In football, attacking teams attempt to break through the opponent's defensive line to create scoring opportunities. This action, known as a Line Break, is a critical indicator of offensive effectiveness and tactical performance, yet previous studies have mainly focused on shots or goal opportunities rather than on how teams break the defensive line. In this study, we develop a machine learning model to predict Line Breaks using event and tracking data from the 2023 J1 League season. The model incorporates 189 features, including player positions, velocities, and spatial configurations, and employs an XGBoost classifier to estimate the probability of Line Breaks. The proposed model achieved high predictive accuracy, with an AUC of 0.982 and a Brier score of 0.015. Furthermore, SHAP analysis revealed that factors such as offensive player speed, gaps in the defensive line, and offensive players' spatial distributions significantly contribute to the occurrence of Line Breaks. Finally, we found a moderate positive correlation between the predicted probability of being Line-Broken and the number of shots and crosses conceded at the team level. These results suggest that Line Breaks are closely linked to the creation of scoring opportunities and provide a quantitative framework for understanding tactical dynamics in football.

Spatial transcriptomics measures the expression of thousands of genes in a tissue sample while preserving its spatial structure. This class of technologies has enabled the investigation of the spatial variation of gene expressions and their impact on specific biological processes. Identifying genes with similar expression profiles is of utmost importance, thus motivating the development of flexible methods leveraging spatial data structure to cluster genes. Here, we propose a modeling framework for clustering observations measured over numerous spatial locations via Gaussian processes. Rather than specifying their covariance kernels as a function of the spatial structure, we use it to inform a generalized Cholesky decomposition of their precision matrices. This approach prevents issues with kernel misspecification and facilitates the estimation of a non-stationarity spatial covariance structure. Applied to spatial transcriptomic data, our model identifies gene clusters with distinctive spatial correlation patterns across tissue areas comprising different cell types, like tumoral and stromal areas.

Zero-shot image anomaly classification (AC) and segmentation (AS) are vital for industrial quality control, detecting defects without prior training data. Existing representation-based methods compare patch features with nearest neighbors in unlabeled test images but struggle with consistent anomalies -- similar defects recurring across multiple images -- resulting in poor AC/AS performance. We introduce Consistent-Anomaly Detection Graph (CoDeGraph), a novel algorithm that identifies and filters consistent anomalies from similarity computations. Our key insight is that normal patches in industrial images show stable, gradually increasing similarity to other test images, while consistent-anomaly patches exhibit abrupt similarity spikes after exhausting a limited set of similar matches, a phenomenon we term ``neighbor-burnout.'' CoDeGraph constructs an image-level graph, with images as nodes and edges connecting those with shared consistent-anomaly patterns, using community detection to filter these anomalies. We provide a theoretical foundation using Extreme Value Theory to explain the effectiveness of our approach. Experiments on MVTec AD with the ViT-L-14-336 backbone achieve 98.3% AUROC for AC and AS performance of 66.8% (+4.2%) F1 and 68.1% (+5.4%) AP over state-of-the-art zero-shot methods. Using the DINOv2 backbone further improves segmentation, yielding 69.1% (+6.5%) F1 and 71.9% (+9.2%) AP, demonstrating robustness across architectures.

Digital representations of individuals ("digital twins") promise to transform social science and decision-making. Yet it remains unclear whether such twins truly mirror the people they emulate. We conducted 19 preregistered studies with a representative U.S. panel and their digital twins, each constructed from rich individual-level data, enabling direct comparisons between human and twin behavior across a wide range of domains and stimuli (including never-seen-before ones). Twins reproduced individual responses with 75% accuracy and seemingly low correlation with human answers (approximately 0.2). However, this apparently high accuracy was no higher than that achieved by generic personas based on demographics only. In contrast, correlation improved when twins incorporated detailed personal information, even outperforming traditional machine learning benchmarks that require additional data. Twins exhibited systematic strengths and weaknesses - performing better in social and personality domains, but worse in political ones - and were more accurate for participants with higher education, higher income, and moderate political views and religious attendance. Together, these findings delineate both the promise and the current limits of digital twins: they capture some relative differences among individuals but not yet the unique judgments of specific people. All data and code are publicly available to support the further development and evaluation of digital twin pipelines.

The Waymo Open Motion Dataset (WOMD) has become a popular resource for data-driven modeling of autonomous vehicles (AVs) behavior. However, its validity for behavioral analysis remains uncertain due to proprietary post-processing, the absence of error quantification, and the segmentation of trajectories into 20-second clips. This study examines whether WOMD accurately captures the dynamics and interactions observed in real-world AV operations. Leveraging an independently collected naturalistic dataset from Level 4 AV operations in Phoenix, Arizona (PHX), we perform comparative analyses across three representative urban driving scenarios: discharging at signalized intersections, car-following, and lane-changing behaviors. For the discharging analysis, headways are manually extracted from aerial video to ensure negligible measurement error. For the car-following and lane-changing cases, we apply the Simulation-Extrapolation (SIMEX) method to account for empirically estimated error in the PHX data and use Dynamic Time Warping (DTW) distances to quantify behavioral differences. Results across all scenarios consistently show that behavior in PHX falls outside the behavioral envelope of WOMD. Notably, WOMD underrepresents short headways and abrupt decelerations. These findings suggest that behavioral models calibrated solely on WOMD may systematically underestimate the variability, risk, and complexity of naturalistic driving. Caution is therefore warranted when using WOMD for behavior modeling without proper validation against independently collected data.

Neural density estimation has seen widespread applications in the gravitational-wave (GW) data analysis, which enables real-time parameter estimation for compact binary coalescences and enhances rapid inference for subsequent analysis such as population inference. In this work, we explore the application of using the Kolmogorov-Arnold network (KAN) to construct efficient and interpretable neural density estimators for lightweight posterior construction of GW catalogs. By replacing conventional activation functions with learnable splines, KAN achieves superior interpretability, higher accuracy, and greater parameter efficiency on related scientific tasks. Leveraging this feature, we propose a KAN-based neural density estimator, which ingests megabyte-scale GW posterior samples and compresses them into model weights of tens of kilobytes. Subsequently, analytic expressions requiring only several kilobytes can be further distilled from these neural network weights with minimal accuracy trade-off. In practice, GW posterior samples with fidelity can be regenerated rapidly using the model weights or analytic expressions for subsequent analysis. Our lightweight posterior construction strategy is expected to facilitate user-level data storage and transmission, paving a path for efficient analysis of numerous GW events in the next-generation GW detectors.

Estimating the causal effect of fertility on women's employment is challenging because fertility and labor decisions are jointly determined. The difficulty is amplified in low- and middle-income countries, where longitudinal data are scarce. In this study, we propose a novel approach to estimating the causal effect of fertility on employment using widely available Demographic and Health Survey (DHS) observational data. Using infecundity as an instrument for family size, our approach combines principal stratification with Bayesian Additive Regression Trees to flexibly account for covariate-dependent instrument validity, work with count-valued intermediate variables, and produce estimates of causal effects and effect heterogeneity, i.e., how effects vary with covariates in the survey population. We apply the approach to DHS data from Nigeria, Senegal, and Kenya. We find in the survey sample and general population that an additional child significantly reduces employment among women in Nigeria but has no clear average effect in Senegal or Kenya. Across all three countries, however, there is strong evidence of effect heterogeneity: younger, less-educated women experience large employment penalties, while older or more advantaged women are largely unaffected. Robustness checks confirm that these findings are not sensitive to key modeling assumptions. While limitations remain due to the cross-sectional nature of the DHS data, our results illustrate how flexible non-parametric models can uncover important effect variation.

In statistical process control Weibull distribution can be used to model the time between events or failures (TBE) in a process with increasing decreasing or constant failure rates. Specifically it helps in monitoring processes where the time between defect occurrences is of interest providing insight into the process reliability and performance. In this paper we consider the two sided problem of monitoring either an increase or a decrease in the scale parameter of the Weibull distribution with control charts assuming the shape parameter to be fixed. A larger scale parameter indicates that events are more spread out over time suggesting fewer defects while a smaller value may suggest deterioration in the process resulting in a higher number of defects. When the scale parameter is unknown it is estimated from Phase I observations and the plug in control limits are obtained by replacing the parameter by its estimated value from the Phase I observations. Given the well accepted fact that estimated control limits often do not perform as expected, the control limits of the Weibull chart are adjusted to achieve the desired in control (IC) performance using two criteria that are conditional average run length and standard deviation of conditional ARL. A performance study is carried out in order to assess in control and out of control performances of the proposed charts.

Understanding the distinction between causation and correlation is critical in Alzheimer's disease (AD) research, as it impacts diagnosis, treatment, and the identification of true disease drivers. This experiment investigates the relationships among clinical, cognitive, genetic, and biomarker features using a combination of correlation analysis, machine learning classification, and model interpretability techniques. Employing the XGBoost algorithm, we identified key features influencing AD classification, including cognitive scores and genetic risk factors. Correlation matrices revealed clusters of interrelated variables, while SHAP (SHapley Additive exPlanations) values provided detailed insights into feature contributions across disease stages. Our results highlight that strong correlations do not necessarily imply causation, emphasizing the need for careful interpretation of associative data. By integrating feature importance and interpretability with classical statistical analysis, this work lays groundwork for future causal inference studies aimed at uncovering true pathological mechanisms. Ultimately, distinguishing causal factors from correlated markers can lead to improved early diagnosis and targeted interventions for Alzheimer's disease.

The field of environmental epidemiology has placed an increasing emphasis on understanding the health effects of mixtures of metals, chemicals, and pollutants in recent years. Bayesian Kernel Machine Regression (BKMR) is a statistical method that has gained significant traction in environmental mixture studies due to its ability to account for complex non-linear relationships between the exposures and health outcome and its ability to identify interaction effects between the exposures. However, BKMR makes the crucial assumption that the error terms have a constant variance, and this assumption is not typically checked in practice. In this paper, we create a diagnostic function for checking this constant variance assumption in practice and develop Heteroscedastic BKMR (HBKMR) for environmental mixture analyses where this assumption is not met. By specifying a Bayesian hierarchical variance model for the error term variance parameters, HBKMR produces updated estimates of the environmental mixture's health effects and their corresponding 95% credible intervals. We apply HBKMR in two real-world case studies that motivated this work: 1) Examining the effects of prenatal metal exposures on behavioral problems in toddlers living in Suriname and 2) Assessing the impacts of metal exposures on simple reaction time in children living near coal-fired power plants in Kentucky. In both case studies, HBKMR provides a substantial improvement in model fit compared to BKMR, with differences in some of the mixture effect estimates and typically narrower 95% credible intervals after accounting for the heteroscedasticity.

Model-based clustering integrated with variable selection is a powerful tool for uncovering latent structures within complex data. However, its effectiveness is often hindered by challenges such as identifying relevant variables that define heterogeneous subgroups and handling data that are missing not at random, a prevalent issue in fields like transcriptomics. While several notable methods have been proposed to address these problems, they typically tackle each issue in isolation, thereby limiting their flexibility and adaptability. This paper introduces a unified framework designed to address these challenges simultaneously. Our approach incorporates a data-driven penalty matrix into penalized clustering to enable more flexible variable selection, along with a mechanism that explicitly models the relationship between missingness and latent class membership. We demonstrate that, under certain regularity conditions, the proposed framework achieves both asymptotic consistency and selection consistency, even in the presence of missing data. This unified strategy significantly enhances the capability and efficiency of model-based clustering, advancing methodologies for identifying informative variables that define homogeneous subgroups in the presence of complex missing data patterns. The performance of the framework, including its computational efficiency, is evaluated through simulations and demonstrated using both synthetic and real-world transcriptomic datasets.

Sample size calculation is crucial in biomedical in vivo research investigations mainly for two reasons: to design the most resource-efficient studies and to safeguard ethical issues when alive animals are subjects of testing. In this context, power analysis has been widely applied to compute the sample size by predetermining the desired statistical power and the significance level. To verify whether the assumption of a null hypothesis is true, repeated measures analysis of variance (ANOVA) is used to test the differences between multiple experimental groups and control group(s). In this article, we focus on the a priori power analysis, for testing multiple parameters and calculating the power of experimental designs, which is suitable to compute the sample size of trial groups in repeated measures ANOVA. We first describe repeated measures ANOVA and the statistical power from a practical aspect of biomedical research. Furthermore, we apply the G*Power software to conduct the a priori power analysis using examples of repeated measures ANOVA with three groups and five time points. We aim not to use the typical technically adapted statistical language. This will enable experimentalists to confidently formulate power calculation and sample size calculation easier and more accurately.

Conventional score-based diffusion models (DMs) may struggle with anisotropic Gaussian diffusion processes due to the required inversion of covariance matrices in the denoising score matching training objective \cite{vincent_connection_2011}. We propose Whitened Score (WS) diffusion models, a novel framework based on stochastic differential equations that learns the Whitened Score function instead of the standard score. This approach circumvents covariance inversion, extending score-based DMs by enabling stable training of DMs on arbitrary Gaussian forward noising processes. WS DMs establish equivalence with flow matching for arbitrary Gaussian noise, allow for tailored spectral inductive biases, and provide strong Bayesian priors for imaging inverse problems with structured noise. We experiment with a variety of computational imaging tasks using the CIFAR and CelebA ($64\times64$) datasets and demonstrate that WS diffusion priors trained on anisotropic Gaussian noising processes consistently outperform conventional diffusion priors based on isotropic Gaussian noise. Our code is open-sourced at \href{this https URL}{\texttt{github.com/jeffreyalido/wsdiffusion}}.

Recent advances in Structural Health Monitoring (SHM) have attracted industry interest, yet real-world applications, such as in ship structures remain scarce. Despite SHM's potential to optimise maintenance, its adoption in ships is limited due to the lack of clearly quantifiable benefits for hull maintenance. This study employs a Bayesian pre-posterior decision analysis to quantify the value of information (VoI) from SHM systems monitoring corrosion-induced thickness loss (CITL) in ship hulls, in a first-of-its-kind analysis for ship structures. We define decision-making consequence cost functions based on exceedance probabilities relative to a target CITL threshold, which can be set by the decision-maker. This introduces a practical aspect to our framework, that enables implicitly modelling the decision-maker's risk perception. We apply this framework to a large-scale, high-fidelity numerical model of a commercial vessel and examine the relative benefits of different CITL monitoring strategies, including strain-based SHM and traditional on-site inspections.

We live in a multivariate world, and effective modeling of financial portfolios, including their construction, allocation, forecasting, and risk analysis, simply is not possible without explicitly modeling the dependence structure of their assets. Dependence structure can drive portfolio results more than the combined effects of other parameters in investment and risk models, but the literature provides relatively little to define the finite-sample distributions of dependence measures in useable and useful ways under challenging, real-world financial data conditions. Yet this is exactly what is needed to make valid inferences about their estimates, and to use these inferences for essential purposes such as hypothesis testing, dynamic monitoring, realistic and granular scenario and reverse scenario analyses, and mitigating the effects of correlation breakdowns during market upheavals. This work develops a new and straightforward method, Nonparametric Angles-based Correlation (NAbC), for defining the finite-sample distributions of any dependence measure whose matrix of pairwise associations is positive definite (e.g. Pearsons, Kendalls, Spearmans, Tail Dependence Matrix, and others). The solution remains valid under marginal asset distributions characterized by notably different and varying degrees of serial correlation, non-stationarity, heavy-tailedness, and asymmetry. Importantly, NAbCs p-values and confidence intervals remain analytically consistent at both the matrix level and the pairwise cell level. Finally, NAbC maintains validity even when selected cells in the matrix are frozen for a given scenario or stress test, thus enabling flexible, granular, and realistic scenarios. NAbC stands alone in providing all of these capabilities simultaneously, and should prove to be a very useful means by which we can better understand and manage financial portfolios in our multivariate world.

Spatial transcriptomics has revolutionized tissue analysis by simultaneously mapping gene expression, spatial topography, and histological context across consecutive tissue sections, enabling systematic investigation of spatial heterogeneity. The detection of spatially variable (SV) genes-molecular signatures with position-dependent expression-provides critical insights into disease mechanisms spanning oncology, neurology, and cardiovascular research. Current methodologies, however, confront dual constraints: predominant reliance on predefined spatial pattern templates restricts detection of novel complex spatial architectures, and inconsistent sample selection strategies compromise analytical stability and biological interpretability. To overcome these challenges, we propose a novel Bayesian hierarchical framework incorporating non-parametric spatial modeling and across-sample integration. It takes advantage of the non-parametric technique and develops an adaptive spatial process accommodating complex pattern discovery. A novel cross-sample bi-level shrinkage prior is further introduced for robust multi-sample SV gene detection, facilitating more effective information fusion. An efficient variational inference is developed for posterior inference ensuring computational scalability. This architecture synergistically addresses spatial complexity through adaptive pattern learning while maintaining biological interpretability. Comprehensive simulations and empirical analyzes confirm the improved performance of the proposed method in resolving complex spatial expression patterns compared to existing analytical frameworks.