transformed into robust statistical tools for the analysis of observational and experimental data regarding regulated and other cognitive phenomena. Full article

This article provides a critical assessment of the Birnbaum–Saunders (BS) distribution, a pivotal statistical model for lifetime data analysis and reliability estimation, particularly in fatigue contexts. The model has seen successfully applied across diverse fields, including biological mortality, environmental sciences, medicine, and risk models. Moving beyond a basic scientometric review, this study synthesizes findings from 353 peer-reviewed articles, selected using PRISMA 2020 protocols, to specifically trace the evolution of estimation techniques, regression methods, and model extensions. Key findings reveal robust theoretical advances, such as Bayesian methods and bivariate/spatial adaptations, alongside practical progress in influence diagnostics and software development. The analysis highlights key research gaps, including the critical need for scalable, auditable software and structured reviews, and notes a peak in scholarly activity around 2019, driven importantly by the Brazil-Chile research alliance. This work offers a consolidated view of current BS model implementations and outlines clear future directions for enhancing their theoretical robustness and practical utility. Full article

The optimal allocation of funds within a portfolio is a central research focus in finance. Conventional mean-variance models often concentrate a significant portion of funds in a limited number of high-risk assets. To promote diversification, Shannon Entropy is widely applied. This paper develops a portfolio optimization model that incorporates Shannon Entropy alongside a risk diversification principle aimed at minimizing the maximum individual asset risk. The study combines empirical analysis with numerical simulations. First, empirical data are used to assess the theoretical model’s effectiveness and practicality. Second, numerical simulations are conducted to analyze portfolio performance under extreme market scenarios. Specifically, the numerical results indicate that for fixed values of the risk balance coefficient and minimum expected return, the optimal portfolios and their return distributions are similar when the risk is measured by standard deviation, absolute deviation, or standard lower semi-deviation. This suggests that the model exhibits robustness to variations in the risk function, providing a relatively stable investment strategy. Full article

Background: Health disparities research increasingly relies on complex survey data to understand survival differences between population subgroups. While Peters–Belson decomposition provides a principled framework for distinguishing disparities explained by measured covariates from unexplained residual differences, traditional approaches face challenges with complex data patterns and model validation for counterfactual estimation. Objective: To develop validated Peters–Belson decomposition methods for survival analysis that integrate ensemble machine learning with transfer learning while ensuring logical validity of counterfactual estimates through comprehensive model validation. Methods: We extend the traditional Peters–Belson framework through ensemble machine learning that combines Cox proportional hazards models, cross-validated random survival forests, and regularized gradient boosting approaches. Our framework incorporates a transfer learning component via principal component analysis (PCA) to discover shared latent factors between majority and minority groups. We note that this “transfer learning” differs from the standard machine learning definition (pre-trained models or domain adaptation); here, we use the term in its statistical sense to describe the transfer of covariate structure information from the pooled population to identify group-level latent factors. We develop a comprehensive validation framework that ensures Peters–Belson logical bounds compliance, preventing mathematical violations in counterfactual estimates. The approach is evaluated through simulation studies across five realistic health disparity scenarios using stratified complex survey designs. Results: Simulation studies demonstrate that validated ensemble methods achieve superior performance compared to individual models (proportion explained: 0.352 vs. 0.310 for individual Cox, 0.325 for individual random forests), with validation framework reducing logical violations from 34.7% to 2.1% of cases. Transfer learning provides additional 16.1% average improvement in explanation of unexplained disparity when significant unmeasured confounding exists, with 90.1% overall validation success rate. The validation framework ensures explanation proportions remain within realistic bounds while maintaining computational efficiency with 31% overhead for validation procedures. Conclusions: Validated ensemble machine learning provides substantial advantages for Peters–Belson decomposition when combined with proper model validation. Transfer learning offers conditional benefits for capturing unmeasured group-level factors while preventing mathematical violations common in standard approaches. The framework demonstrates that realistic health disparity patterns show 25–35% of differences explained by measured factors, providing actionable targets for reducing health inequities. Full article

The paper shows an alternative perspective of the reduced chi-square as a measure of the goodness of fitting methods. The reduced chi-square is given by the ratio of the fitting over the propagation errors, that is, a universal relationship that holds for any linearity, but not for a nonlinearly parameterized fitting model. We begin by providing the proof for the traditional examples of one-parametric fitting of a constant and the bi-parametric fitting of a linear model, and then, for the general case of any linearly multi-parameterized model. We also show that this characterization is not generally true for nonlinearly parameterized fitting. Finally, we demonstrate these theoretical developments with an application in real data from the plasma protons in the heliosphere. Full article

This article presents biplots derived from factor analysis of correlation matrices for both continuous and ordinal data. It introduces biplots specifically designed for factor analysis, detailing the geometric interpretation for each data type and providing an algorithm to compute biplot coordinates from the factorization of correlation matrices. The theoretical developments are illustrated using a real dataset that explores the relationship between volunteering, political ideology, and civic engagement in Spain. Full article

We developed a class of bivariate integer-valued time series models using copula theory. Each count time series is modeled as a Markov chain, with serial dependence characterized through copula-based transition probabilities for Poisson and Negative Binomial marginals. Cross-sectional dependence is modeled via a bivariate Gaussian copula, allowing for both positive and negative correlations and providing a flexible dependence structure. Model parameters are estimated using likelihood-based inference, where the bivariate Gaussian copula integral is evaluated through standard randomized Monte Carlo methods. The proposed approach is illustrated through an application to offense data from New South Wales, Australia, demonstrating its effectiveness in capturing complex dependence patterns. Full article

In an infinite-/super-population (SP) setup, regression analysis of longitudinal data, which involves repeated responses and covariates collected from a sample of independent individuals or correlated individuals belonging to a cluster such as a household/family, has been intensively studied in the statistics literature over the last three decades. In general, a longitudinal, such as an auto-correlation structure for repeated responses for an individual or a two-way cluster–longitudinal correlation structure for repeated responses from the individuals belonging to a cluster/household, are exploited to obtain consistent and efficient regression estimates. However, as opposed to the SP setup, a similar regression analysis for a finite population (FP)-based longitudinal or clustered longitudinal data using a survey sample (SS) taken from the FP-based on a suitable sampling design becomes complex, which requires first defining the FP regression and correlation (both longitudinal and/or clustered) parameters and then estimating them using appropriate sampling weighted-design unbiased (SWDU) estimating equations. The finite sampling inferences, such as predictions of longitudinal changes in FP totals, would become much more complex, meaning that it would be necessary to predict the non-sampled totals after accommodating the longitudinal and/or clustered longitudinal correlation structures. Our objective in this paper is to deal with this complex FP prediction inference by developing a design cum model (DCM)-based estimation approach. Two competitive FP total predictors, namely design-assisted model-based (DAMB) and design cum model-based (DCMB) predictors are compared using an intensive simulation study. The regression and correlation parameters involved in these prediction functions are optimally estimated using the proposed DCM-based approach. Full article