Papers

We propose a two-view weighted-concordance operator (WCO) framework for offline change-point detection in weakly dependent text networks. Weighted word-co-occurrence graphs yield first-order direct-co-occurrence and second-order shared-context views, projected into paired Euclidean observations using maps learned from an independent pilot corpus. A WCO scan detects changes in cross-view dependence. A dependent multiplier bootstrap tests for a change, while a segment-wise block bootstrap gives a descriptive stability interval for its location. We establish null weak convergence, bootstrap validity, asymptotic size control, consistent localization under a single identifiable change, and perturbation bounds for token-level errors. CUSUM and Gaussian-kernel MMD scans provide complementary benchmarks. In the 1915-1921 New Youth corpus, the method detects a change in November 1919, with a descriptive 95 percent stability interval from April 1919 to June 1920, consistent with the linguistic transition surrounding China's May Fourth and New Culture movements.

We propose a new approach for analyzing Time-Dependent Perturbed Angular Distribution data. In this, a likelihood is constructed with the help of conditional probabilities of single events and binning of time data is avoided. This likelihood is used in a Bayesian framework to calculate the posterior probability density function for the $g$ factor of interest. This approach is compared to more traditional approaches that use binned data by analyzing simulated datasets. In many cases the resulting posterior probability densities are observed to be multimodal and the results can thus often not be summarized with a single Gaussian approximation. We find that results from the new approach are more reliable for low-statistics datasets.

Ranks depend on the observations used for comparison. Reusing those observations can add association between forecast and outcome rank contrasts even when the evaluated forecast and outcome stay fixed. We characterize assignments that preserve association between specified population-rank contrasts, including forecast rank minus baseline rank compared with outcome rank minus baseline rank. Conditional on independent training, whole trajectories are sampled independently from a common law, with unrestricted dependence within each trajectory. The expected score separates into its target and an explicit interaction between map pairs. When reassigning references, we keep the learned maps, reference law and coefficient row sums fixed. Zero weighted reference overlap for every map pair is necessary and sufficient for preservation uniformly over permitted maps and laws. An unbiased three-trajectory kernel estimates the interaction; independent evaluation and validation provide finite-sample lower bounds. Complete U-statistics estimate the same target directly when all draws can be recombined. Sharp shared-baseline ranges, including ties, tighten both constructions. In a Beijing air-quality archive, interaction accounts for 91.4% to 94.5% of seven learned forecasts' expected shared scores under the empirical archive law. Separate results address category-fitting error and temporal feedback. In a matched category-control null experiment, distinct references reduce rejections from 402 to 41 out of 1,000 panels.

Quantifying the heterogeneity is an important issue in meta-analysis. The conventional heterogeneity statistic, $I^2$, heavily depends on study sample sizes and tends to approach one as the sample sizes increase. To overcome this limitation, a sample size independent measure, ${\rm ICC}_{\rm MA}$, has recently been developed to quantify the heterogeneity, yet this method is restricted to meta-analysis with continuous outcomes. In practice, however, binary outcomes are more widely encountered, with the log odds ratio (lnOR) frequently adopted as an effect size to compare the effects of two treatments in terms of odds. To fill the gap, we propose a new heterogeneity measure for meta-analysis with binary outcomes by introducing a latent continuous variable model. Under this framework, the proposed measure admits a closed-form expression within the random-effects meta-analysis model with lnOR as the effect size. We define this sample size independent measure as ${\rm ICC}_{\rm MA}^{\rm OR}$, and moreover propose a new estimator, $I^2_A$, to evaluate this measure. Simulation studies demonstrate that our new estimator is nearly unbiased and aligns closely with its counterpart applied for standardized mean differences when the continuous variable is observable. A real data application further demonstrates that the proposed heterogeneity statistic for binary outcomes and its counterpart for continuous outcomes provide interpretable and coherent estimates across different outcome types.

Randomized trials with limited concurrent control information—including but not limited to unequal-randomization settings—can offer ethical and practical advantages, especially in pediatric and rare diseases, but they often lose power because fewer control patients are available for direct comparison. Borrowing information from external controls may improve efficiency, but can also inflate the Type I error rate when the external and trial populations are not sufficiently comparable. We propose RECaST-Surv, a Bayesian transfer-learning framework for time-to-event outcomes that extends the RECaST method to survival settings. The method learns a structural survival model from external control data and calibrates it to the concurrent control arm of the current trial through a Cauchy random effect. To improve frequentist operating characteristics, we further develop a bootstrap-based procedure to calibrate the testing rule for Type I error control. RECaST-Surv can accommodate multiple external datasets and requires only summary-level information from external sources. Simulation studies show that the method maintains near-nominal Type I error across challenging settings while improving power by roughly 10%–12% over standard analyses. In an Amyotrophic Lateral Sclerosis trial emulation, RECaST-Surv increased power from 82.8% to 95.7% relative to the no-borrowing RCT analysis, while maintaining acceptable error control.

In the canonical Difference-in-Differences design, the control group's post-treatment change serves as an imputation of the treated group's counterfactual change in the same period, an imputation justified by parallel trends. However, differences in group composition can produce between-group differences in how outcomes would evolve over time, rendering this imputation vulnerable to confounding. An alternative imputation – such as one based on the treated group's pre-treatment change – avoids such between-group confounding but introduces the risk of confounding from within-group temporal shifts. Ideally, both imputations, each vulnerable to different sources of confounding, would have concordant values, thereby yielding the same causal conclusions. When the imputations are discordant, conclusions under parallel trends hinge more critically on that assumption since alternative imputations would point to different results. Yet in these scenarios, existing pretrends-based sensitivity analyses can show low sensitivity because they ignore post-treatment deviations from pretrends in the control group. This paper therefore proposes a discordance-based sensitivity model in which parallel pretrends are necessary but not sufficient for low sensitivity. I formally justify this model in terms of the expected distance between the ATT under parallel trends and under alternative assumptions, weighted by the joint plausibility of those assumptions. I then provide a decision-theoretic rationale for benchmarking violations of parallel trends using the worst-case discordance between the parallel trends imputation and alternative imputations. Finally, I apply both pretrends- and discordance-based sensitivity models to assess how a labor supply shock influenced electoral support for apartheid-era policies in South Africa, showing how the two approaches yield different results.

Many datasets arise as multivariate time series observed at irregular time intervals, particularly in Earth observation and astronomical measurements. Classical time-series models assume that time is discrete and observations occur at equally spaced intervals, limiting their ability to capture dynamics when observation gaps vary. Existing approaches to irregular sampling rely on continuous-time formulations, which assume that observation intervals are sufficiently small. We address this limitation by introducing a discrete-time framework that accommodates irregular observation gaps while preserving multivariate dependence structures. We introduce a framework for the analysis of irregularly observed multivariate time series based on hypercomplex autoregressive processes. The framework embeds multivariate observations into a hypercomplex algebraic structure, allowing multiple variables and their interactions to be represented within a single mathematical entity while incorporating irregular observation gaps. The resulting process admits a structured matrix representation, which enables the model to be expressed as a state-space system. This formulation provides an estimation methodology in which model parameters can be inferred using Kalman filtering techniques. The state-space representation allows recursive estimation and prediction in the presence of irregular sampling intervals. The performance of the methodology is illustrated through data and applications to remote sensing and astronomical datasets, where observations occur at nonuniform time intervals. The results demonstrate that the approach captures dynamics and cross-variable interactions difficult to model using traditional time-series techniques. The proposed framework provides a methodology for analyzing irregularly sampled multivariate time series and opens possibilities for modeling observational data across disciplines.

Randomized controlled trials provide internally valid estimates of treatment effects, but their results may not directly apply to broader target populations due to differences in baseline covariate distributions, adherence to treatment or variations in outcome mechanisms. Under standard transport and time-to-event identifiability assumptions, we develop nonparametric, debiased machine learning estimators for transporting and generalizing causal survival treatment effect differences from a source population to a target population in discrete time. We derive the efficient influence functions for the transport and generalization survival difference estimands and propose cross-fitted one-step estimators that are doubly robust and achieve semiparametric efficiency bounds under weak regularity conditions. We further introduce estimators that exploit known effect modifier subsets through an additive parameterization of the survival function, reducing the dimensionality of the reweighting and yielding smaller or equal asymptotic variance. We establish asymptotic normality, double robustness, and rates of convergence for all proposed estimators. Finite-sample properties are illustrated through Monte Carlo simulations under flexible and misspecified nuisance estimation scenarios. We apply the methods to data from the Women's Health Initiative to estimate the effect of hormone therapy on coronary heart disease across trial and observational populations.

Parametric copulas capable of capturing full-range tail dependence in both lower and upper tails are useful in many applications, including as pair-copula building blocks in vine copula models. However, it is challenging to create such copulas that have closed-form density functions, which limits their practical applicability in complex modeling scenarios. To the best of our knowledge, all existing full-range tail dependence copulas do not have closed-form density functions. In this paper, we propose a new Archimedean copula family, called the full-range Archimedean copula of type I (FRA1), that captures full-range tail dependence in both tails and admits a closed-form density function. The copula has two parameters, one controlling the strength of dependence in the lower tail and the other controlling that in the upper tail. We provide results on dependence properties of the copula, and discuss how to effectively estimate the parameters based on maximum likelihood. We build a vine copula model only using the FRA1 copula, and demonstrate that the model can achieve comparable performance of an ordinary vine copula model while avoiding the need of pair-copula model selection. The new copula is also applied to data from the Medical Expenditure Panel Survey, demonstrating that an FRA1 vine model can effectively capture diverse temporal and cross-sectional dependence patterns in medical expenditures. Finally, the new copula is implemented in CopulaOne, an R package for full-range tail dependence copulas.

We develop a class of linear state space models for matrix-valued time series data where the state is a latent matrix normal process. We derive matrix versions of the Kalman filter, log-likelihood, and smoother enabling estimation of the latent state matrix as well as the model's parameters. To conduct Bayesian inference, we provide algorithms that draw from the joint posterior distribution of the latent state matrices conditional on the observed data and parameters. We apply these methods to a large panel of U.S. macroeconomic time series across the 50 U.S. states. The proposed framework accommodates mixed-frequency data, heteroskedasticity, and outliers within a unified matrix-valued structure. Empirically, we find that a small number of latent factors captures the joint dynamics across states and variables, providing a parsimonious and scalable approach to modeling high-dimensional macroeconomic systems.

Time-to-event outcomes are central in oncology and rare diseases, where treatment effects are often summarized by differences in survival curves or Restricted Mean Survival Time (RMST). In real-world data, estimating these causal effects relies on the absence of unobserved confounding, an assumption that is rarely satisfied. We develop a sensitivity analysis framework for causal treatment effects with survival outcomes under the Marginal Sensitivity Model (MSM). We introduce doubly valid and doubly sharp (DVDS) bounds for differences in survival functions and RMST, extending recent DVDS results to the time-to-event setting while accounting for informative censoring. In practice, our method yields tighter bounds and improved computational efficiency compared to a previous approach from the literature, on simulated and real data. For tractability, we assume independence between censoring and unobserved confounding, a limit that should be addressed in future works.

Benford's law specifies a marginal distribution for significant digits, whereas the usual first-digit Pearson $p$-value is calibrated under an independent multinomial sampling model. We separate these statements with four constructions that share the same one-time or pooled Benford target but have different joint structures. Under a wrapped-Gaussian circular Markov construction, the nominal 5% Pearson test rejects 21.6% of samples at a fixed persistence level even though every one-time marginal is exactly Benford; a sequence-level second-order moment-matching calibration reduces the rejection rate to 4.8%. The same strategy performs well in the randomized-rotation and random-composition designs. The effect persists across changes in sample size and sequence length, and a grid approximation to a continuous log-significand Cramér-von Mises discrepancy shows the same design dependence. In the wrapped-Gaussian design examined here, corrected procedures retain rejection probabilities that rise with the size of a smooth marginal departure. Finally, we distinguish calibration from an information boundary: significand-only methods cannot detect changes that leave the complete significand process unchanged, but they readily detect perturbations that alter it. Benford conformity is a marginal statement; a Benford $p$-value is valid only relative to a specified statistic, sampling law, and calibration procedure; an integrity claim requires substantive competing models.

We develop a method for measuring the incremental effect of advertising when randomized exper- iments are unavailable. Firms generate abrupt interventions in their own marketing as a byproduct of operations: budgets are cut, channels launch, programs pause. We propose a two-stage proce- dure that treats these events as quasi-experiments. The first stage discovers and dates interventions by exact Bayesian run-length inference on marketing activity series. The second stage runs a causal impact analysis against a variance-constrained structural time series counterfactual, with simulation-based inference, five qualification conditions, and a closed-form power bound. We validate the procedure on the two experimental benchmarks that Meta released with its GeoLift framework. The method identifies the day of intervention exactly in both cases. On the experiment where advertising was removed, it recovers the effect within 6.2 percent of the experimental esti- mate (implied return of 1.50 versus 1.60). On the experiment where advertising was added, its 90 percent interval covers the experimental estimate and excludes zero. Of six estimators evaluated on the same released data, ours is the only one that requires no geographic panel and produces intervals that are both correct on both experiments and narrow enough to act on.

We study inference on the drift of a critical Galton–Watson process with immigration, a count time series with a unit root. Climate change motivates such nonstationary models for weather-related disaster counts. The drift is the expected increase in the count per period. Ordinary least squares is inconsistent for the drift, so we study state-weighted least squares, giving greater weight to observations following small counts, where conditional variance is lower. Under strict recurrence, we apply null-recurrent regenerative limit theory to obtain a polynomial convergence rate and a standard normal studentized limit. Our main contribution is the recurrence boundary, where we establish a logarithmic convergence rate and a parameter-free non-Gaussian studentized limit. Estimating the optimal weights yields the same first-order limiting distribution as knowing them. Simulations show lower root mean squared error than time-weighted least squares with weights $1/t$, and improved state-weighted confidence-interval coverage when the unit root is imposed.

Functional principal component analysis (FPCA) provides low-rank representations of functional data but generally produces dense components, making it difficult to identify the localised regions contributing to dominant modes of variation. This limitation is particularly relevant in Raman spectroscopy, where spectra are observed over an ordered domain and interpretation often focuses on chemically meaningful spectral regions. This study proposes variable-projection sparse FPCA (VP-SFPCA) for interpretable functional dimensionality reduction through sparse weight functions that promote localisation. The method formulates sparse FPCA as a regularised matrix-factorisation problem that incorporates the functional inner-product geometry and distinguishes sparse weight functions used to generate component scores from orthonormal loading functions used for reconstruction. Variable projection conditionally minimises over the loading functions, reducing the optimisation problem to the sparse weights. Performance was evaluated through simulation studies and empirical analyses of surface-enhanced Raman scattering (SERS) spectra, with conventional FPCA and SCAD-SFPCA serving as dense and sparse functional benchmarks, respectively. In the simulations, VP-SFPCA recovered localised functional structure while requiring substantially less computation than SCAD-SFPCA. In the empirical analysis, VP-SFPCA retained this computational advantage while yielding held-out reconstruction error close to that of conventional FPCA. Several prominent features of the estimated weight functions also coincided with established adenine SERS bands. Overall, VP-SFPCA provides a computationally practical approach to improving the interpretability of dominant functional modes through localisation.

The Taylor diagram is used to evaluate and compare predictive models with observed data and has many applications in climate and environmental sciences. Three statistics of interest–the centered root-mean-squared error, standard deviation, and the product-moment correlation coefficient–are related by the law of cosines; Taylor diagrams leverage this fact to allow visualization of all three statistics in a two-dimensional plot without any loss of information. In this work, we present a novel model evaluation tool–the Wasserstein-Taylor diagram–formed from integrating the Wasserstein distance from optimal transport into a Taylor diagram framework. This tool is built upon the fact that the law of cosines still holds in the Taylor diagram if the centered root-mean-squared error and product-moment correlation coefficient are replaced by the centered 2-Wasserstein distance and quantile correlation coefficient, respectively. The advantage of this Wasserstein-Taylor diagram is that one can use the distribution perspective afforded by the Wasserstein distance to compare observed and predicted data sets of different sizes and even to compare statistical models with only observed data. We further show that the quantile correlation coefficient on empirical measures converges to the quantile correlation coefficient on the sampled measures.

The problem of identifiability in linear parametric models (LPMs) whose nodes follow either an ordered logit model or a regular one-parameter exponential family is evaluated. The results go beyond classical structural equation models as well as results for nodes with observations from a homogeneous family of distributions. The main result establishes that the orientation of every edge joining an ordinal node to an exponential-family node is identifiable from the joint distribution alone at every parameter value, provided the ordinal node has at least three categories and the exponential-family node at least three points of support, with no restriction on the sufficient statistic. Converses show that both requirements are necessary: the three-category requirement is binding only for affine sufficient statistics, and the three-point requirement is binding under the canonical link. The guarantee extends to orienting every such mixed ordinal-exponential family edge of a given $d$-node undirected skeleton. Numerical experiments illustrate the theoretical results by successfully separating orientations within a Markov equivalence class, which are indistinguishable by conditional independence alone.

Hierarchical and grouped time series arise when a multivariate time series is forced to satisfy a set of aggregation constraints, motivating forecast reconciliation methods that ensure coherent forecasts of such hierarchical structures. Many real-world applications involve discrete or bounded supports, introducing additional challenges that are not addressed Gaussian-based reconciliation methods. We develop a post-hoc hierarchical forecasting approach to construct coherent forecast hierarchies for discrete and bounded time series. The method constructs coherent forecasts by convolution and exponential tilting, preserving the distributional properties and the underlying support throughout the hierarchy. We evaluate the proposed approach against state-of-the-art reconciliation methods for both discrete and continuous settings, demonstrating strong performance across a range of experiments. Through simulation studies and empirical applications in epidemiological and demographic data, we show that the method provides reliable and coherent distributional forecasts in challenging scenarios.

The log Gaussian Cox Process (LGCP) is one of the most widely used models for the analysis of spatial point patterns. Although Bayesian methods and software for fitting LGCPs are now well established, practical tools for model criticism, predictive assessment, and model comparison remain comparatively underdeveloped. This paper develops a practical Bayesian cross-validation framework for LGCPs while placing it within a broader framework for Bayesian model assessment. Our approach is motivated by the conceptual and computational challenges that arise when defining predictive validation for point processes, including the choice of holdout data, prediction task, scoring rule, and computational strategy. We propose a leave-region-out cross-validation framework in which the fundamental unit of prediction is a bounded spatial region rather than an individual event. Predictive performance is assessed through the logarithmic scoring rule for joint probabilistic forecasts, while computational efficiency is achieved by combining a new likelihood approximation with a Bayesian unlearning strategy and Laplace approximations to obtain leave-region-out predictive distributions without repeated model refitting. We validate the proposed approximations against Monte Carlo estimates obtained via brute-force refitting, demonstrate the methodology on simulated and real spatial point pattern datasets defined on Euclidean domains and networks, and provide implementations in the R-INLA, inlabru, and MetricGraph packages.

Dynamic networks describe evolving relational systems in which abrupt structural changes may signal anomalous events or important transitions. Detecting such changes requires distinguishing genuine structural signals from fluctuations in network observations and learned representations. We propose a DeepWalk-based framework for detecting and localizing structural changes in dynamic networks. For each snapshot, we learn low-dimensional node embeddings, align them to a fixed reference using orthogonal Procrustes transformations, and aggregate them by mean pooling into comparable graph-level vectors. We then construct a multivariate cumulative sum (CUSUM) scan statistic to identify changes in the embedding mean. Under stated regularity conditions, we derive bounds on stochastic fluctuations under the null hypothesis and sufficient conditions for reliable detection and consistent localization under the alternative. The analysis connects detection performance with network sparsity, spectral separation, embedding dimension, and change magnitude, clarifying the balance between structural signals and representation variability. Simulation studies demonstrate the effectiveness of the proposed method in detecting and localizing structural changes across a range of dynamic network settings. An application to an international trade network further illustrates its practical usefulness in identifying shifts in trade allocation.

Highly reliable products with extended lifetimes present a challenge in reliability analysis: obtaining enough failure data under normal operating conditions is often incompatible with reasonable time and cost constraints. Step-Stress Accelerated Life Tests (SSALTs) offer a practical solution by progressively increasing stress levels to accelerate product degradation, allowing results to be extrapolated to normal conditions. However, the small sample sizes and Type-I censoring inherent to these experiments render classical maximum likelihood-based inference vulnerable to data contamination. Robust point estimation has been studied in the literature. However, robust test statistics have not yet been developed in this context. In this paper, we propose robust test statistics for SSALTs under exponential lifetime distributions, based on the minimum density power divergence estimator (MDPDE). This paper directly works with the exact failure times recorded before the end of the experiment. Once this limit time is reached, all surviving components are censored. This creates a mixed discrete-continuous distribution, which is a major analytical breakthrough in the context of SSALT. We introduce the restricted version of the MDPDE, establish its asymptotic properties, and construct Z-type and Rao-type test statistics for linear hypotheses on the model parameters. The proposed tests are shown to maintain their nominal significance levels and statistical power under data contamination, where classical MLE-based procedures fail. An extensive simulation study confirms the robustness gains of the proposed methods, and a real data application illustrates their practical value.

Streaming binary response data arise in many applications, including virtual learning platforms where student responses are collected sequentially and estimated probabilities of correct responses may inform future question assignment. Logistic regression provides an interpretable framework for such analysis, but the data may support multiple plausible predictor subsets. Bayesian model averaging (BMA) accounts for such model uncertainty by averaging inference across competing models. Since repeatedly applying BMA to accumulating data can be computationally burdensome, we develop an online implementation based on renewable estimation. At each update, retained summaries and new observations are used to approximate the joint posterior of models and model-specific coefficients without revisiting historical data, enabling point and interval estimates that incorporate model uncertainty. Simulations show that online BMA closely approximates its offline counterpart in coefficient estimation, model and variable importance, prediction, and interval estimation of predictive probabilities, while substantially reducing computational cost. In a virtual learning application, we find substantial uncertainty across competing predictor subsets and large variability in credible interval widths across questions. Our method distinguishes questions with precise estimates from those with substantial uncertainty, providing information beyond point estimates for adaptive question assignment.

Complete-case coarsening discards observed confounder values from partially complete records. We study its consequences for average treatment effect estimation with two ordered, partially observed confounders under monotone sequential missing at random. We specialize the standard coarsening-at-random transformation to the causal influence function, establish the canonical gradient, and give an exact drift identity for a cross-fitted estimator with sequential multiple robustness. In the submodel where both sequential and complete-case missing-at-random assumptions hold, we express the efficiency loss from coarsening as a nonnegative expectation involving two iterated projections. The gain is strict when the intermediate confounder supplies residual information where second-stage missingness occurs. Oracle simulations and deterministic quadrature illustrate this efficiency comparison. When second-stage response depends on the intermediate confounder, the comparison instead concerns identification: coarsening can introduce persistent bias. Estimated-nuisance simulations include a bounded-propensity design and a Gaussian stress design. The latter exhibits substantial interval undercoverage and can reverse the finite-sample precision ordering, qualifying the practical interpretation of the efficiency bound.

AI and large language models can recover clinically meaningful features from electronic health records (EHRs), but predictive usefulness does not establish admissibility for causal inference. We introduce information set emulation: an AI typed lift attaches source evidence, clinical and recording times, decision-time availability, representation version, proposed causal roles, and unresolved ambiguity to extracted features under a locked target trial. Causal certificates record auditable evidence for those roles. Features with unresolved downstream roles are routed to compatible reporting or separate analyses. Typed evidence defines an observational fiber of causal worlds consistent with the observed law. The locked scalar estimand maps this fiber to a compatible image whose squared Chebyshev radius equals the residual minimax mean squared error when the image is nonempty and compact. This classical identity provides a target-specific measure of information ambiguity. The contribution is its integration with a joint EHR observation map and an auditable certificate architecture. Under explicit exchangeability, positivity, and nuisance-consistency conditions, we give identification and cross-fitted augmented inverse probability weighted estimation, distinguishing empirical and population targets. An EHR compression-drift identity separates the roles of frame presence, treatment assignment, and outcome observation. Artificial simulations and a common-law finite-world example illustrate estimation failures and information-radius reduction. Synthetic Phase 0 notes demonstrate audit diagnostics; a separate role-specific analysis spread illustrates routing and is not an exact fiber radius. All experiments are synthetic. The framework specifies when reconstructed information can support a point claim and when compatible reporting is required.

AI-generated covariates from notes, conversations, images, and wearable streams can change the causal question when their roles are left unspecified. A generated feature may represent a treatment version, pre-action state, history, design variable, mediator, outcome proxy, observation process, or intercurrent event; these roles are not interchangeable. We formulate a causal type discipline for sequential experiments: a versioned representation map, a causal role classifier, a claim-status filter, and an estimand lock. The lock fixes a standardized proximal effect before generated covariates enter the analysis. Under audit correctness and standard identification assumptions, admissible role assignments preserve this estimand. We apply the established conditional-covariance characterization of compression bias to substitution of generated representations for design-relevant states. A standardized decomposition separates compression, conditional-law, and standardization drift. Further results cover mediator adjustment, post-action leakage, marker-intervention conflation, outcome-guided discovery, and state-measurement error. Cluster-level orthogonal estimators distinguish empirical and superpopulation targets under repeated sessions and missing outcomes. Simulations show that refinement helps when it retains design-relevant information, whereas design erasure, leakage, and same-data marker selection can produce bias or undercoverage. The framework places causal semantics and claim status before confirmatory inference with generated representations.

Levene's test for homoscedasticity is a standard procedure used to evaluate whether multiple groups of independent observations share a common variance. Because Levene's test relies on an Analysis of Variance (ANOVA) applied to transformed absolute or squared deviations, it structurally mirrors the statistical properties of ANOVA itself. Let $\mu_j$ and $\sigma^2_j$ denote the expectation and variance of the observations in group $j$. It was previously established that for a given significance level $\alpha$, ANOVA can result in a logical contradiction: failing to reject the global null hypothesis $H_0: \mu_1 = \mu_2 = \mu_3$ while simultaneously rejecting the localized hypothesis $H_0': \mu_1 = \mu_2$ with the same or higher confidence. In this paper, we show that Levene's test directly inherits this same “paradox” regarding group variances $\sigma^2_j$. We provide theoretical reasoning and a numerical illustration of this inconsistency, demonstrating how the addition of a well-behaved third group can dilute the test statistic and mask a significant localized variance discrepancy.

Alzheimer's disease is clinically staged as a three-class progression: cognitively normal (CN), mild cognitive impairment (MCI) and Alzheimer's disease (AD). The intermediate MCI class is biologically heterogeneous and overlaps with both extremes and it is the dominant source of classification error. This work develops a leakage-controlled framework for subject-level CN/MCI/AD classification that fuses four sources of information: a 3D Tau PET model, a 3D structural MRI model, a tabular ROI-and-plasma model and a hierarchical PET–plasma model. All branches are derived from a custom preprocessing and feature-extraction pipeline applied to $881$ aligned subjects from the ADNI cohort. They are aligned at the subject level and evaluated under identical, no-leak cross-validation folds, so that the multimodal fusion, built entirely on synchronized out-of-fold predictions, avoids optimistic bias. The final model is a fixed, parameter-free convex combination of the four branches. A nested superlearner serves as a robustness analysis and reproduces, rather than improves on, the fixed weights. The fusion improves significantly over every individual branch, with the largest gain on the MCI class, while a logistic meta-learner provides a complementary, MCI-oriented operating point on the same accuracy-sensitivity frontier. The work is presented as an honest baseline. It shows that multimodal fusion improves robustness, but that MCI remains the central bottleneck. This reflects a limit of the cross-sectional information rather than of the fusion mechanism and motivates reformulating the task as a continuous progression problem.

Clinical protocols may require rescue medication when a patient's condition crosses a prespecified threshold. The outcome under continued non-rescue is then unobserved after first crossing, preventing point identification without extrapolation assumptions. In this paper, we develop sharp partial identification and inference for this hypothetical estimand while retaining the original no-rescue intervention. We show that bounding this mean reduces exactly to restricting conditional mean effects of withholding rescue at first-crossing histories. Building on this representation, restrictions on prespecified crossing-stratum averages yield three results. (i) A finite convex program gives sharp bounds without modeling post-crossing trajectories, attained by full-data laws that preserve the observed distribution. (ii) Confidence intervals incorporate sampling uncertainty and numerical error to cover the entire sharp set, including strata with no observed crossings. (iii) Under local feasibility conditions, sampling and numerical errors control endpoint accuracy even with zero-probability strata, whereas valid coverage requires no such conditions. Our experiments show that the stratum-average restrictions can yield narrower confidence intervals in larger samples, and that accounting for uncertainty in empty strata maintains valid coverage when rescue is rare.

Policy learning aims to determine who should be treated based on individual characteristics. In high-stakes settings such as medicine and public policy where safety is a central concern, improving the average outcomes alone may not be sufficient: decision makers may also seek to protect individuals from harm, in line with the Hippocratic principle of “do no harm.” In this paper, we propose conformal policy learning (CPL), a policy learning procedure with a new distribution-free safety guarantee that controls the probability of assigning treatment to an individual who would be harmed relative to control. CPL views each treatment decision as testing a hypothesis of counterfactual harm and assigns treatment by thresholding conformal p-values. These p-values use observable proxies and selective calibration to address the challenge that the potential outcomes under comparison are never simultaneously observed. For randomized experiments, under standard exchangeability conditions, CPL provides finite-sample safety guarantee at a user-specified level, without imposing any outcome modeling assumptions. Moreover, when the outcome model is consistently estimated, CPL achieves asymptotically optimal welfare subject to the safety constraint. In observational studies, CPL with learn-then-balance weights achieves doubly robust safety guarantees. We evaluate CPL through extensive simulations and apply it to an empirical study of AI-powered interventions designed to reduce conspiracy beliefs.

Two features intrinsic to survey sampling complicate semiparametric efficiency analysis: design-induced dependence among sampling indicators and the randomness of finite-population targets under the superpopulation law. For general semiparametric full-data models, we show that the observed-data experiment under a broad class of dependent designs is locally asymptotically normal with the tangent-space structure of a reference Poisson experiment. Under the joint superpopulation-design law, first-order efficiency depends on the design only through the limiting inclusion-probability function. Standard missing-at-random projection in the reference experiment characterizes the observed-data efficient influence function. Finite-population targets are treated through first-order asymptotic expansions, extending the analysis beyond exact random sums to nonlinear census characteristics. Superpopulation and finite-population centerings yield equivalent notions of local regularity and efficiency, with their bounds linked by a Pythagorean decomposition that gives a generalized finite-population correction. We then give general and design-specific conditions under which cross-fitted estimators with estimated nuisance functions attain both efficiency bounds. For the finite-population mean, the bound equals the large-sample limit of the Godambe-Joshi anticipated-variance lower bound. For scalar targets, we characterize optimal limiting inclusion probabilities. Simulations and California Academic Performance Index data illustrate the theory.