Papers

Covariate-adaptive randomization procedures are widely used in clinical trials to improve covariate balance. In modern applications, experimenters often have access to many covariates, motivating the need for a theory of covariate-adaptive randomization procedures with a diverging number of covariates. This paper studies two classes of covariate-adaptive randomization procedures, referred to as imbalance-efficient covariate-adaptive randomization and imbalance-robust covariate-adaptive randomization, when the feature dimension diverges. We derive convergence rates for the imbalance of the covariates used in randomization. For both procedures, the imbalance is of a smaller order than that under complete randomization when the feature dimension is $o(n)$, whereas it is of the same order when the feature dimension is $\Omega(n)$. For imbalance-robust covariate-adaptive randomization, we further establish the asymptotic properties of the imbalance of additional covariates and use these results to derive the asymptotic distribution of the difference-in-means estimator for the average treatment effect and construct asymptotically valid confidence intervals. Furthermore, we provide extensive numerical and empirical studies to illustrate the practical relevance of our theoretical results.

In this article, we explore a new paradigm for statistical inference. The approach centers around the point estimate based on observed data, simulating replicates using the estimate as the truth to produce clones of the estimate, with inference deriving from the clone distribution. It avoids prospective finite-dimensional model assumptions, but it makes no probabilistic claims concerning the truth; it suggests an alternative system of uncertainty quantification that is operable in nonparametric function estimation. The procedures are demonstrated using examples of smoothing spline ANOVA models in nonparametric regression. The paradigm also applies in parametric regression, where the proposed inference closely resembles traditional inference operation-wise. Conceptual discussions are scattered throughout.

Many questions across the sciences take the same form: several coupled series are observed together, and the analyst wants to know not merely that they move together but which one moves first, and how strongly. This paper sets out a complete method built on one organising idea: the direction of a coupled system is exactly the part of its behaviour that changes when the record is played backwards. Tools built on contemporaneous covariance alone (correlation matrices, distance measures, spanning trees, undirected centralities, principal components) carry no information about direction: a reversible system and a circulating one can share identical covariance at every sampling of the same point-in-time record. Formally, direction is a circulation matrix carried by the lagged covariance. Its vanishing is exactly statistical time reversibility for linear systems, feature maps carry the characterisation to nonlinear ones, and under the Gaussian benchmark its magnitude is an entropy-production functional of the identified circulation, the quadratic component of the divergence per unit time between the forward and reversed records. Around this estimand we build a cross-fitted estimator removing first-order bias, delete-block jackknife standard errors, and a randomisation test exact under its stated block null, with a familywise correction and a nonlinear extension. A sampling theory says when the arrow is measurable at all, and a design layer separates transmission from the ordering of clocks. A laboratory of four systems with known answers compares the method with correlation networks, Granger causality, transfer entropy, and connectedness indices, reporting the failures of each when read as a measure of direction, including our own. Complete algorithms and worked examples in two languages make the paper the base reference for a series of applications.

Early-phase clinical trials for dose selection typically enrol few patients and aim to identify doses that are both safe and promising for further study. While traditional approaches identify the maximum tolerated dose, modern trials for targeted therapies often seek the optimal biological dose, defined as the lowest dose achieving sufficient biological activity with acceptable safety. In immunology settings, assessment of biological activity is based on multiple biomarkers or clinical endpoints. Clinicians leading dose-selection efforts would thus benefit from transparent summaries of the probabilities of observing combinations of biomarker outcomes across doses. However, such inference is challenging in small samples where complex modelling assumptions are difficult to verify. To address this limitation, we propose COBRA-DOSE, a framework for posterior predictive inference based on two endpoints that models dependence via copulas and accounts for uncertainty in both marginal distributions and dependence structures through Bayesian model averaging. This approach avoids reliance on a single model and yields interpretable quantities for clinical decision making. We demonstrate the performance of COBRA-DOSE using DEN-181, a phase I immunology trial in rheumatoid arthritis. We also provide a general implementation of our approach through the CobraDose package in R.

Cardiac fibrosis reduces electrical conductivity and is a leading cause of arrhythmia. Arrhythmic waves typically rotate around non-conducting fibrotic patches, so the geometry and topology of these patches (spatially isolated regions of fibrotic tissue within the heart muscle) play an important role in arrhythmia dynamics. Despite their clinical relevance, these structures remain poorly understood. We address this open problem using histopathological images of human hearts affected by cardiac fibrosis. Each patch is represented as a spatial graph via skeletonization, where nodes are embedded as points in Euclidean space and edges encode geometric properties of the underlying tissue. The core methodological contribution of this work is the introduction of spatial graph space, a metric space equipped with a rotation-invariant Fused Gromov Wasserstein metric that enables comparison of spatial graphs with differing numbers of nodes and edges. Building on this, we perform a distribution-level statistical testing and depth measures for spatial graphs. To enable the interpretation of the spatial graph sample distribution, we introduce DepthPlot, a novel visualization tool for depth measures in metric spaces. Applying our methodology to compare patients and the spatial position of patches within the ventricles, we find that fibrotic textures exhibit strong patient-specific features, while some hearts display notable geometric similarities, potentially reflecting shared pathological mutations or other unknown factors. Through quantitative depth measures, we characterize test outcomes via central and peripheral spatial graphs, demonstrating that the proposed framework yields statistically and clinically meaningful insights into fibrotic texture characterization.

This study develops a weighted framework for measuring the discrepancy between two nonnegative lifetime distributions through cumulative past extropy. We propose two measures, referred to as the weighted cumulative past extropy inaccuracy (WCPEI) and the weighted cumulative past extropy Kullback-Leibler divergence (WCPED). The generalized weight function is considered in this study. We investigate a number of theoretical properties of these measures. Empirical distribution function-based nonparametric estimator is subsequently constructed for the weighted cumulative past extropy inaccuracy ration (WCPEIR). Its finite-sample behavior is studied through Monte Carlo simulation experiments for different sample sizes. To illustrate the practical relevance of the WCPED, two applications are considered. First, an extropy-based goodness-of-fit procedure for testing uniformity is developed using the proposed divergence measure. Its power is then compared with that of several established uniformity tests under a variety of alternatives. Second, an image analysis application is presented in which the proposed measure is employed to assess changes in the distributions of pixel intensities when the image resolution is altered. The framework is further extended to a dynamic setting by conditioning on the lifetime information available up to a specified time point. This leads to the dynamic weighted cumulative past extropy inaccuracy (DWCPEI) and dynamic weighted cumulative past extropy divergence (DWCPED). Their theoretical properties are derived, and the corresponding nonparametric estimation procedures are proposed. The finite-sample performance of these estimators is evaluated through simulation studies using R software.

We develop bootstrap-assisted robust binary segmentation (BARBS), a recursive binary segmentation method for multiple change point detection under general nonstationary temporal dynamics. A novel Gaussian multiplier bootstrap for the CUSUM statistics is proposed, offering robustness to complex dependence structures. Through meticulous calibration of the critical values at each stage of the recursion, BARBS ensures control of the Type I error under the null hypothesis of no change points. When change points are present, BARBS identifies the correct number of changes with a prespecified probability, and the resulting change point location estimators attain the same uniform consistency rate as classical binary segmentation. Building on this, we introduce second-stage refined estimators that achieve the optimal individual localization rate, and establish their asymptotic distributions and nearly optimal uniform localization rates under both fixed and vanishing jump magnitudes. Extensive numerical experiments across various settings confirm the robustness and superior performance of BARBS relative to existing approaches. To illustrate the practical relevance of the proposed methodology, we analyze U.S. inflation data, yielding change points that align with several documented macroeconomic episodes.

We propose a distributed selective inference framework tailored for high-dimensional quantile regression. To enable valid post-selection inference in this context, we address the computational challenge posed by the non-smooth quantile loss via a response-surrogation strategy. This strategy transforms the problem into a penalized least-squares formulation, thereby facilitating distributed selective inference. For valid post-selection inference, a randomized procedure is introduced, in which the Lasso selection event is characterized through the associated Karush-Kuhn-Tucker conditions and the conditional distribution of the aggregated estimator is derived given the selection event. The resulting algorithm requires only three rounds of communication between local machines and the central server. Under standard regularity conditions, we establish the asymptotic validity of the proposed procedure and develop a large-deviation approximation to the selective likelihood for computationally tractable implementation. Simulation studies and a real-data application demonstrate the satisfactory finite-sample performance of the proposed method.

Causal mediation analysis is typically formulated under no interference, an assumption often violated in networked populations. We develop a nonparametric framework for a single large observed network that allows simultaneous treatment and mediator spillovers and high-dimensional network confounding. Exposure and mediator mappings define causal estimands without restricting the true interference mechanism, separating own from spillover effects without prespecified aggregation models. Under strengthened conditional independence conditions, we identify own controlled direct, natural direct, and natural indirect effects and give primitive sufficient conditions in terms of structural errors. We construct augmented inverse probability weighted estimators that are doubly robust for controlled effects and multiply robust for natural effects, using graph neural networks to learn high-dimensional nuisance functions from node features and the adjacency matrix. Under approximate neighborhood interference, weak network dependence, and suitable first-stage rates, we establish asymptotic normality of the effect estimators and consistency of a network HAC variance estimator. In simulations the graph neural network estimator outperforms machine learning methods built on hand-constructed neighborhood features, and a reanalysis of an agricultural insurance experiment in rural China finds insurance knowledge to be a substantive mediating channel while perception-based mediators are not.

Many operational decisions are sequences of interventions under a cumulative resource limit, such as a maintenance schedule within a crew-hour budget. Choosing among them calls for the outcome and the cumulative cost each would produce, counterfactual quantities identified from observational data. Two strategies with the same expected cost can exceed the budget at very different rates, so constraining the mean does not bound how often an overrun occurs. Prior two-step architectures, recently extended to continuous doses, constrain the mean cost rather than its tail and allocate at a single decision point. Methods that do bound a cost tail take its distribution from a specified model rather than identifying it from data. We present a predict-then-optimize framework. In the prediction step, any estimator returning an outcome value and a cost distribution supplies what the decision rule consumes, so the predictor is interchangeable. In the optimization step, a chance-constrained selection over a finite candidate set bounds the probability that the cumulative cost exceeds the budget. That tail does not decompose across stages, so each strategy is scored whole. Sweeping the tolerated violation probability traces a safety-utility frontier, and distribution-free finite-sample bounds cover violation and outcome shortfall. Four of five environments, spanning clinical treatment and equipment maintenance, supply exact counterfactual ground truth; the fifth carries real outcomes from a digital-health micro-randomized trial. Across them, the rule holds the budget where a point-estimate rule overruns it, at an outcome cost the frontier makes explicit. All code is available at https://github.com/mfriendly/counterfactual-chance-selection

We consider the classical additive measurement-error model $X=Y+Z$, where the latent random variable $Y$ has unknown distribution $F_Y$ and the error $Z$ has a known distribution. We develop direct estimators for three functionals of $F_Y$: (i) $F_Y(x)$ at continuity points; (ii) interval probabilities $F_Y(y)-F_Y(x)$ when $x<y$ are continuity points; and (iii) the size of a jump at a prespecified discontinuity. We derive non-asymptotic bias and variance bounds, and establish asymptotic unbiasedness and consistency. Unlike previous work, we do not require $F_Y$ to admit a density, have a mixture representation, or satisfy global Sobolev smoothness assumptions. The framework accommodates arbitrary latent distributions, including those with both discrete and continuous components, and distributions with multiple jumps. These results rely on a link between Fourier inversion theorems and the algebraic structure of a class of estimators proposed in Mynbaev, Martins-Filho and Henderson (2022). A simulation study evaluates feasible tuning procedures and, where available, compares the finite-sample performance of the proposed estimators with existing methods.

In the linear regression model, we construct a nonparametric estimate of the regression parameter vector $\boldgreek\beta$ that is insensitive to a possible nuisance autoregression in the model errors. The main tool for estimating $\boldgreek\beta$ is based on the autoregression rank scores of the model. The resulting estimator is invariant to the autoregression parameters and thus remains insensitive to potential hidden linear trends or other structured disturbances, which frequently occur in economic, hydrological, and related applications.

We propose a robust barycenter for distribution-valued data by incorporating the Huber loss directly into the optimal transport cost. In contrast to metric-space Huber means, which apply the Huber loss to the Wasserstein distance after optimization, our construction acts on individual transport displacements, preserving quadratic behavior locally while limiting the influence of large displacements. The resulting Huber-Wasserstein barycenters form a natural interpolation between Wasserstein means and $L^1$-type Wasserstein medians. We establish the analytical and statistical foundations of this construction. For optimal transport with Huber loss, we prove regularity and uniqueness properties of dual potentials, existence of optimal transport maps, and stability as the Huber parameter varies. For the associated barycenter problem, we prove existence and characterization results, consistency of empirical plug-in estimators, and a finite-sample breakdown point essentially equal to $1/2$. In dimension one, we further derive the pointwise influence function and asymptotic distribution, quantify the associated robustness-efficiency trade-off, and show that displacement-wise Huberization can retain first-order information that is lost by distance-based Huberization under localized shape contamination. Numerical experiments on contaminated distribution-valued data demonstrate the robustness of the proposed barycenters and illustrate their interpolation between mean- and median-like behavior.

Mediation analysis is a powerful tool to decompose treatment effects into direct and indirect components, enabling explanations of total treatment effects in a formal statistical framework. However, applying such analyses to settings with time-to-event outcomes, time-dependent mediators and confounders remains challenging. Existing methods are statistically complex, computationally intensive, and rarely available in user-friendly software. The difference method offers a simple alternative, but its performance in this setting has not been systematically evaluated. We conducted a simulation study and real-world data analysis to fill this gap in the literature. Using Cox proportional hazards, Aalen additive hazards, and accelerated failure time (AFT) models with time-varying covariates, the difference method was compared across different data generation processes with time-dependent mediators and confounders, focusing on bias in estimated indirect effects. The parametric mediational g-formula was used as benchmark comparator. If correctly specified, the Aalen model based difference method produced unbiased estimates in the absence of a time-dependent confounder that was directly caused by the treatment. Similar results were obtained when using the Cox model based difference with rare outcomes, but not with common outcomes. The AFT model based difference method was biased in almost all scenarios, due to collapsibility issues. Only the parametric mediational g-formula was unbiased in all scenarios. In contrast to specialized methods, the difference method requires additional, often unrealistic, assumptions, such as the absence of a direct causal relationship of the treatment on time-dependent confounders. If those assumptions hold, however, it may be used as a simple and efficient alternative.

This paper presents WIRED, an R package algorithm for joint probabilistic forecasting of multiple related time series. WIRED combines a library of simple marginal predictive distributions, CRPS-based adaptive mixture weights, and a Gaussian or Student t copula for cross-series simulation. We evaluate the implementation in a benchmark with four synthetic data-generating processes (DGPs), three forecast horizons, 30 replicates per DGP-horizon pair, nine ablations and external baselines, and a rolling-origin study on the built-in EuStockMarkets data. The central contribution is architectural and diagnostic. WIRED separates adaptive marginal expert aggregation from dependence reconstruction; the benchmark supports explicit dependence modeling, but shows that the current CRPS-extrapolated softmax weighting is not yet robust enough to dominate simpler bootstrap or equal-weight alternatives. The paper therefore identifies a working layer of the design, a bottleneck in the marginal aggregation layer, and a concrete research path for more regularized probabilistic ensemble construction.

Bayesian inference for A/B testing is a family of prior and stopping-rule configurations with fundamentally different statistical properties, but it is often discussed as a single method, and no systematic overview exists. This paper organizes common configurations into a three-tier hierarchy: 1) posterior coherence with no error control, 2) false positive rates bounded under continuous monitoring via Bayes factor stopping, and 3) false discovery rate control and calibrated shrinkage via empirical Bayes. Many commercial platforms operate at the lowest tier by default. We show that Bayes factor stopping is near-optimal for a broad class of cost functions, including most proposed in the A/B testing literature; because the same rule also controls the false positive rate, the choice between a decision-theoretic and a frequentist formulation is largely one of parameterization. Furthermore, the empirical Bayes prior is the only path to the third tier, but winner-selected corpora, pooled programs, and heterogeneous metrics can each prevent calibration regardless of corpus size. Simulations against group-sequential and always-valid frequentist baselines show that flat-prior posterior stopping exactly reproduces naive peeking, that a well-calibrated empirical Bayes prior achieves the lowest estimation error, and that expected-loss stopping minimizes regret only when shipping a null-effect variant is nearly free. Error rates, estimation accuracy, and regret are all different risks, and the appropriate method follows from the risks an experimentation program needs to control, not the other way around.

In this contribution we study max-stable random fields on the rooted tree under shifts to descendant subtrees. Branch-Brown–Resnick stationarity is characterised through homogeneous spectral classes, punctured tail measures, and local spectral tail fields. For lognormal representers, it is equivalent to invariance of the variogram under addition of a common prefix. We give Gaussian, max-autoregressive, regenerative cascade, and free-group cluster constructions, and show that summability on countably branching trees need not satisfy a zero–one law. We also derive the associated branch-invariant extreme-value and Archimax copulas.

Between the classical (frequentist) approach, which is based solely on the data, and a fully Bayesian set-up where one assumes a prior distribution for the model parameters, lies the Empirical Bayes (EB) approach which appears to be a good compromise between the aforementioned two approaches. Even though many researchers have suggested various variants of the EB method, the standard practice is to derive the Bayes estimator under a family of suitable priors indexed by its own parameter(s), called the hyperparameter(s), and then replace the unknown hyperparameter(s) by their estimate(s) obtained from the marginal distribution of the data. But the fundamental question that is being raised here is: does the EB method really work to produce an improved estimator - the so-called Empirical Bayes Estimator (EBE)? In this work we are going to revisit the widely cited simple problem of estimating a Binomial parameter using the regular two-parameter Beta family of priors under the quadratic loss function, and prove that the Type-II maximum likelihood (ML-II) step does not work. If we further restrict our attention to one-parameter symmetric Beta family of priors then still the resultant EBE does not show any remarkable performance compared to the MLE details of which have been provided with extensive computations. The Binomial study has been extended to the Poisson model as well.

Prognostic regression models often synthesize data from multiple sites, whether within a multi-site study, across federated settings, or in individual participant data meta-analysis. Here, a site is any data source, such as a hospital, registry, trial, or study, and need not be a physical center. Analysts must then decide whether one regression model represents all sites or whether site-specific models are needed. Established measures such as coefficient-level tau^2 quantify heterogeneity but do not distinguish its source. We focus on diagnosing whether coefficient heterogeneity reflects case-mix or site-specific context effects. Case-mix heterogeneity can arise when linear regression terms approximate multivariable non-linear relationships in populations with different covariate distributions. Contextual heterogeneity arises when comparable patients require different regression relationships across sites. We do this by fitting site-specific local regressions in a dimension-reduced space and partitioning the smoothed coefficient surfaces into a cross-site reference and site-specific deviations. An autoencoder and custom loss structure the latent space around local prognostic relationships. We then project this partition onto the outcome scale to derive observation- and site-level summaries. We demonstrate the approach on a COPD trial with two sites. In the three leading latent slope coordinates, coefficient-surface variation was predominantly contextual. The derived observation-level outcome-scale variance partition was case-mix-leading, whereas its between-site aggregation was concentrated in contextual differences rather than case-mix shifts. A permuted-site negative control assesses whether the contextual summary can arise when site labels carry no signal. This diagnostic distinction can inform whether joint or site-specific regression models should be evaluated.

Motivated by sequential space-filling designs for computer experiments, we study algebraic constructions of extensible point sets in the $d$-dimensional unit cube whose two-dimensional coordinate projections are all quasi-uniform. Our two constructions share a common parametrization in terms of finite configurations of distinct rational directions on the projective line $\mathbb{P}^1(\mathbb{Q})$. First, using a cubic number field, we construct explicit Kronecker sequences for which the mesh ratios of all two-dimensional coordinate projections remain uniformly bounded over every initial segment of length $N\ge 2$. Second, using a real quadratic field, a split prime, and a compatible $p$-adic embedding, we construct nested rank-1 lattice designs with the same uniform projection property at every nesting level. The proofs combine algebraic norm estimates with transference principles between simultaneous and dual Diophantine approximation, yielding lower bounds for the separation radii and upper bounds for the covering radii, both of optimal order in the number of points, uniformly over all coordinate pairs. We also investigate how the choice of rational projective coefficients affects the resulting mesh ratios. This leads to a minimax problem for finite configurations on $\mathbb{P}^1(\mathbb{Q})$, in which one seeks to minimize the maximum mesh ratio over all two-dimensional coordinate projections. These constructions provide extensible point sets with uniformly controlled bivariate geometry.

The two-stage approach and Bayesian joint modeling are commonly used to analyze longitudinal biomarker measurements together with time-to-event outcomes. Using data from an HIV clinical trial of 467 patients with repeated CD4 measurements and all-cause mortality as the survival outcome, we compared a baseline two-stage approach with a Bayesian joint model. The two-stage analysis fitted a linear mixed-effects model and included each patient's predicted baseline CD4 value as a fixed covariate in a Cox proportional hazards model. The joint model simultaneously modeled the longitudinal CD4 process and survival while linking mortality risk to the current underlying CD4 value. The estimated association between ddI and mortality was similar in direction and magnitude across the two approaches. The two-stage estimate was HR = 1.342 (95% CI: 1.006-1.789), whereas the joint-model estimate was HR = 1.383 (95% CrI: 0.952-2.010). The estimated protective association of CD4 was stronger under the joint model (HR = 0.776) than under the two-stage approach (HR = 0.826). Because the approaches used different summaries of the longitudinal CD4 process, the observed differences cannot be attributed solely to measurement error or informative dropout. The findings demonstrate that the treatment of longitudinal biomarker information can materially affect statistical inference.

Cramer's V is the effect size reported beside almost every chi-square test, read against Cohen's labels, yet a large fraction of such numbers describe sampling noise and the standard bias correction (Bergsma 2013) does not fix it. We assemble three results and claim only the consequence of each. First, the squared effect size phi^2 admits no unbiased estimator at any sample size: under fixed-N multinomial sampling the expectation of any estimator is a polynomial in the cell probabilities, while phi^2 is not. Second, unbiasedness transfers across a rescaling of the effect size only if the rescaling is affine, and among affine choices V^2 = phi^2/k is the one bounded in [0,1] with value 1 at perfect association. Third, we give an interval with conservative, asymptotically valid coverage, obtained by projecting a likelihood-ratio confidence set for the cell probabilities through the effect-size map; its lower endpoint is zero in closed form exactly when the test of independence fails to reject. Because nothing is unbiased, the only question is where the irreducible error is placed. Bergsma's correction puts zero error at the null but several percent under the alternative; a delete-one jackknife on the V^2 scale spreads it thin everywhere (absolute bias at most 0.008 over a 180-design grid). Pooling does not remove bias: across 3,000 simulated meta-analyses, pooling 200 studies drives the naive estimator's chance of landing within 0.01 of the truth to zero, while the jackknife's rises to 0.99. The projected interval covers 0.997-1.000 across the tested designs, while a noncentral inversion undercovers (0.936 at phi^2 = 0.18) at two to three times the width. The point estimate and the interval are different problems with different answers; conflating them is why the literature has neither. We give a routing rule and a browser tool that implements it.

An e-detector for a pre-change class $\mathcal P$ is a nonnegative process $M$ such that $\mathbb E_P[M_\tau] \leq \mathbb E_P[\tau]$ for all stopping times $\tau$ and all $P \in \mathcal P$. Thresholding e-detectors controls the average run length (ARL): declaring a change at the first time $T_b$ when $M$ crosses $b$ ensures that $\inf_{P \in \mathcal P}\mathbb E_P[T] \geq b$. But e-detectors do substantially more than control the ARL; they also satisfy a optional-horizon inequality: \[ P(T_b\leq\sigma)\leq \mathbb E_P[\sigma]/b \] for every data-dependent stopping time (monitoring horizon) \(\sigma\) and $P\in \mathcal P$. In particular, every e-detector-based procedure obeys $P(T\leq t)\leq t/b$ at each fixed $t$, thus avoiding early false alarms. Remarkably, the converse also holds: every stopping time $T$ that satisfies the optional-horizon inequality must in fact arise from thresholding an e-detector. We also derive a universal representation of stopping times that satisfy (only) ARL control. These are represented by weak e-detectors, that only require $\mathbb E_P[M_\tau] \leq \mathbb E_P[\tau]$ to hold at all threshold stopping times $T_b$. Appendices present universal representations for other (less common) change detection metrics.

Simulating realistic time-to-event data is essential for planning and evaluating complex clinical trial designs. Conventional approaches often sample event times from parametric families, such as Weibull or log-normal distributions, which restrict hazard shapes and may poorly represent observed survival data. We propose an empirical copula-based framework for simulating multivariate data containing continuous, binary, count, and right-censored time-to-event variables. The method completes censored historical survival data using a two-zone procedure that combines conditional Kaplan-Meier imputation with a parametric tail. It matches a target survival distribution through a log-scale location-scale transformation and a power distortion of the empirical percentile function, while preserving historical dependence through a Gaussian copula fitted to rank correlations. In an oncology trial of previously treated non-small-cell lung cancer, the method reconstructs overall survival and progression-free survival curves for the experimental arm using control-arm data and a small set of target percentiles. Simulations preserve rank correlations among baseline covariates and the dependence between progression-free and overall survival, with censored Kendall's tau of 0.522 compared with 0.549 in the observed data. The method is implemented in the R package EmpiricalSim.

We present a hierarchical Bayesian framework for non-homogeneous pairwise interaction Gibbs point process models, where the global and local effect functions are modeled via basis function expansions. We further propose a testing procedure in order to assess complete spatial randomness. The proposed methodology is exemplified through two real benchmark data examples involving water striders and forest fires.

Detection and attribution of climate change relies on fingerprinting–a linear errors-in-variables regression framework in which both predictors and responses exhibit internal variability governed by a proportional covariance structure, subject to a variability inflation factor. Accurate estimation of the scaling factors (regression coefficients) depends on inferring the precision matrix of the regression errors from limited climate model control runs. In high-dimensional settings, existing approaches often overlook the variance inflation of the predictors and suffer from imprecise precision matrix estimates, yielding biased estimators, underestimated uncertainties, and confidence intervals with poor coverage. We propose a nonlinear, rotation-invariant shrinkage framework for estimating the precision matrix that restores the asymptotic optimality of the total least squares estimator in high-dimensional regimes. Our procedure jointly estimates the scaling factors and the variability inflation factor, thereby correcting estimation bias, and incorporates consistent variance estimators to enable valid uncertainty quantification. We also develop a residual consistency test to assess model adequacy. Numerical studies demonstrate precise estimation, improved confidence interval coverage, and higher efficiency. Applied to annual mean near-surface air temperature data from 1951–2020, our method produces narrower and more reliable confidence intervals, yielding refined attribution results.

Organizations decide whom to treat under a budget and want to know what a targeting rule would have earned before deploying it. Off-policy evaluation promises this from logged data, but the deployable rule is a deterministic top-k policy: it removes all averaging over actions, so weak overlap hits the estimate directly. We benchmark six estimators across five datasets and two known-effect sweeps, and validate the mechanisms against a non-simulated paired reference. First, weak overlap is governed by logger-target action alignment, not by logging sharpness alone: what governs support is the logger's probability of the target's actions. Sharpening a logger built from the target's own score barely moves overlap over the tested range; action-level disagreement collapses it. Effective sample size ranks this risk across logging environments, but is weak at ranking candidates within the single log a practitioner holds, and its cut point does not transfer. Second, the optimizer's curse is not fixed by cross-fitting the outcome nuisance. When the rule is fit on the data used to evaluate it, cross-fitting the nuisance alone leaves the reuse bias in place and makes it worse. Honest policy-level splitting avoids the reuse by targeting the learning procedure's value – a change of estimand, not a de-biasing of the full-sample policy. Third, propensity-estimation error is the largest degradation we measure: an out-of-fold estimate hurts IPS more than any other stress we apply, leaves doubly-robust estimation almost unchanged, and can invert the overlap diagnostic itself. Logging is synthesized and propensities floored at 0.02, so every failure occurs with bounded weights; the floor also reduces the two tuned hybrids to their untuned parents, leaving four practically distinct estimators, and all exact-value surfaces are synthetic or semi-synthetic. We release the benchmark; public data only.

A predictive model can fit its data even when its information set is insufficient; fit alone cannot establish sufficiency. This Perspective introduces Level II-A, a new design-based inference framework to test this distinction, illustrated in anticipatory EEG using contingent negative variation. A pre-event endpoint is committed before the delay to the imperative event is randomised. That later-assigned delay thereby becomes a negative-control probe of whether past-adapted information was sufficient for an already committed result. Under the past-adapted factorisation, accounts using only pre-commitment information cannot systematically order the endpoint by that delay. Leakage-safe preprocessing, a frozen label-blind comparator and retained-sample qualifications carry the exclusion to the confirmatory residual. A qualified material negative ordering supports conditional insufficiency without identifying a mechanism; an adequately sensitive null supports a bounded affirmative conclusion calibrated by the pipeline's false-adequacy rate. A non-compensatory rule separates these from diagnostic failure, selection-limited, opposite-direction and inconclusive outcomes. No human EEG data are analysed. In the synthetic benchmark, grid-based false-adequacy boundaries are $15\,\mu\mathrm{V\,s^{-1}}$ for assignment isolation and $30\,\mu\mathrm{V\,s^{-1}}$ for the sequential e-value route, in both directions. The design transfers wherever endpoint commitment precedes an exogenous label, probing sufficiency only where a declared alternative predicts ordering by it. It turns "the past explains it" from a working explanatory assumption into a magnitude-qualified, testable claim.

The presence of unmeasured confounding factors during the collection of observational data may lead to biased estimates of the effect of an exposure on an outcome. Consequently, a central problem in causal inference based on observational data is sensitivity analysis with respect to unmeasured confounding. Existing sensitivity analyses generally focus on worst-case bounds. We propose an exact method for quantifying the significance of confounding, defined here in terms of the complete range of analytical estimates of the stratification-based Risk Ratio over the set of all joint distributions compatible with the observed characteristics. We refer to the proposed method as Inverse Confounding Analysis (ICA). The proposed ICA method extends the widely used E-value approach but, in contrast to it, does not restrict the analysis to a worst-case lower bound. Instead, it provides exact estimates over the entire set of admissible configurations. This requires several additional input parameters, namely the frequencies of the exposure, the confounder, and the outcome. The ICA method is based on an inverse problem: reconstructing the set of admissible joint distributions from specified frequencies and pairwise associations. We formulate this reconstruction problem as a system of nonlinear equations and obtain an analytical solution. Surprisingly, the complete solution set can be parameterized linearly by a single free parameter. The corresponding stratification-based Risk Ratio is then represented as a fractional-linear function of this parameter. This representation makes it possible to derive exact analytical measures of the significance of confounding over the entire set of admissible statistical configurations.

Structured potential outcomes such as microscopy images may be recorded after an unknown, unit-specific transformation. If that transformation can depend on treatment, covariates or the intrinsic outcome, raw-coordinate analyses may mix biological effects with acquisition geometry. We study the unrestricted observation model X = {\Gamma} . Y(A) and characterize its observable information: a target is uniformly recoverable exactly when it is constant on group orbits, while a Borel maximal invariant retains every measurable invariant target. We then distinguish observability from statistical losslessness. A quotient-faithful reconstruction theorem shows that quotient reduction is sufficient for the full transformed experiment exactly when the conditional law of the raw observation given treatment, covariates and the quotient has a parameter-free version. Conditional Haar contamination on a compact group yields Blackwell equivalence as a special case; it is not imposed in the main model. We also separate independent site-specific product actions from shared diagonal actions and show why componentwise canonicalization can discard relative cross-site information. Under explicit metric and kernel regularity, an approximate-contamination theorem bounds quotient-law Wasserstein error and the induced perturbation of population maximum mean discrepancy. For finite-support multichannel lattice images, we construct a maximal invariant under integer translations and quarter turns, combine its characteristic Gaussian kernel with a complete paired-swap test, and retain the original simulations and RxRx1 HUVEC study. Under the sharp null, the quotient test rejected in 0.052 of simulation replicates; at unit effect strength its power was 0.992. The primary RxRx1 contrast had an enumerated paired-swap p-value of 0.0078.