Papers

Standard industry classification systems such as GICS assign each firm to a single sector, but the economic relationships through which shocks propagate, such as supplier agreements, customer concentration, intellectual property licensing, cloud service dependencies, and power purchase contracts frequently cross sector boundaries and are often disclosed only in unstructured text. We formulate the construction of a firm-level adjacency matrix as a measurement problem and propose an LLM based pipeline that extracts a weighted, directed, point in time corporate network from public disclosures. Applied to the most recent 10 K and 10 K filings of 42 Nasdaq 100 constituents, the proposed pipeline produces a network containing 149 directed edges. An adversarial audit confirms 88% of sampled edges with weights of at least 0.1, increasing to 100% when economically plausible but weakly documented relationships are included. Refuted edges are concentrated entirely in the lowest-weight portion of the network. The resulting network is consistent with GICS where sector classifications are informative, exhibiting a 1.9-fold increase in within-sector connectivity, while also recovering economically meaningful cross-sector relationships that standard classifications cannot represent. Examples include nuclear power-purchase agreements connecting utilities with hyper scale technology firms and GPU-cloud dependencies within the emerging AI infrastructure ecosystem. Ablation studies further demonstrate that multi-agent fusion, inverse-document-frequency filtering, and relative thresholding each make measurable contributions to network quality.

In this paper, we propose a new thresholding technique for detecting anomalies in multivariate normal random samples, under the assumption that anomalous observations are sparse and differ from the rest of the data in their mean. The mean vector of the non-anomalous data is assumed to be zero, while the covariance matrix is unknown. We derive conditions on the mean shift of the anomalous observations, as well as on the covariance matrix and its estimator, under which the proposed procedure achieves asymptotically exact detection, meaning that the expected number of misclassified observations converges to zero as the sample size increases. In addition, we establish conditions under which exact anomaly detection is impossible for any procedure. The performance of the proposed method is illustrated through an extensive simulation study and compared with other widely used anomaly detection methods. Real-data analyses involving wearable activity measurements and air pollution time series provide an assessment of its performance in real-world settings.

Predictive models deployed at scale influence future data, a phenomenon called performativity. And there is always one way to cope: Train the model on new data, deploy it again, and repeat. This process, called retraining or repeated risk minimization, creates a feedback loop between model and data that real-world learning systems can't avoid. Results on performative prediction shed light on this dynamic: If the model's influence on the data is small, retraining reaches a fixed point. What remains open is why fixed points should naturally exist, and what governs retraining when the model's influence is strong. In this work we develop a new perspective on retraining – the stable signal principle – that addresses these questions. We start from the assumption that the prediction target has at least some small model-independent component, a stable signal, such as the intrinsic quality of an item. We prove that when a nonzero stable signal exists, repeated risk minimization, suitably regularized, converges geometrically to the direction of this stable signal. This is true even if the model's influence on the target is arbitrarily large relative to the stable signal. Regularization emerges naturally as a force to control performativity, rather than to promote generalization, revealing a new facet of an old concept. We extend the analysis to a broad family of affine retraining operators under arbitrary model-induced feature changes, heterogeneous time-varying effects, and nonlinear responses. The stable signal perspective also applies to data feedback loops in language modeling, providing new explanations for the stability of language model training from model-generated data.

Hallucinations and artificial text in LLM-generated outputs often appear as distributional deviations between prompt and response hidden-state distributions. Since prompts or retrieved contexts typically serve as reference samples and responses as query samples, with major differences in length, these asymmetries motivate the use of change test statistics that treat the two samples differently. We consider an asymmetric two-sample test ASK-NN based on the directed k-nearest-neighbor graph. Our statistic counts reference points whose nearest neighbor in the pooled sample is also a reference point. Under the permutation null, it admits an exact finite-sample conditional mean and variance; we further establish asymptotic normality and consistency under fixed alternatives. ASK-NN is computationally effective and easy to implement. Empirically, it is competitive with kernel and graph-based baselines on synthetic benchmarks, artificial-text detection, and LLM hallucination detection from token-level hidden states.

Synthetic sequential tabular data are increasingly used for privacy-preserving data sharing and research, yet conventional tabular metrics often overlook temporal structure. Existing single-table and relational evaluation protocols largely collapse records into static distributions, leaving key temporal properties insufficiently evaluated. We introduce Seq2Synth, a unified benchmark for assessing these properties. Its taxonomy characterizes temporal and schema properties to determine applicable evaluations, covering timestamp, cross-sectional, longitudinal, and structural fidelity, alongside trajectory-aware utility and privacy. Across seven core datasets from a 13-dataset benchmark and eight generators, models with near-perfect static fidelity still violate basic temporal constraints, producing duplicate timestamps, irregular intervals, and incomplete observation grids. Moreover, static and temporal-aware rankings diverge substantially, showing that temporal fidelity must be evaluated directly rather than inferred from static or relational scores. Project page and online appendices are available at: https://seq2synth.github.io/.

Binary Iterative Hard Thresholding (BIHT) is a simple, yet effective, greedy method for recovering a sparse vector from one-bit sign measurements. In its original form, BIHT performs a “gradient-descent” step, followed by hard thresholding. A convergence analysis of this algorithm was left open in the introductory work of Jacques, Laska, Boufounos, and Baraniuk [IEEE Trans. Inform. Theory (2013)] and has remained unresolved for over a decade, with subsequent sharp analyses studying a normalized variant instead, that additionally projects every iterate onto the unit sphere. This paper resolves that gap and characterizes when per-iteration normalization is algorithmically necessary. In the noiseless setting, we prove a universal, sample-optimal convergence theorem for the original BIHT algorithm. Specifically, with $\widetilde O(s/\epsilon)$ measurements, a deterministic, computable finite-time iterate has directional error at most $\epsilon$, simultaneously for every $s$-sparse unit vector. This matches the optimal sample dependence achieved by normalized BIHT in prior work. Under sign corruptions, we prove a sharp separation. If at most a $\tau$ fraction of signs are flipped adversarially, then BIHT, without per-iterate normalization, still reaches the robust error floor at an early iterate with a matching $\widetilde O(s/\epsilon)$ sample complexity rate as its normalized variant. This recovery, however, is not stable. We prove a scalar lower bound showing that any nontrivial corruption pattern, even one that involves only one flipped sign together with one clean sign, forces the iterates to oscillate indefinitely. Consequently, no general last-iterate convergence theorem can hold for BIHT under sign corruptions, while its normalized surrogate provably escapes this instance.

The random-intercept cross-lagged panel model (RI-CLPM) is widely used to separate stable between-person differences from within-person dynamics. Yet fitting an RI-CLPM does not guarantee that the data can support meaningful within-person inference. We introduce the concept of RI-CLPM readiness, defined by measurement comparability and diagnostic sensitivity. Using Monte Carlo simulations with powRICLPM, we show that power to detect within-person cross-lagged effects depends jointly on reliability, ICC, number of waves, sample size, and target effect size; high ICC, modest reliability, and few waves can substantially reduce power even in large samples. We then review reporting practices in 186 empirical RI-CLPM applications. Many studies reported sample size, wave count, and reliability, but longitudinal measurement invariance, ICC or within-person variance, and sensitivity analyses were reported much less consistently. Null within-person paths were common but often interpreted without sufficient attention to diagnostic sensitivity. We argue that RI-CLPM results should be interpreted conditionally on data readiness and offer practical reporting recommendations.

We show how, associated with any decision problem, we may derive related functions measuring uncertainty, discrepancy and dependence of distributions. Such "coherent" functions have special properties, which we characterise, and each function essentially determines the others. The theory is applied to the Bayesian formulation of the problem of choosing an experiment in order to make a subsequent prediction. It is shown that coherent choice criteria may be based on any of the coherent functions, with related functions yielding identical solutions.

Binary logistic regression is among the most widely used classification algorithms, yet a classifier is only trustworthy if its predicted probabilities are well calibrated. The classical checks – the Pearson chi-square and deviance statistics – break down precisely in the modern setting where predictors are continuous and the data are sparse (one covariate pattern per observation). Four decades of research have produced dozens of alternative goodness-of-fit and calibration algorithms, yet practitioners still default to the Hosmer-Lemeshow test because it ships with their software. This paper provides a unified taxonomy and a large-scale, reproducible simulation benchmark; more than twenty tests are implemented in the open-source R package ebrahim.gof. We evaluate them across five covariate distributions and four misspecification scenarios, with 10,000 replications each, measuring both Type I error and power. Several classical tests prove liberal, rejecting correct models far too often, while others have little power. A compact core – McCullagh, Osius-Rojek, le Cessie-van Houwelingen, Stute-Zhu, and the GiViTI calibration test – delivers the best balance of correct size and high power, and is consistently more powerful than the ubiquitous Hosmer-Lemeshow test. A low-birth-weight application reinforces the point: a model with omitted interactions slips past nearly every test, exposed only by pairing sensitive tests with a calibration (reliability) curve. We translate these findings into practical, evidence-based guidance for assessing logistic regression fit.

Multiple-try Metropolis (MTM) is a Markov chain Monte Carlo (MCMC) algorithm that improves local transition efficiency by evaluating multiple candidate draws at each iteration. However, for complicated target distributions exhibiting severely non-Gaussian topography or multiple well-separated modes, locally optimal transitions may be insufficient for effective global exploration. In this work, we propose compound auxiliary Metropolis (CAM), a general multi-candidate MCMC method that incorporates both the local state of the chain and auxiliary information into the multi-candidate framework of MTM. Using an auxiliary generating distribution, CAM accommodates a flexible definition of auxiliary information. As examples, we consider three different auxiliary variables: one that promotes state-independent exploration and two that use a reference distribution to improve mixing. These auxiliaries are tested against distributions that present challenging targets for modern MCMC methods. In particular, we focus on the challenges presented by multiple well-separated modes and topography that requires long mixing for local MCMC moves. We find that CAM is able to sample effectively from these distributions, using MTM as a baseline to evaluate the benefit introduced by the auxiliary information. CAM also compares favourably with the No-U-Turn Sampler, showing similar performance for milder test distributions and better performance for the most difficult settings.

Score-based generative models exhibit a puzzling behavior: they often appear to cover all modes of a target multimodal distribution and yet may fail to learn the correct relative mode amplitudes, which can be interpreted as mixture weights. We resolve this apparent paradox by relating the diffusion score matching (DSM) loss to the error in estimating mixture weights from generated samples. We show that, even when the target score is insensitive to mixture weights, generated samples can recover the weights accurately if the scores at intermediate noise levels are informative about the weights. Accordingly, we define the diffusion score sensitivity index (DSSI) as the variation in the DSM loss relative to changes in a parameter. We then show that the DSSI governs the accuracy with which the parameter of the target distribution can be estimated from generated samples. For Gaussian mixtures in arbitrary dimensions, we prove that the mixture weight estimation errors are on the same order as the DSM loss under mild conditions. Empirically, we show the emergence of sensitivity during the noising process of benchmark data distributions under typical noise schedules, and that these sensitivity values predict how well a well-trained model recovers mixture weights. Furthermore, we show that the choice of noise schedule can reduce diffusion sensitivity, leading to mode amplification. Although we focus on mixture weights, the proposed sensitivity framework governs the recovery of any qualitative parameter of the target distribution.

Researchers increasingly use automated classifiers to label unstructured data for statistical analysis. Existing rectification methods can correct errors in these automated labels using a probability-sampled audit set, but they usually treat the audit labels as correct. In practice, human audit labels are often noisy, and only some audited items are reviewed by an expert or adjudicator. We propose Partially Adjudicated Design-Based Supervised Learning (PA-DSL), a method for this setting. It uses adjudicated cases to correct noisy human labels and then uses the corrected audit information to debias analyses based on the full set of automated labels. The estimator is valid for a broad class of downstream analyses when the audit and adjudication probabilities are known. In synthetic and Wikipedia Detox semi-synthetic experiments, PA-DSL maintains nominal coverage and reduces RMSE by 10-17% relative to using only adjudicated labels when noisy human labels contain recoverable signal.

The Hosmer-Lemeshow test is the routine check of fit for logistic regression, yet it is weak against a wrong link, and the directed tests that are stronger lose their level when a single covariate is recorded in error. We apply Farrington's correction to its risk groups, which removes the single-record terms of the statistic and keeps the within-group products of residuals. The result is the score test for records of similar fitted risk sharing a miscalibration: locally most powerful against a smooth misfit in either direction, and as robust to gross errors as the Hosmer-Lemeshow test. One alignment functional, mapped in advance for asymmetric links, decides when it is more powerful than the Hosmer-Lemeshow test, at second order with ten groups and at first order with many. For the many groups of large samples, normal limits for both statistics correct the chi-squared reference of the widely used grouping rule of Paul and colleagues, under which the Hosmer-Lemeshow test reached a size of 12% or lost all its power, and they explain why that rule hid a clear misfit in 8873 SUPPORT patients that groups of 25 records detected. In pre-registered simulations, one gross covariate error in a thousand records raised the false-alarm rates of Stukel's, the cubic calibration and the GiViTI tests to 25-39%, while the risk-grouped tests stayed near 5%; among these, the corrected test was the most powerful in all 34 settings with negative alignment and a visible difference. The test is in the R package ebrahim.gof.

Self-distillation (SD) is typically studied when the student is retrained on the teacher's original training inputs. In many practical deployments, however, the labeled training data are no longer available, and one has access only to the trained predictor and fresh unlabeled covariates. We study SD in this prediction-only regime through a fresh-X prediction-mixed scheme: a pure-distilled student is trained on fresh covariates pseudo-labeled by the teacher, and the final predictor is an affine combination of the teacher and student predictions. For ridge regression under proportional asymptotics, we derive deterministic equivalents for the optimally mixed prediction risk under general anisotropic covariance and deterministic signal. We show that this risk is strictly smaller than the teacher risk for almost every pair of teacher and student regularization levels, including when the fresh covariates are out-of-distribution and even when their covariance is isotropic. We further show that the optimal mixing weight cannot be identified from unlabeled data alone, but can be consistently estimated in a single post-training step using a small independent labeled calibration set, without additional model fitting. Finally, for binary logistic regression, we show that prediction mixing can outperform both the teacher and the pure-distilled classifier.

Emergency department (ED) boarding occurs when admitted patients remain in the ED while awaiting inpatient beds. Boarding is a major driver of ED crowding and has been associated with poor patient outcomes. We propose a framework to help EDs reduce boarding time and length of stay by using information about current patients and bed availability to proactively request inpatient beds before admission decisions are finalized. We formulate the problem as a Markov decision process in which predictions of each patient's admission probability and time to disposition are aggregated to guide early inpatient bed requests. This formulation leads to three data-driven policies based on approximate dynamic programming, reinforcement learning, and a newsvendor-type approach. Using a simulation model based on data from a large ED, we evaluate these policies across a wide range of settings. The simulation study shows that proactive aggregate bed requests can reduce average boarding times for admitted patients by 30-70% and average length of stay for all ED patients by 6-15%, while creating only modest idle time for prepared inpatient beds. The newsvendor heuristic provides the most attractive tradeoff between ED performance and inpatient bed idle time, whereas the reinforcement learning heuristic produces smoother bed-request patterns when stability in downstream hospital processes is especially important. Our work shows how EDs can use prediction tools to make proactive bed-request decisions that improve ED operations while helping managers balance reductions in ED delays against inpatient bed idle time. Our findings also illustrate the value of evaluating both simple myopic heuristics and more sophisticated reinforcement learning-based approaches, since each can offer distinct advantages depending on the performance measures and implementation constraints most important to managers.

In this paper, we propose to design, develop, and implement the new DMAIC methodology for Six-Sigma quality management of AM. First, we define the specific quality challenges arising from AM layer-wise fabrication and mass customization (even one-of-a-kind production). Second, we present a review of AM metrology and sensing techniques, from materials through design, process, environment, to post-build inspection. Third, we contextualize a framework for realizing the full potential of data from AM systems, and emphasize the need for analytical methods and tools. We propose and delineate the utility of new data-driven analytical methods, including deep learning, machine learning, and network science, to characterize and model the interrelationships between engineering design, machine setting, process variability and final build quality. Fourth, we present the methodologies of ontology analytics, design of experiments (DOE) and simulation analysis for AM system improvements. In closing, new process control approaches are discussed to optimize the action plans, once an anomaly is detected, with specific consideration of lead time and energy consumption.

Online change point detection is the process of identifying distributional changes in time-ordered data in real time. In applications such as mobile health (mHealth), repeated testing is often performed as new data arrive, creating a multiple testing problem. Traditional approaches for controlling the family-wise error rate (FWER) are not well suited to this setting because the tests are highly dependent and the number of tests is not fixed in advance. In this work, we introduce a sequential family-wise error rate (sFWER), defined as the probability of at least one false positive within a moving monitoring window. We propose a simulation-based calibration procedure to estimate monitoring thresholds that control the sFWER at a desired level. Through simulation studies, we demonstrate that the proposed procedure achieves the desired error control, while commonly used alternatives are either overly conservative or fail to adequately control false alarms. Finally, we illustrate the proposed approach using passively collected smartphone data from a cohort of adolescents and young adults with affective instability.

We develop data-driven algorithms for maintaining $N$ independent identical machines under a block replacement policy, in which each machine is replaced upon failure and all machines are jointly replaced at regular intervals of length $k$. The goal is to learn the cost-minimizing interval $k^*$ from operational data when the lifetime distribution is unknown. At each decision epoch, the operator selects $k \in \{1, 2, \ldots, K\}$, observes the resulting failure history (a mixture of complete and right-censored lifetimes) and incurs a per-unit-time cost governed by the renewal function. We formulate this as a stochastic multi-armed bandit and propose Hoeffding- and Bernstein-based lower-confidence-bound algorithms achieving $O(K \log T)$ regret, matching the Lai–Robbins lower bound. Exploiting a nested observation property unique to block replacement, correlated variants attain $O((K-k^*)\log T)$ regret and require only $O(1)$ direct pulls of suboptimal arms $k < k^*$. A complementary Kaplan–Meier renewal algorithm estimates the lifetime distribution nonparametrically from censored data, achieving almost-sure policy consistency and empirically near-zero incremental regret at long horizons. We additionally analyze two average-cost MDPs: a time-elapsed formulation establishing that block replacement is optimal within its policy class for any lifetime distribution, and an age-vector formulation proving a monotone threshold structure under increasing failure rate distributions and providing a gold-standard cost benchmark. Numerical experiments confirm the theoretical ordering and reveal structural cost gaps between optimal block and age-dependent replacement.

Unadjusted samplers such as unadjusted Hamiltonian Monte Carlo and underdamped Langevin are well-known to be biased. Metropolis–Hastings adjustment has been conventionally incorporated into Hamiltonian Monte Carlo to eliminate the bias. However, this adjustment can significantly increase the iteration complexity due to the small step size required for reasonable Metropolis acceptance rates. In this work, we extend the delocalization of bias phenomenon, previously established for the overdamped Langevin algorithm, to these two unadjusted algorithms. We show that to control the $W_2$ bias of any $K$-dimensional marginal of a high-dimensional distribution, $O(\sqrt{K})$ integration steps suffice up to $\log d$ terms, assuming either weak or sparse interactions among variables. The discrete-time integrators here introduce technical difficulties beyond those of the overdamped setting, which we address through a broadly applicable matrix-polynomial framework that characterizes their propagators. Our result for the underdamped Langevin algorithm is valid for all large friction parameters, implying that the Leimkuhler-Matthews integrator for the overdamped Langevin dynamics also exhibits delocalization of bias.

We present a novel viewpoint for uncertainty quantification. Uncertainty measures are not primitives, in need of axioms and argumentation, but instead consequences, of higher-level modelling decisions. We show how epistemic and aleatoric uncertainty measures can be derived via decomposition of a subjective risk, based on a strictly proper loss. Reverse cross entropy provides a prominent example, where decomposition recovers the classic information-theoretic uncertainty terms. The same approach recovers numerous measures previously proposed across the UQ literature, providing them a common theoretical foundation. This suggests a new approach to UQ: given a modelling scenario and strictly proper loss, the corresponding epistemic and aleatoric terms are induced by the subjective-risk decomposition. We then extend our view to learning theory: we introduce and analyse subjective risk analogues of excess risk, approximation error and estimation error, and identify the connections to UQ. We consider this a first step towards a full learning-theoretic framework for uncertainty quantification.

Inference for infectious disease transmission on dynamic contact networks is complicated by latent infection times, partially observed network evolution, measurement error in contact data, and infection originating from outside the observed population. Existing likelihood-based approaches typically address these challenges separately and often rely on restrictive assumptions such as fully observed networks, closed populations, or symptom onset as a surrogate for infection time. We develop a unified complete-data likelihood framework for epidemic processes evolving on partially observed dynamic networks. The proposed formulation represents disease progression, network evolution, and observation mechanisms as interacting continuous-time stochastic processes within a common probabilistic framework. Specifically, we couple a susceptible-exposed-infectious-removed (SEIR) epidemic process with a status-dependent dynamic contact network and explicit observation models for symptoms and contacts. The resulting framework accommodates latent incubation periods, intermittent network observation, contact measurement error, and external infection pressure while preserving a coherent likelihood structure. Our principal contribution is the derivation of a complete-data event-history likelihood for the joint epidemic-network process under partial observation. The likelihood provides a rigorous foundation for likelihood-based and Bayesian inference through data augmentation, clarifies how information from disease progression and contact dynamics jointly determines parameter estimability, and reveals a broad class of existing epidemic network models as special cases. More generally, the framework contributes to statistical inference for partially observed interacting stochastic systems on evolving networks and establishes a foundation for uncertainty-aware analysis of complex transmission processes.

This paper introduces a Bayesian spike-and-slab framework for spectral analysis of time series data. The proposed method combines frequency selection and dimensionality reduction with a refined grid of candidate frequencies, enabling high-resolution recovery of oscillatory components while promoting sparsity through a structured spike-and-slab prior. A stochastic search algorithm efficiently explores the posterior space, yielding posterior inclusion probabilities that quantify the relevance of each frequency. We extend the framework to multivariate signals via a hierarchical prior on frequency inclusion patterns, allowing the model to capture both shared and component-specific rhythms across multiple time series. Extensive simulation studies demonstrate the method's robustness and superior performance in frequency estimation and spectral power reconstruction compared to existing approaches. Applied to actigraphy data from individuals with partial-onset seizures, the univariate model identifies clinically relevant circadian and ultradian rhythms. In a second application, for the joint analysis of physical activity and skin temperature from a healthy individual, the multivariate model reveals partially overlapping rhythmic components consistent with known physiological coupling. This work establishes a powerful and interpretable approach to spectral analysis, with broad applicability to wearable data, chronobiology, and personalized health monitoring.

High-dimensional categorical data arise in genetics, biomedicine, and the social sciences, yet visualization tools for such data remain far less developed than those for continuous variables. Existing methods either scale poorly, rely heavily on low-dimensional displays detached from the original data matrix, or prioritize predictive accuracy over interpretability. To address this gap, we introduce categorical Generalized Association Plots (cGAP), a visualization framework for nominal, ordinal, and binary data that preserves the original data matrix while augmenting it with interpretable geometric structure. cGAP uses Homogeneity Analysis (HOMALS) to embed subjects and category levels in a three-dimensional Euclidean space and maps the embedding to red-green-blue coordinates so that similar patterns receive similar colors. The framework integrates three coordinated views: a HOMALS-guided heatmap of the raw data matrix, a subject proximity matrix, and a variable proximity matrix. Seriation algorithms are then used to reorder rows and columns to reveal coherent clusters, outliers, and local-to-global structure. We also derive barycentric traceability, projection-distortion, and contrast-preservation properties that clarify how embedding geometry is transferred to the display. We demonstrate the versatility of cGAP through applications to student-animal classification data, mammalian dentition profiles, mushroom records from the UCI Machine Learning Repository, and the Clusters of Orthologous Genes database. These examples show that cGAP supports transparent exploratory analysis by maintaining traceability between derived visual structure and the original categorical observations. cGAP provides a full-matrix, heatmap-based visualization environment for investigating complex categorical datasets across scientific domains.

An omnibus goodness-of-fit statistic can fail to exploit simple diagnostic evidence efficiently. For example, under a standard normal null, an exceptionally large observation is direct evidence of a scale or tail departure even when the primary omnibus statistic does not cross its critical value. This motivates a simple augmentation principle: retain an established primary test, but reserve a small part of its null rejection budget for secondary statistics that encode natural features such as variation, asymmetry, or tail behavior. We implement this principle by calibrating each secondary acceptance region under the null conditional on acceptance at all preceding stages. Once calibrated, the resulting test is a fixed rectangular acceptance rule; the ordering is a mechanism for choosing its boundaries and assigning ordered first-rejection contributions, not a sequential-sampling scheme. An unconditional stage-budget parameterization makes the central trade-off explicit: additional sensitivity is purchased by removing a prespecified, usually small, amount of rejection probability from the primary stage. We establish strong consistency of the quantile-based Monte Carlo calibration and give an observation-specific pooled-rank version with exact randomized finite-m null size. In an experiment under a standard normal null with n=10, we augment the Kolmogorov–Smirnov statistic with sample variance and sample skewness. Assigning only 0.75% of the total Type I error budget to the two secondary statistics changes power against N(0.5,1) from 0.2742 to 0.2733, while increasing power against N(0,0.2^2) from 0.4693 to 0.9827. This focused experiment is a proof of principle rather than an exhaustive comparison of normality tests: a small unconditional allocation to prespecified diagnostics can greatly broaden power while preserving almost all of the primary test's power.

We exploit the new framework of multivariate geometric extreme value theory for the statistical analysis of river flow extremes at multiple locations on a river network. Current methodologies within the geometric framework are limited to a relatively low number of dimensions. This is insufficient for the purposes of flood risk estimation, since the number of gauging stations on a river network is often of the order $10-20+$. In order to create a parsimonious model in higher dimensions, we translate recent theoretical work on geometric extremal graphical models into statistical practice. We define the gauge function, a key object in geometric extremes, in a structured way using block graphs, which are a natural way of expressing the river network. We introduce both simple models, and more complex ones that can accommodate both simultaneous and non-simultaneous flows, and apply them to extreme flows at 10 locations on a river network around Preston, in north-west England. The models are shown to fit well and indicate strong extrapolation performance. We also introduce a correction coefficient for the geometric framework to address potential over- or under-estimation of marginal probabilities. The overall utility of our approach is illustrated through calculation of probabilities of simultaneous flooding at four locations on the network.

Motivated by batch and semi-batch process operation, we study finite-horizon open-loop dynamic optimization problems with uncertain parameters. A common computational approach replaces the expected performance criterion by an average over finitely many sampled parameter realizations. We develop a statistical theory for the resulting sample-based optimal value as an estimator of the population optimal value. The analysis is based on a stability estimate showing that terminal losses depend Lipschitz continuously on the time-integrated control, which records the cumulative input delivered up to each time. This estimate yields a functional central limit theorem for the sample-based objective and a statistical limit theorem for the corresponding optimal value error. As a consequence, we obtain confidence intervals for the population optimal value. When the population optimizer is unique, the limit is Gaussian and leads to a plug-in confidence interval. When multiple optimal policies may exist, we use a subsampling confidence interval that does not require uniqueness. The methodology is illustrated on two fed-batch case studies in which feed-rate profiles are optimized under parametric uncertainty.

The Planetary Boundary Layer (PBL) governs the exchange of energy and moisture and hosts the highest concentrations of pollutants before they mix into the free troposphere. The height of the PBL (PBLH) is therefore a key variable in meteorological and air-quality applications. Despite the wide range of methods available to derive PBLH from atmospheric observations, the associated uncertainties are rarely quantified. This study presents a methodology for propagating radiosonde measurement uncertainty into PBLH estimates obtained from state-of-the-art retrieval methods, including the parcel method, gradient-based methods, and the Richardson-number method. The framework relies on three components. First, it uses the GCOS Reference Upper-Air Network (GRUAN) Data Product, which provides traceable uncertainty estimates for all variables required in PBLH retrievals. Second, it employs a state-space model that captures the structure of atmospheric profiles and enables the generation of physically plausible simulated vertical profiles consistent with both observations and their uncertainties. Third, a Monte Carlo approach is used to propagate measurement uncertainty into the PBLH estimates, refining the retrieval and quantifying its uncertainty. Beyond providing uncertainty estimates, the methodology also shows preliminary signs of increased robustness in PBLH detection across several case studies, particularly in situations where standard gradient-based methods exhibit sensitivity to measurement uncertainty.

We develop a general framework for understanding when graph alignment is information-theoretically feasible in sparse inhomogeneous random graph models, by studying the set of vertices on which the underlying matching can be recovered. Our main theorem gives a general lower bound on this set by leveraging the balanced load function introduced by Hajek (1990). The corresponding obstruction is captured by a new graph parameter, the self-overlap, which measures the extent to which a graph can imitate itself under a non-trivial relabelling. We then show that this criterion is sharp in a broad class of sparse inhomogeneous models, recovering known Erdős–Rényi phenomena and yielding sharp thresholds for Chung–Lu graphs and stochastic block models.

Modern generative models are increasingly trained using model-generated signals, creating both opportunities for self-improvement and risks of collapse. We study optimal self-distillation (SD) for rectified flow (RF): given a suboptimal teacher velocity field, can a student trained on a mixture of true RF velocities and teacher velocities provably improve the teacher? For linear RF with ridge regularization on fixed interpolation pairs, we prove an exact affine path identity, derive the optimal mixing coefficient in closed form, and show strict improvement in integrated velocity risk whenever the teacher risk is nonstationary along the regularization path. The optimal coefficient obeys a sign rule: positive mixing corrects under-regularized teachers, while negative mixing corrects over-regularized teachers. We also give one-shot generalized cross-validation (GCV) and validation tuning procedure that avoids grid search over mixing weights and repeated refitting. Combining this theorem with RF Wasserstein convergence bounds, we show that optimal self-distillation improves the velocity estimation terms controlling continuous-time and finite-step generation error. Experiments with Gaussian models, Gaussian mixtures, and image data show that optimal self-distillation improves velocity risk, mode recovery, and finite-step generation relative to both the teacher and pure distillation.

We propose a goodness-of-fit test for semiparametric copula regression models. Such models express the regression function in terms of marginal distribution functions and copula densities and therefore provide a flexible way to avoid fully nonparametric estimation in high-dimensional regression problems. Their performance, however, depends crucially on the specification of the parametric copula family. Instead of testing the copula model itself, we assess misspecification directly at the level of the induced regression function. To this end, we introduce a weighted $L^2$-distance between the true regression function and its best approximation within the postulated copula regression model. A kernel-based estimator of this distance is proposed and shown to be consistent and asymptotically normal under both the null hypothesis of correct specification and fixed alternatives. We derive a classical specification test and, using a self-normalized sequential statistic, construct pivotal confidence intervals and tests for relevant deviations from the model. Finite-sample simulations demonstrate accurate level approximation and good power properties of the proposed procedures.