Papers

We study the non-uniqueness of exact two-sided $p$-values in continuous one-parameter natural exponential families (NEFs). For directed one-sided problems, the tail $p$-value agrees with the $p$-values using UMP, UMPU, and likelihood-ratio (LR) tests. For a two-sided simple null, we distinguish four constructions: equal-tail, density-ordered, UMPU, and LR $p$-values. At a fixed null parameter, UMPU and equal-tail $p$-values coincide if and only if the null law is symmetric about its mean; under a regular two-branch density-level condition, the same fixed-null symmetry characterization holds for UMPU versus density ordering and equal-tail versus density ordering. Requiring any of these coincidences throughout the NEF characterizes the Gaussian family. We combine these results with the theorem of Bar-Lev, Bshouty and Letac that UMPU and LR $p$-values coincide throughout a continuous NEF precisely for the normal, gamma and inverse-Gaussian families. We also investigate the two LR pairings not covered by those results. If equal-tail and LR $p$-values coincide throughout a NEF satisfying our standing regularity assumptions, then $(V^{2/3})^{\prime \prime \prime }=0$ on the mean domain. The same coincidence also forces an explicit density-at-the-mean identity. For an i.i.d.\ sample with canonical sufficient statistic $T_n=\sum_{i=1}^nX_i$, persistence of equal-tail-LR coincidence throughout the family along an unbounded sequence of sample sizes forces Gaussianity. A corresponding density-LR statement is given conditionally on an explicitly stated differentiated local Edgeworth expansion. Finally, inverse-Gaussian and hyperbolic-secant examples quantify numerical $p$-value differences, disagreement of rejection decisions, and differences in power.

Modern time series are often long, serially dependent, and non-stationary. Existing change-point methods either target specific changes or become computationally intensive when using nonparametric costs on long series. Many also require thresholds to be carefully calibrated under serial dependence. We introduce SCAN, an offline method for detecting multiple distributional change-points in long, serially dependent univariate time series. SCAN compares adjacent windows using an integral probability metric, calibrates local discrepancies with a dependence-aware bootstrap, and refines candidate locations using a scaled 1-Wasserstein criterion, enabling detection of changes in mean, variance, and broader distributional structure within a unified framework. An ensemble over multiple window sizes reduces sensitivity to window size and threshold specification. We establish consistency of the estimated number and locations of change-points under exponential alpha-mixing dependence, and show that the localization statistic reduces to a CUSUM-type statistic under pure mean shifts. In simulations with up to one million observations, SCAN generally achieves higher covering and F1-scores than competing methods across mean and joint mean-variance shifts, particularly under serial dependence. On real data, SCAN identifies labeled activity transitions in sensor data and interpretable structural changes in hourly Bitcoin prices. Implementations are available in the Python package scan-cpd and R package scanr.

In this work, we explore particle learning strategies for the joint estimation of static parameters and latent states within conditional sequential Monte Carlo (CSMC) algorithms. Building on this idea, we propose the p(parameter)-CSMC algorithm, which incorporates both parameter learning and ancestor sampling, leading to much better mixing properties compared to (particle) Gibbs sampling in settings where strong internal correlations may challenge effective exploration. We also include two applications in the context of a branching process model: one using synthetic data, where we estimate the infectivity profile while assuming the reproductive number to be known, and another using real data, where we address the joint inference of the reproductive number and the infectivity profile based on daily hospital incidence from the arrival of the SARS-CoV-2 lineage B.1.1.7 (Alpha) in Norway in February 2021. We show that, in these settings, performance is dramatically enhanced, with substantially faster mixing and markedly reduced autocorrelation compared with standard particle Gibbs.

Artificial Intelligence trustworthiness scores are moving from research dashboards into compliance claims and procurement decisions. A compliance claim is a statistical decision based on the comparison between an estimated compliance metric and a set threshold. The recently proposed integrated SAFE AI metrics are based on three basic rank-graduation measures of accuracy, explainability and robustness, expressed on a common footing. The metrics are integrated into a single compliance score, so far reported as a point value. In this paper we propose to add an uncertainty layer to the SAFE AI compliance score. All component metrics are estimated on a shared test sample, so their errors covary. We estimate the full covariance of the component vector with a paired bootstrap, and quantify departures from the source-wise independence baseline suggested by the integrated-metrics framework's variability decomposition. A closed-form identity splits such departure into an uncertainty-weighted effective dimension and an exposure-weighted data-driven correlation, with both depending on the aggregator and the estimated uncertainty of the component metrics. The application of our proposal to both real and simulated data shows that the assumption of independence can either narrow or widen confidence bands, while the direction and magnitude of the effect depend on the aggregator type, machine learning model, and perturbation family. The resulting confidence region supports compliance decisions, which can be documented in a formal uncertainty certificate.

Public benchmark scores may reflect skill, prior exposure to the questions, or both, and for most models the training data are unknown. We present CleanScore, a black-box audit using scored outputs only. Each benchmark question becomes a parent item with one public form and two independently written fresh forms preserving its numbers, facts and answer. The audit reports an interval for the public-form advantage rather than a verdict, and a private negative-control bank with an explicit transport radius separates exposure from ordinary form mismatch. A registered controlled-exposure experiment detects planted exposure and stays quiet under fresh-form exposure. A registered audit of five open models on 200 GSM8K and 200 ARC-Challenge items finds no exposure-consistent advantage, bounding surface-form inflation below five points. Registered positive controls then bound what such a null can mean. Leaking an item raises accuracy on paraphrases the model never saw almost as much as on the leaked wording, leaving 52% to 110% of the effect invisible to a paraphrase audit. On ARC a planted 49-point advantage shows an observable gap of -0.020, and about 20 points survive rewriting stem and options, across four training seeds. A surface-form null bounds far less than the phrase contamination audit implies.

In the Western United States, snowmelt is essential to the agricultural industry in addition to being a key source of municipal drinking water. Consequently, accurate snowpack forecasting is critical for water policy and management. Automated Snow Telemetry (SNOTEL) stations provide accurate daily measurements of snow water equivalent (SWE) that exhibit strong correlations in space and in time. We tackle the problem of predicting future SWE values across the SNOTEL network. Specifically, we use a Gaussian Process-based linear transformation to remove spatial correlations before training a long short-term memory (LSTM) neural network on the decorrelated SWE data. This approach allows the LSTM to learn a clean temporal signal at each station. We show that this separation of spatial and temporal components yields better predictive success than multiple baseline models. Furthermore, we incorporate conformal prediction to quantify uncertainty in the resulting SWE forecasts, providing a distribution-free approach to illustrate a potential framework for establishing predictive intervals for spatiotemporal data. Together, accurate point forecasts and distribution-free uncertainty quantification provide a framework for SWE accumulation forecasting on subseasonal scales or projecting SWE with future data while motivating and supporting future work in predicting a large-scale, spatiotemporally complete SWE map.

Bayesian variable selection becomes computationally challenging when models contain many dependent parameters. We study Piecewise Deterministic Markov Process (PDMP) samplers as a continuous-time alternative to conventional Markov chain Monte Carlo for spike-and-slab variable selection. In sticky PDMP samplers, active parameters evolve continuously until they reach zero, where they may remain for a random duration before re-entering the model. While one parameter enters or leaves the model, the remaining parameters continue to evolve along the deterministic flow, offering a potentially advantageous mechanism for exploring posteriors with strongly dependent parameters. We make two methodological contributions. First, we extend existing sticky PDMP methods beyond independent spike-and-slab priors to dependent model priors and dependent slab distributions. Second, we investigate the use of unbiased stochastic gradients to reduce the computational cost of variable selection when the likelihood decomposes into many factors while retaining the same target distribution. We study these extensions to two psychometric models: a Gaussian random intercept cross-lagged panel model and an ordinal Markov random field. For the former, marginalization yields a fixed-dimensional sufficient-statistic representation that permits efficient model evaluation. For the latter, the model factorizes, which enables subsampling over person-node contributions. In simulation studies, we compare ZigZag, Bouncy Particle, and Boomerang dynamics with reversible-jump MCMC, and examine the effects of prior dependence and stochastic-gradient subsampling on sampling efficiency. We illustrate the methodology using data from an empirical study on mental well-being. Finally, we discuss the advantages and challenges when using PDMP samplers for Bayesian variable selection.

We propose a multivariate extension of the pseudo-Voigt profile-a weighted convex combination of Gaussian and Cauchy distributions-within a finite mixture modeling framework for robust model-based clustering and outlier detection. To ensure parsimony and coherence within clusters, shared location and scale parameters are imposed between the Gaussian and Cauchy components. Parameter estimation is carried out via an Expectation Maximization algorithm, with latent variables facilitating efficient likelihood-based inference. The performance of the proposed model is evaluated through simulation studies and applications to real-world data. Comparisons with established robust models, including mixtures of contaminated normal distributions, are provided to illustrate the model's clustering accuracy and outlier detection capabilities. The framework is shown to be particularly effective for data characterized by heavy-tailed behavior.

Aggregated relational data (ARD) record how many ties sampled respondents have to prespecified groups without revealing individual dyads. We develop a conditional test for prespecified cross-group concordance beyond an additive-activity network model. When the groups form an exhaustive partition, respondent degree is observed exactly. For arbitrary fixed activity values under an independent-Bernoulli additive-logit null, conditioning two respondents on equal degree yields a finite nonpositive sign restriction for their two disjoint group-count differences. Analyst-randomized pair thinning gives a conservative baseline. Under a stronger fixed-cell design with group-specific smooth activity profiles and positive cross-role overlap, an observable clipped full-pair statistic gives conservative one-network inference with graph-independent sampled respondents. Finite and growing matched-law constructions establish that the target contains bivariate information absent from a collapsed binary count. The full-pair procedure is uniformly consistent on a primitive relative-open neighborhood of a specified rank-one alternative. Fixed-dimensional lattice local limits make the conditioning and availability requirements explicit.

The increasing availability of serosurveys that measure antibody responses to multiple antigens requires the development of methods that can exploit the full information content of such data, both biological and spatial. However, the non-Gaussian and potentially multimodal distributional behaviour of antibody responses makes the development of such methods inherently complex, especially in a multivariate setting. Here, we extend the latent variable framework of Giorgi and Wallin (2026), in which continuous antibody concentrations are modelled through an individual-level latent seroreactivity process that represents the level of immune activation to a given antigen. We focus primarily on the bivariate setting and set out a series of guiding principles that justify the resulting joint modelling structure. The proposed model captures distinct sources of correlation between antibody responses, arising both from shared exposure to the same environment and from biological processes occurring within the same host. Spatial dependence is introduced through a novel bivariate Matérn random field, which we use to construct a parsimonious class of cross-covariance functions between antigen-specific spatial processes. We illustrate the application of the framework to analyse data on bivariate antibody measurements from a malaria serosurvey in the Kenyan highlands. Results from the application and a simulation study show that ignoring this correlation substantially degrades inference on joint properties of the antibody distributions and on individual-level seroreactivity, but matters less when interest lies exclusively in each antibody's marginal distribution. Finally, we discuss how the framework could be extended to settings with more than two antigens, and highlight the modelling challenges that arise as the number of antigens grows.

Statistical tests are often asked to do too much. A single reported result is expected to describe what the observed data say, reassure readers about repeated-sampling behavior, and remain convincing when the working model is perturbed. Those tasks are connected, but they are not equivalent. Fisherian inductive inference and Neyman-Pearson decision theory clarify the first two; robust testing, sensitivity analysis, fragility measures, multiverse analysis, and distributional-stability methods speak to the third. I propose Evidence-Calibration-Stability (ECS) as a framework for keeping these roles separate while reporting them together. Evidence is post-data. Calibration belongs to the design or procedure. Stability is the post-data distance from the benchmark analysis to a conclusion-reversing perturbation within a declared model neighborhood. Full ECS support is conjunctive: a strong coordinate cannot rescue a failed one. For finite-dimensional affine perturbations, I derive an exact ellipsoidal stability radius. For smooth nonlinear margins, a uniform quadratic-remainder condition yields a certified lower bound over a declared neighborhood, showing when the affine formula is only a surrogate. I also establish coordinate invariance and a matrix extension for multiple claims, and distinguish confirmatory calibration from descriptive calibration profiles when prespecification is unavailable. Simulations for the one-sample t test and Student's historical sleep data show that the three coordinates can lead to different interpretations. ECS is a formal synthesis, not a claim that evidence, power, or robustness is itself new.

Background/Aims: Adjustment for prognostic baseline covariates can improve precision in randomized trials. Previous work has shown that jointly modeling primary and secondary endpoints can yield additional precision by borrowing information across endpoints. We investigated whether these approaches can be combined to achieve efficiency gains beyond those obtained through covariate adjustment alone. Methods: We extended a previously proposed one-factor structural equation modeling framework for borrowing information from secondary endpoints to incorporate baseline covariates while retaining the average treatment effect on the primary endpoint as the estimand. To mitigate sensitivity to model misspecification, we combined this estimator with a conventional covariate-adjusted estimator using cross-validated model averaging. We evaluated operating characteristics in simulations and applied the methods to a randomized trial of very low versus normal nicotine content cigarettes. Results: When the structural equation model was correctly specified, endpoint borrowing improved efficiency beyond conventional covariate adjustment across all simulated settings. Model misspecification could induce bias and undercoverage. Model averaging reduced bias and improved coverage relative to the structural equation model estimator, although coverage remained imperfect under severe misspecification. In the trial application, the model-averaged estimate was 21% more precise than the unadjusted estimate and 13% more precise than covariate adjustment alone. Conclusion: Secondary endpoints can contribute meaningful information about the average treatment effect on a primary endpoint even after baseline covariates have been incorporated. These gains require stronger assumptions than conventional covariate adjustment; model averaging provides a practical compromise between efficiency and robustness.

The growing availability of tensor-valued data across multiple institutions creates opportunities for collaborative analysis, but also raises challenges related to data privacy, high dimensionality, and client heterogeneity. This paper introduces a personalized federated tensor regression framework that addresses all three simultaneously. Each client's coefficient tensor is decomposed into a globally shared low-Tucker-rank component and a locally sparse deviation, estimated via a two-stage privacy-preserving procedure. We establish finite-sample upper bounds and minimax lower bounds that quantify the privacy-accuracy trade-off, and prove the consistency of the supporting initialization and rank-selection steps. Simulation studies confirm that the federated approach improves estimation and prediction over purely local methods, especially when per-client data are scarce, and an MRI-based ADHD study illustrates its strong performance under real privacy constraints.

We develop $L^1$ bounds for the difference between a test function of a random sum and a standard normal random variable, where the summands are assumed to be independent but not necessarily identically distributed. The bounds are obtained through a new version of the approximate zero bias transformation specifically developed for random sums. Although the identical distribution assumption is relaxed, the bounds are of order $1/\sqrt{n}$, matching the order of existing bounds in the literature under the same distributional assumption on the number of summands. The main results are then applied to three real-world settings: random sums obtained from simple random sampling with outliers, total insurance claims, and generative AI response times.

Recursive application of the law of total variance decomposes the marginal variance of an outcome into components attributed to explanatory variables and a residual component. The resulting decomposition depends on the chosen conditioning order, and its components do not in general have causal interpretations. We develop a graph-based framework for defining causal counterparts of ordered variance components and establishing their identification from observed data. Under topological orderings, identification can be assessed component by component against the full causal graph, without requiring the variables included in the decomposition to form a causally sufficient system. We also consider scientifically motivated departures from topological orderings, in which selected intermediate variables are conditioned on to obtain controlled-effect interpretations, motivated by the context of disparities in healthcare delivery. We relate the resulting estimands to causal attribution and variable-importance approaches in machine learning, and propose model-based plug-in estimators together with an approximate Bayesian procedure for uncertainty quantification. A simulation study examines finite-sample performance and sensitivity to outcome-model misspecification and flexible machine-learning estimation.

Joint analyses across multiple institutions are increasingly important in biomedical and epidemiological research, particularly for rare diseases where datasets are typical small. However, privacy regulations and institutional policies often prevent the sharing of individual-level patient data. In this paper we present an accurate and single-communication federated inference algorithm. Single-communication federated inference enables statistical analyses through a single exchange of summary statistics between participating centers and a coordinating server, preserving privacy while reducing communication and computational costs compared with iterative federated learning. We extend a recently proposed single-communication federated inference strategy that is based on second-order Taylor expansions by using third-order expansions to better approximate local log-likelihood functions. The proposed method is evaluated through simulation studies based on real data and compared with existing federated inference strategies. The simulation studies assess the performance of the proposed method, with a particular focus on scenarios involving small local sample sizes, where quadratic approximations may fail to capture skewness and other higher-order characteristics of the log-likelihood function. They demonstrate that incorporating higher-order information of the log-likelihood function improves the accuracy while preserving the privacy, communication efficiency, and scalability required for collaborative biomedical and epidemiological research.

Trial-based economic evaluations are widely used to assess the cost-effectiveness of healthcare interventions and inform decision-making. Cost and effectiveness outcomes are typically collected using multi-item questionnaires administered at multiple time points, and are often subject to item-level missingness. In principle, imputation (i.e., replacing missing value with estimated or substituted values) should be performed at the item level to fully exploit available information. However, this is rarely implemented in practice due to several statistical challenges, including the longitudinal data structure, cross-item dependence, heterogeneous missingness patterns, and the mixture of skewed cost and count data. In this paper, we develop a Bayesian longitudinal model for imputing item-level missing data in trial-based economic evaluations that accommodates these complexities within a unified framework. The approach combines a transition-model formulation for longitudinal dependence with flexible distributional assumptions and explicit modelling of cross-item relationships, allowing item-level responses of different types to be coherently modelled over time. Motivated by a real-world trial, we demonstrate the flexibility and practical applicability of the proposed approach. We further discuss how the model can be extended to settings where data may be missing not at random.

Expected shortfall (ES) is widely used to measure tail risk in finance and economics, but its prediction is challenging due to non-elicitability and model uncertainty. This paper proposes a two-stage cross-validation model averaging method for ES forecasting. In the first stage, conditional value-at-risk is estimated using quantile model averaging. In the second stage, a transformed response is constructed and mean squared error-based model averaging is applied to estimate ES. We establish theoretical properties of the proposed method under both correct specification and model misspecification, showing consistency of the estimators and asymptotic optimality of the forecasting risk. Simulation studies and empirical applications to U.S. stock return and macroeconomic GDP growth data show that the proposed approach provides accurate and stable ES forecasts and is computationally efficient.

Recommendation impressions are a finite resource, hence delivering a recommendation to a user who would discover the content organically yields no incremental value and displaces other recommendations that could. We address this by extending an existing production recommendation model to a causal architecture using holdback data that is already collected as part of routine experimentation infrastructure, requiring no new data collection. A central challenge is that attribution windows differ between treated and holdback observations: treated users are attributed a stream within a short direct-response window, while holdback users are attributed organic streams over a multi-day window. This mismatch makes naive treatment-effect subtraction invalid. We resolve this with a dual-threshold targeting policy that delivers a recommendation only when the probability of a treated stream is high and the probability of organic stream is low. In a production-scale A/B test on millions of Spotify users, this policy reduces recommendation impressions by 7% with no statistically significant reduction in overall recommended content consumption. We further show that joint training with holdback data improves calibration of the treated head relative to the production baseline, and argue this can be taken as evidence that causal models learn more generalisable representations than models trained on observational data alone.

The existing literature on model calibration focuses mainly on classification and probabilistic prediction. In this work, we address calibrated point predictions for the conditional mean. Although existing impossibility results preclude exact out-of-sample calibrated predictions, we develop calibrated confidence intervals that provide uncertainty quantification around such predictions. Our results come with distribution-free theoretical guarantees and are applicable in model-agnostic, finite-sample settings under exchangeability by leveraging conformal prediction. Calibrated confidence intervals rely on a general underlying binning scheme. We present two examples of such a binning scheme, one based on a data-independent partition and the other on isotonic regression. Under structural assumptions, we prove that calibrated confidence intervals based on isotonic regression come with strong asymptotic consistency properties and have an asymptotically vanishing width. We illustrate the empirical performance of our methods by applying them first in a simulated setting and then to a highly imbalanced insurance dataset.

In this paper, we study the problem of augmenting a tiny target sample with a massive auxiliary sample. Utilizing Tukey's factorization, there are two popular approaches: the inverse probability weight (IPW) and the full-likelihood (FL) methods. We show that the IPW approach suffers from the limited target sample problem while the FL method may estimate some model parameters at the rate of the massive auxiliary sample size, a phenomenon we call full efficiency gain. We study the theory behind the full efficiency gain for exponential families and mixtures of exponential families. We also study the efficiency gain for the IPW method under a nonparametric procedure and show how it can achieve a parametric rate of the target sample size. As a side note, we also discuss how one may use FL to train neural network models simultaneously for both the target distribution and the odds model.

Recent work encourages political scientists to move from post-only toward within-subject designs for improved precision from repeated measurements. We formalize a potential-outcomes framework for two-period within-subject designs that allows for unequal allocation and heterogeneous treatment and carryover effects. We characterize the pooled estimator and evaluate the carryover test used to justify pooling. We find: first, pooling identifies the average treatment effect only when the gap in the average carryover effects is zero across the two treatment sequences. The unit-clustered standard error for the pooled estimator is identical to its design-based counterpart. Second, under mild conditions, the carryover test has strictly less power than the average-treatment-effect test with post-only data. The resulting two-step procedure, which pools only after a nonrejected test, produces confidence intervals that typically undercover. When the gap is zero, undercoverage occurs if and only if pooling is more efficient than post-only analysis, precisely when the within-subject design is worthwhile. When the gap is nonzero, undercoverage is typical unless the gap or sample size is large. Third, we derive a sensitivity analysis and find published conclusions robust to plausible carryover gaps. We therefore endorse within-subject designs but recommend justifying a zero carryover gap substantively and reporting sensitivity to departures.

Randomized controlled trials (RCTs) are the gold standard for evaluating treatment effects, but fixed eligibility criteria and enrollment decisions can be inefficient, especially when treatment effects vary across patient subpopulations. Adaptive enrichment trials update enrollment using interim data to improve efficiency. Enrichment methods are developed for two settings: prespecified subgroups, and continuous covariates where enrollment is guided by a learned cutoff. Many enrichment designs adopt discontinuous rules that favor one single subgroup, which may induce "winner's curse" bias if final estimation does not account for the data-dependent enrollment decision and require additional bias correction. We propose a unified framework that bridges these settings by formulating enrichment as a regularized optimization over the enrolled covariate distribution. In a two-stage design, Stage 2 selects an enrollment mixture by maximizing a power objective while penalizing deviation from a prespecified baseline target population through a Kullback-Leibler divergence term, providing a smooth alternative to pick-the-winner rules; the same formulation extends naturally to optimizing enrollment over continuous covariates. The resulting estimand is the average treatment effect in the trial population induced by the data-adaptive enrollment rule, so uncertainty quantification must account for randomness in learning the optimal enrollment rule, in addition to outcome estimation. We derive an influence-function representation for the estimated optimal enrollment rule and account for it in the final estimator, yielding an explicit asymptotic variance decomposition into decision uncertainty and outcome-estimation uncertainty. Simulations demonstrate improved power relative to conventional enrichment approaches while substantially reducing winner's curse bias in treatment effect estimation.

Mean-robust estimation of spectral density and long-run variance is crucial for many statistical inference procedures. However, existing methods often degrade when serially dependent data exhibit volatile, time-varying trends, or sudden jumps, particularly in small samples. While differencing and kernel averaging are standard tools for achieving mean robustness and consistency, they are not inherently compatible. Combining them can compromise optimality. Specifically, tight differencing, an operation of taking small-lag differences to enhance local de-trending, introduces strong correlations that distort the high-order properties of kernel-averaged estimators. To resolve this incompatibility, we introduce a novel class of centrosymmetric kernels explicitly designed to integrate with tight differencing. We demonstrate that the optimal tight difference sequence for serially dependent data differs from classical sequences designed for independent data. Notably, these proposed optimal sequences are data-independent and can be applied directly without pre-fitting. Finally, the proposed estimators are demonstrated to be useful across various statistical inference tasks, including tests for stationarity and white noise.

Prediction intervals are increasingly recommended in random-effects meta-analysis because they describe the range of true effects expected in a future study or setting. Conventional frequentist intervals can have inadequate finite-sample coverage because uncertainty in the between-study variance is not fully propagated. We propose a confidence-distribution propagation method that carries uncertainty through the random-effects hierarchy. The method samples the between-study variance from a confidence distribution obtained by inverting the exact distribution of Cochran's Q and, conditional on each draw, samples the average effect from its corresponding normal confidence distribution before generating a future true effect. Prediction limits are empirical quantiles of the resulting Monte Carlo distribution. Across the scenarios examined, the proposed method improved or maintained coverage relative to existing frequentist intervals, including the Nagashima-Noma-Furukawa confidence-distribution bootstrap, with generally modest increases in expected width. The same Monte Carlo sample also yields confidence intervals for the average effect and heterogeneity measures. The method is implemented in the R package cdmeta available at CRAN (https://doi.org/10.32614/CRAN.package.cdmeta).

We develop a novel method of inference for network-dependent high-dimensional random vectors. Dependence is characterized via a functional dependence measure based on graph distance, allowing the approximation theory to capture the interaction between the decay of dependence and the growth of network neighborhoods. We establish Gaussian approximation results for the maximum norm under finite-moment and sub-Weibull conditions, providing explicit conditions under which the dimension may increase with the network size. We also propose a high-dimensional network HAC covariance estimator and establish its convergence properties, yielding a feasible procedure for simultaneous inference. Simulation studies demonstrate favorable finite-sample performance of the proposed method. We apply the procedure to study how spillover effects vary with an index of network homophily by constructing confidence bands for the conditional spillover-effect function. The application reveals heterogeneity and local significance that would be obscured by conventional low-dimensional inference.

Environmental monitoring networks increasingly record pollutant levels as curves observed over time at fixed stations. Yet, exposure and risk assessment often require predicting these curves, with their uncertainty, at unmonitored locations. Conventional smooth-basis methods for such spatially correlated functional data, including spline-based kriging, tend to over-smooth acute, high-frequency episodes such as pollution peaks. We propose a parsimonious wavelet-based Bayesian hierarchical model that anchors a single, shared Matérn correlation matrix at each resolution level, avoiding the parameter inflation of coefficient-specific spatial processes. Adaptive sparsity is enforced through a spatially informed regularized horseshoe prior, allowing the model to borrow strength across neighboring locations. At the same time, a non-centered parameterization ensures stable inference under the No-U-Turn Sampler. In simulation studies across distinct signal-to-noise regimes, incorporating spatial dependence substantially stabilizes reconstruction under severe noise relative to strictly independent models. Applied to PM$_{10}$ concentrations from Mexico City and benchmarked against ordinary kriging for functional data and a hierarchical Bayesian wavelet alternative, the model captures acute pollution events and, beyond improving point prediction, delivers sharper and better-calibrated credible intervals at unobserved locations.

Hybrid controlled trials (HCTs) augment randomized controls with external controls (ECs) to address practical challenges in randomized controlled trials (RCTs) and improve statistical power in settings such as rare diseases, oncology, and pediatrics. However, prospective sample-size determination is challenging because the required RCT sample size depends on the comparability of ECs with RCT controls, which are unavailable at the planning stage. We propose a 5+3 design for HCT sample-size determination based on an inverse probability weighting estimator of the average treatment effect. The framework uses five conventional RCT design parameters and three additional scalar parameters characterizing EC comparability: the number of outcome-drift-free ECs, an overlap coefficient for the covariate distributions of the RCT and ECs, and a correlation coefficient linking the sampling mechanism to the control potential outcome. We establish the asymptotic distribution of the estimator and prove that its variance is determined by these design parameters under the proposed working models, yielding sample-size calculations for both continuous and binary outcomes. Simulation studies evaluate finite-sample performance, and a real clinical application illustrates its practical use. The method is implemented in the hctdesign R package.

Goodness-of-fit tests for logistic regression are routine in clinical risk modelling, yet the classical tests say whether a model misfits, not where. A pretrained network is not a test until its level, power and blind spots are established. We audit DeepGOF-1, which renders the residuals of a fitted logistic model as a map over the ranks of two covariates, scores the map with a frozen convolutional network, and calibrates the score by the analyst's parametric bootstrap. The level is first-order valid under standard bootstrap regularity and two conditions, consistency against a named alternative is decided by one forward pass, and local power has an explicit limit. In simulation the level holds from 20 patients to 8,873; the network adds power over a chi-square statistic of the same map when misfit is sparse among many covariates; the map finds a missed interaction that one-covariate diagnostics cannot see; and, applied to a published risk model on new patients, it is an exactly valid test of calibration within patient subgroups, where the calibration belt has little power. In the SUPPORT study of 8,873 inpatients, DeepGOF-1 rejects a linear in-hospital mortality model, its map shows the U-shaped risks of blood pressure and respiratory rate that a calibration curve hides, and it guides the repairs. It ran in 13 seconds; the projection test, the strongest omnibus rival, took 9 hours 53 minutes and 4.5 GB on the same data, too slow for routine use. The test is deepgof1() in the R package ebrahim.gof.

Covariate adjustment can improve precision in estimating treatment effects in clinical trials, and regulatory guidance increasingly encourages its implementation. Despite its benefits, covariate adjustment can require advanced statistical techniques or tailored approaches for different estimands, which can deter its use in practice. To address this issue, we introduce a simplified approach to covariate adjustment using stable balancing weights that applies directly across many clinical trial estimands, including the average treatment effect, relative risk, Mann-Whitney estimand, and survival ratio. More precisely, our results cover any estimand that is a Hadamard differentiable functional of the arm-specific distributions. Once the weights are obtained, our adjusted estimator can be implemented with the same software used for an unadjusted analysis, provided that software can take observation weights. This construction improves asymptotic efficiency relative to unadjusted estimation and preserves the plug-in relationship between arm-specific marginal and subgroup-specific summaries.