Papers

We study multi-armed bandits (MAB) with multiple optimal arms, motivated by the fact that many practical decision making problems admit multiple correct answers. For $K$-armed bandits with $A$ optimal arms, we first provide a sharper analysis of previous sub-sampling algorithms (De Heide et al., 2021; Zhu and Nowak, 2020), establishing a $\tilde{O}\Big(\frac{K-A}{\sqrt{KA}}\sqrt{T} \Big)$ minimax regret, where $T$ is the total number of interactions and $\tilde O(\cdot)$ drops all constant and logarithmic factors, improving the previous $\tilde{O}(\sqrt{KT/A})$ regret. We then provide a matching lower bound up to logarithmic factors, indicating that our established rate is nearly minimax-optimal. We further show that the knowledge of $A$ up to $\tilde{O}(1)$ factors is necessary to achieve near-optimal regret, as near-optimal algorithms for one number of optimal arms must incur substantially larger regret than optimal regret for a smaller number. Overall, our results provide a comprehensive minimax characterization of $K$-armed bandits with $A$ over the entire range of $1 \leq A \leq K-1$.

Correlated predictors can support competing sparse explanations with similar predictions, making joint uncertainty about variable inclusion difficult to capture with mean-field approximations. We develop an adaptive fitting procedure for mixtures of product distributions in Gaussian regression with a point-mass spike-and-slab prior. It minimizes reverse Kullback-Leibler divergence directly on inclusion indicators and active coefficients, jointly refining component parameters and weights as the mixture grows. This avoids an additional divergence penalty on unused latent coefficients under independent augmentation. Our analysis relates approximation accuracy to mixture size, support coverage and dependence within supports, and establishes contraction, selection consistency and a Bernstein-von Mises approximation under explicit conditions on the prior, posterior concentration and variational error. On all 250 simulated datasets with exact posterior references, mixtures reduce errors in inclusion probabilities, grouped support probabilities and coefficient covariance relative to multistart mean field. Comparisons at fixed mixture size and common initialization favor direct joint refinement over augmented or restricted refinement in posterior divergence. Complete stagewise fitting can nevertheless be more accurate near collinearity. The results support direct joint refinement for posterior approximation while showing that local gains do not ensure superiority of the full adaptive search.

High-frequency athlete-tracking data can be summarized as quantile cubes (Thomas and Hannig, Journal of Quantitative Analysis in Sports, 2026): counts of time spent in bins of velocity, acceleration and movement angle. In our application each athlete-match session has 100 such bins, with counts from under a hundred to several thousand. Whether a bin's negative binomial distribution is close to normal depends on its shape, the product of mean and dispersion, not on the count alone. We develop a hybrid generalized fiducial framework that uses exact negative binomial structural equations where the estimated shape is small and moment-matched normal approximations where it is large, providing uncertainty quantification for hundreds of regression and dispersion parameters without a prior. Only the normal components contribute to the fiducial Jacobian, which is block diagonal in closed form, and we prove a Bernstein-von Mises theorem for the correctly specified hybrid model. Simulations show near-nominal coverage, agreement with a flat-prior Bayesian analysis, and that the partition should be based on the estimated shape rather than on the mean or the observed responses. In 216 sessions from 17 professional women's soccer athletes, the estimated position and age effects concentrate at the velocity extremes and highest accelerations, but an athlete-level permutation check shows these patterns cannot be distinguished from label noise.

Tax fraud remains a central challenge for public revenue authorities worldwide, imposing fiscal losses estimated to reach up to 1 trillion euros annually in the EU alone. Fraudulent firms intentionally manipulate reported figures to conceal their activity. Business networks can provide complementary information and reveal fraud that covariates alone may miss. We propose a Bayesian positive-unlabeled (PU) classification framework that combines firm-level covariates with multilayer network information. As a policy relevant case study, we apply the framework to firms in a regulated segment of the Greek energy market, a sector exposed to excise tax evasion. Confirmed fraud labels exist only for audited cases, while the remaining observations are unlabeled rather than verified compliant. We develop a Bayesian Gaussian process (GP) classifier integrating covariates with multilayer network information through a Product of Experts (PoE) construction and incorporating a nondetection probability for missed positives. We derive identification bounds for the nondetection rate under an anchor condition and show that, for a fixed latent risk function, a common nondetection rate affects calibration but not ranking. Simulations show strong ranking performance relative to PU and network-based alternatives, while illustrating the difficulty of estimating the nondetection rate. In real audit data, the method identifies high risk firms with posterior uncertainty, estimates the number of undetected fraudulent cases, and identifies whether risk is driven by covariates, networks, or both. Of the six highest ranked firms, the two that had already been reinspected independently were both confirmed as noncompliant, providing an independent validation of these cases. The remaining four were selected by the tax authority for follow-up inspection.

Tree-based scan statistics (TBSSs) are machine learning methods for disproportionality analyses. They simultaneously scan for thousands of hierarchically related health outcomes to detect potential signals of harm from drugs and vaccines, controlling for multiplicity. TBSSs have been extensively used to mine insurance claims databases to detect potential drug adverse events. Current TBSS implementations do not allow comparative safety evaluations with time-to-event outcomes. Explicitly accounting for event timing in analyses can improve power to detect signals compared to methods that use only event counts. We propose three TBSS methods that explicitly leverage event timing to detect potentially harmful effects of drugs. The first assumes proportional hazard rates for each node of the outcome hierarchy and uses a permutation scheme for inference. The second builds on exponential survival models for the terminal nodes of the hierarchy, assuming constant hazard rates at each node, and uses a parametric bootstrap for inference. The third uses robust asymptotic approximations of the hazard rates in connection with an approximate parametric bootstrap. We compare the proposed methods with standard event count based TBSSs in simulation scenarios. Finally, we present results from a database study comparing two glucose-lowering medications among adults with type 2 diabetes.

We consider estimating the one-step-ahead conditional distribution of a multivariate stochastic process. Many existing approaches rely on assumptions such as finite-range memory, sparsity, or additivity, which can be poorly suited to processes with long-range nonlinear interactions. However, without such structural assumptions, nonparametric estimation is challenging due to the curse of dimensionality. To address this challenge, we introduce a new estimation approach based on the predictive states of a process, possibly with infinite-range memory. We show that our estimator achieves fast convergence rates when the past history can be compressed into a low-dimensional statistic that is sufficient for predicting the future. Specifically, we show that the statistical complexity of the estimation problem is determined by the intrinsic dimension of the predictive state space. We establish guarantees for an instantiation of our method based on deep neural network estimators, and we support these theoretical results with experiments.

Data-driven subgroup identification is increasingly used in clinical trials, yet the effect reported for a discovered subgroup is typically the standard analysis: a Cox or generalized-linear-model treatment coefficient fitted within that subgroup. Selection by an effect-driven rule — rewarding large estimated effects subject to screening and size criteria — inflates the reported coefficient: a winner's curse invalidating naive intervals whether or not the identifier's internal estimand was de-biased by cross-fitting. We develop a procedure-agnostic framework for post-selection inference that separates discovery from reporting: forest search, difference-in-natural-parameters estimators, and causal forests generate interpretable candidate subgroups; selection is aligned with the coefficient to be reported; and the target is the standard-analysis effect of the selected subgroup, the candidate family held fixed — a conditional, data-adaptive estimand. Resampling the search then reduces to jointly perturbing all candidate effects, yielding refit-free multiplier resampling with an infinitesimal-jackknife interval whose coverage we characterize under standard regularity and an explicit condition on the limiting competition. It matches the full bootstrap on a fixed family; on model-generated families it remains valid for the same conditional target, which the bootstrap reproduces only under further conditions. Two trial applications and matched simulations show mitigated selection bias and improved coverage.

Diagnostic meta-analyses commonly assess small-study effects using the Deeks test, which tests for a study-size trend in the log diagnostic odds ratio. Under the hierarchical summary receiver operating characteristic (HSROC) model, this quantity reflects both latent accuracy and threshold unless the curve is symmetric. A threshold trend can therefore generate a log diagnostic odds ratio trend without a latent accuracy trend, or conceal an existing one. We develop a likelihood-ratio test of the latent accuracy trend under a common-shape binomial HSROC model, leaving the threshold trend unrestricted. Its null hypothesis states that the summary curve is unchanged across study sizes. A log diagnostic odds ratio test using the same binomial fit provides a comparison with a different null hypothesis. In simulations, the proposed test remained near its nominal level under its null and had higher power than Deeks with a latent accuracy trend alone. In a colorectal cancer review of faecal immunochemical tests, it detected a negative latent accuracy trend obscured on the log diagnostic odds ratio scale by an opposing threshold contribution. All three tests detected size trends for impedance plethysmography in deep-vein thrombosis, where the fitted curve was nearly symmetric. The proposed test distinguishes changes in the summary curve from changes in operating position.

Proximal causal inference identifies causal effects in the presence of unmeasured confounding by drawing on two sets of proxy variables. Identification typically utilizes bridge functions, defined as solutions to integral equations. However, the mechanism by which fitted bridge functions correct for confounding bias remains opaque, offering little to interpret, inspect or stress-test. We show that the defining equation of a treatment bridge function is already a balance condition, with a cross-proxy form: the weights are functions of the treatment confounding proxies and covariates, and they balance the outcome confounding proxies and covariates (i.e., reweighting the distribution in a particular treatment arm to match the distribution across treatment arms). Several existing identification paths via a treatment bridge function can then be interpreted as providing conditions under which balance on the outcome proxies implies balance on the unobserved confounders, which we call balance propagation. Leveraging this framing, we show that estimation of the treatment bridge function is a type of balancing weight estimation. Finally, we show that an outcome-weighted estimator form can also be obtained for a large class of proximal estimators, including those that utilize an outcome bridge function. Using this framing, we provide conditions under which common estimators are numerically equivalent.

We propose a general goodness-of-fit framework for distributions on separable metric spaces. Under suitable identifiability conditions, probability distributions are characterized by distance profiles, which motivates their use in goodness-of-fit testing, for simple and composite null hypotheses. For composite null hypotheses, parameter estimation is incorporated via a Bahadur-type expansion, and the asymptotic distribution of the empirical process for distance profiles is obtained under the null. We define test statistics based on this empirical process and derive their asymptotic null distributions. We further study the behavior of the proposed tests under fixed and local alternatives, establishing consistency results. Multiplier bootstrap procedures are developed, and their conditional asymptotic validity is established under both simple and composite null hypotheses. The methodology is illustrated with simulation studies and real-data applications for data on the sphere, hyperboloid, and simplex.

Multi-source data integration problems over datasets from different sources covering different but possibly overlapping sets of entities have become increasingly important in many real-world areas, including genomics, single-cell analysis, and healthcare research. In such problems, one often first learns a low-dimensional representation of the entities within each source and then integrates these representations across sources. As the representations from different sources are only identifiable up to some transformation, how to align them across sources using the sources' overlapping entities becomes a key challenge. Existing methods align the sources in a sequential or tree-structured manner, and are therefore sensitive to the chosen order and exploit only part of the available overlapping information. Motivated by this limitation, we propose Global Synchronized Multiple Matrix Integration (GSMMI), which formulates this alignment problem as a global synchronization problem and jointly aligns all sources using all pairwise overlaps at once, thereby making full use of all overlapping information across the sources. We develop an efficient iterative algorithm for GSMMI that is fast and scalable to the large-scale data arising in these applications. We show both theoretically and empirically that GSMMI improves alignment accuracy, with clear improvements even under modest overlap structure. Moreover, we develop GSMMI to be broadly applicable across data types, covering symmetric positive semidefinite, symmetric indefinite, and asymmetric or rectangular matrices, and even settings where sources overlap only in their rows or only in their columns, making it suitable for a wide variety of application scenarios.

Time Series Foundation Models (TSFMs) currently provide state-of-the-art results in forecasting tasks. They are available out-of-the-box and rely on in-context learning to make their predictions, which makes the quality of their performance highly sensitive to the user-selected lookback, covariates, horizon and training data distributions. In practise, the quality of the forecasts are variable but complementary, which highlights the need for a principled ensembling approach, rather than selecting the best context. This paper introduces Latent Inference-Time Guidance for TSFMs, which adaptively combines a pool of TSFM forecasts through a time-dependent latent space with independent components. The framework comes equipped with identifiability and reconstruction guarantees, whilst maintaining the off-the-shelf aspect of foundation models. We provide experiments on datasets at various frequencies and from multiple domains: these show that the approach is competitive with traditional ensembling approaches.

Changes in principal eigenvalues and eigendirections provide complementary diagnostics of structural instability in factor models, but covariance-based inference can be unreliable under heavy tails. We develop two-sample tests for equality of these features of trace-normalized shape matrices under high-dimensional elliptical factor models. Our approach combines Tyler's identity with orthogonalization and cross-fitting to accommodate general location and precision pilots. We derive a spectral limit theory that yields asymptotically valid calibration without upper-tail moment assumptions on the radial variables, allowing the two populations to have different radial distributions and factor ranks. Simulations demonstrate good size control and gains in size-adjusted power over covariance-based benchmarks under heavy-tailed elliptical distributions. An application to S&P~500 stock returns illustrates how the tests distinguish changes in relative component strength from changes in component orientation.

We study tail dependence of a $d$-dimensional random vector whose coordinates are subject to random right censoring. Along each fixed direction the censored problem reduces exactly to a univariate one, and the observed data determine the radius and whether it was produced by the event or censoring vector. An ordinary Kaplan–Meier product limit therefore estimates the joint tail probability in that direction, in every dimension, and with no multivariate survival function, no smoothing and no tuning parameter beyond the threshold. The theory of this directional estimator is formulated under an arbitrary marginal standardization and conditions only imposed on the standardized laws, in particular for any max-domain of attraction. We prove uniform consistency and functional weak convergence at the square root of the effective number of joint extremes, allowing the standardization to be estimated. A multiplicative standardization recovers the heavy-tailed theory, whereas a standardization built from the marginal (non-directional) Kaplan–Meier estimators requires no marginal tail model and targets the normalized tail copula itself. The standardization error is negligible for the former, and for the latter under a mild condition on the joint censoring. Simulation studies validate the finite-sample performance of the estimator. An application to the National Flood Insurance Program dataset comprised of claims generated by Hurricane Ian estimates the joint upper tail of building and contents losses from indemnities, which are subject to capping, simultaneously in both coordinates.

Sequential studies with heterogeneous strata may define the estimand under a target mixture that differs from the sampling distribution. We organize the design problem by guarantee class: one pooled confidence sequence for a single prespecified target, shared pooled inference for a prespecified target set, and stratum-resolved inference when local guarantees must remain available. For target-set pooled inference we derive minimax, gap-aware, and range-capped shared proposals and an adaptive tracking rule. A specialized augmented off-policy score removes between-stratum mean heterogeneity asymptotically, recovering Neyman allocation for efficient single-target pooled inference. Robust directional certification over a convex target set is a classical intersection-union problem and does not require an M-fold vertex split. We derive a Gaussian information lower bound and an exact finite-support characteristic information that coincides with the bounded nonparametric KL-inf limit, and state sufficient conditions for first-order attainment of the Gaussian constant. Within the local-CS architecture, regularly varying boundaries imply a general allocation law with the 2/3 exponent for root-n variance-adaptive widths. Simulations and a PromptEval replay illustrate the resulting guarantee-efficiency frontier.

Longitudinal studies with functional outcomes subject to truncation-by-death frequently report time-indexed survivor average causal effect estimates, defined among individuals who would survive regardless of treatment assignment. Because the survivor stratum can change over time, the resulting effect estimates may pertain to populations with different characteristics. We propose accompanying survivor average causal effect estimates with measures of covariate divergence between the survivor and baseline populations. We study standardized mean differences (SMDs) and the Kullback-Leibler (KL) divergence as moment-based and distributional summaries, respectively. We show that these divergence measures are identified under a subset of standard principal stratification assumptions and that their identification involves nuisance functions already estimated in survivor analyses. We derive the efficient influence functions, enabling construction of one-step bias-corrected estimators with appealing large-sample properties and allowing machine learning for nuisance estimation. We demonstrate that in randomized studies, one-step estimation of SMDs is robust to arbitrary nuisance model misspecification, whereas the KL divergence and broader density ratio estimands are more sensitive to nuisance misspecification. Additionally, we provide a sensitivity analysis framework that partially relaxes a monotonicity assumption required for identification, and construct one-step estimators for the resulting bounds. Through simulation studies, we demonstrate the finite-sample performance of the proposed estimators and illustrate how divergence measures can improve the interpretability of survivor analyses. Finally, we assess covariate divergence in survivor strata over time in amyotrophic lateral sclerosis (ALS) trials, using data from the Pooled Resource Open-Access ALS Clinical Trials database.

Basis-restricted priors in Bayesian inverse problems can lose coverage when the truth has components outside the basis. We show that estimating the observation-noise variance can hide this loss. Under a linear forward model, when the in-span prior variance dominates the noise, the maximum-likelihood noise estimate absorbs the out-of-basis energy in the complement of the model range. Residual-magnitude and observation-coverage checks then stay near nominal while field coverage falls. We study repeated problems sharing one forward operator and one basis, fixed independently of the tested data. After projection onto the complement, and conditionally on the fitted noise scale, every exact test is a test of the scale-free direction of the residuals. We test the shape of their sample spectrum with John's sphericity statistic. Under Gaussian noise its null model is exact at finite sample size, and we derive its null mean and its power at proportional dimension. On synthetic problems and in a preregistered GEBCO topography study, the test detects structured out-of-basis variation that cross-validation and observation-coverage checks largely miss. It cannot detect Gaussian out-of-basis variation that is isotropic in the complement, since that is indistinguishable from a change of noise scale.

Supersaturated screening experiments study many candidate factors with few runs. The experimenter must first identify the active factors, then optimize the response. One-shot regularized regression tends to select many factors, and the second-order response surface model in the selected factors is then large and needs many further runs to fit. We propose Sequential Supersaturated Screening ($S^3$), a two-stage framework for supersaturated designs. $S^3$ builds each screening round by coordinate exchange under a new positive-cone design criterion that uses no practitioner-chosen Welch calibration constant. It then removes low-importance factors one round at a time, using a graduated quantile rule. The criterion scores a design by how far its column correlations sit above the Welch lower bound, and it adapts to the current number of runs and candidate factors. We give a round-by-round bound on the probability that a noise factor is ever fixed, under conditions on noise survival and commitment at each round, together with an explicit upper bound on the total number of Stage 1 runs. Across simulated screening problems and the Borehole benchmark, $S^3$ achieves lower Type I error and higher $F_1$ scores than one-shot cross-validated Lasso (LassoCV). It also improves optimization quality in most settings and runs faster.

Goodness-of-fit testing is a basic tool for assessing whether a fitted procedure has captured the systematic information contained in the covariates. While traditional theory has largely focused on parametric regression models, modern data analysis increasingly relies on flexible black-box learners, whose predictive success alone is insufficient to assess model accuracy. In this paper, we propose SPARK, a general framework for goodness-of-fit testing that applies to traditional statistical models and general black-box learning procedures, continuous and binary responses, and low- and high-dimensional predictors. Based on a debiasing strategy, the residuals from an initial fit of a learning procedure are projected onto nearly orthogonal directions to extract any remaining signal. To capture information across all projection directions, we propose a kernel-based projection method and establish both its asymptotic properties and the consistency of a bootstrap procedure. Comprehensive simulations and real data analyses illustrate the effectiveness and flexibility of our proposed method.

In contemporary randomized controlled trials (RCTs), the number of patients is often small relative to the number of baseline covariates collected. In such settings, maximum likelihood estimators of conditional treatment effects in generalized linear models, along with their standard errors, may exhibit substantial bias. This study examines whether similar bias arises in G-computation estimators of marginal treatment effects, which are known for their robustness to model misspecification when applied with canonical GLMs. We develop theoretical insights, drawing on recent literature on G-computation under proportional asymptotic regimes, in which the number of covariates grows with the sample size. Specifically, we characterize the bias of the standard G-computation estimator and the leave-one-out G-computation estimator under such high-dimensional settings. Monte Carlo simulations using linear and logistic outcome models are conducted to evaluate practical remedies for G-computation estimators, including covariate selection, cross-fitting, leave-one-out cross-fitting, and small sample corrections to standard errors. Further insights are derived from a re-analysis of the BestAIR trial data. Our findings provide guidance for the application of G-computation in modern RCTs, particularly when addressing challenges posed by limited sample size. Keywords: Covariate adjustment, covariate selection, high-dimensional, proportional asymptotics, targeted learning, cross-fitting.

In factorial randomized experiments with $K$ binary treatment components, we study which baseline covariates modify component main effects and interactions. We define effect-modifier cells $(j,S)$, $j\in[p]$ and $\emptyset\neq S\subseteq[K]$, through the coefficients $\theta^\ast_{jS}$ of population linear projections of conditional Walsh–Hadamard contrasts $\tau_{S}$ onto standardized covariates. Using baseline-robust direct scores, we develop frequentist inference for all $p(2^K-1)$ cells. First, we prove a debiased central limit theorem with global insensitivity: the residualization baseline enters the cross-fitted score through an exactly conditionally mean-zero perturbation. The influence-function remainder therefore requires only foldwise weighted $L_2$ consistency of the baseline estimator, with no prescribed polynomial rate or nuisance product-rate condition. A separate, explicit penalty-scale condition controls the baseline's effect on the score Lasso. Second, under explicitly stated uniform nuisance, baseline, studentization, and influence-array conditions derived from bounded sparse-regression primitives, we establish a high-dimensional Gaussian approximation over the full grid, calibrated by a Walsh-spectral multiplier bootstrap. This yields simultaneous confidence bands and Romano–Wolf step-down selection of modified cells with strong familywise error control, without effect-heredity assumptions. The factorial design is fixed in the asymptotic analysis, while the covariate dimension may grow; all $2^K-1$ contrasts are covered jointly.

Multimodality is common in many scientific and engineering applications. However, standard Markov chain Monte Carlo (MCMC) convergence diagnostics often penalise multimodality in practice by conflating overall poor mixing with groups of chains that have mixed well within distinct modes. To diagnose multimodality rather than flag it as a sampling failure, we introduce the MCMC convergence graph: a graph-based diagnostic that computes pairwise R-hat values between chains and summarises them in a graph, revealing sets of chains that explore the same posterior mode. We implement the method in the probabilistic programming framework Stan and demonstrate its use on worked examples ranging from regression models with inherent multimodality in the data, to a pharmacokinetic model for which multimodality reflects non-identifiability. The graph-based diagnostic, which we make freely available in the R package mcmcConvergenceGraph and which accepts MCMC output from any sampler, provides both graphical and numerical summaries of MCMC behaviour for diagnosing multimodality.

Mendelian randomisation (MR) implemented through instrumental variable (IV) analysis is a popular strategy for strengthening causal inference in observational studies. A key assumption for several MR estimators, including MR-Egger regression, is the INstrument Strength Independent of Direct Effect (INSIDE) assumption. However, there is no established empirical test for assessing the plausibility of this assumption. Moreover, INSIDE depends on how genetic variants are coded (i.e., on the choice of the effect allele), which is often arbitrary and therefore hampers assessing the plausibility of this assumption on substantive grounds. In this paper, we show that the all-positive coding scheme (i.e., for all variants, choosing the allele positively associated with the exposure as the effect allele), which is typically used in MR-Egger, is equivalent to a coding-invariant model that can be given a natural interpretation because the direct effect parameters under this coding scheme are in the same direction as the bias of individual-variant ratio estimators. Moreover, using both theoretical arguments and simulations, we show that, under commonly assumed data-generating models in the MR methodological literature, heteroscedasticity of instrument-outcome coefficients according to instrument-exposure coefficients is a feature of at least some types of INSIDE violation, indicating that heteroscedasticity tests could contribute to assessing the plausibility of the INSIDE assumption. We further highlight specific cases where the test would not work. We illustrate its application by re-analysing a real dataset assessing the causal effect of large particle high density lipoprotein cholesterol on age-related macular degeneration.

Degree heterogeneity is one of the most important properties of network data. It is widely observed that degree heterogeneity is often related to the nodal features. In this study, we investigate the estimation and statistical inference for a popularity regression-based latent space model with nodal features. Given the complex dependence structure induced by the latent space model, we aim to derive analytically tractable objective functions that effectively account for this structure for sparse networks. Specifically, we propose a total of four estimators. The first two estimators are developed by utilizing only the first-order structure of the network (e.g., the nodal degree), while the last two estimators are developed by leveraging the higher-order network structures (i.e., reciprocity and transitivity). Rigorous asymptotic theory is established based on various non-standard U-statistics. We find that different estimators might have different convergence rates. The extension to higher-order moments-based estimators is also discussed. Extensive numerical experiments and a real data analysis of link prediction for an author citation network are conducted for illustration purposes.

Scenario analysis is widely used to stress test financial portfolios, yet conventional approaches often summarize scenario gains using point estimates that overlook dependence between stressed and unstressed risk factors. We develop a machine learning framework for quantifying uncertainty in realized next-day scenario gains through prediction intervals whose widths can be calibrated online. Adaptive conformal scenario analysis (ACSA) calibrates scenario-specific quantile predictions and provides a long-run empirical coverage guarantee over realized scenarios. Our main method, kernel scenario analysis (KSA), estimates scenario-conditional quantiles directly from the specified stress and current market information. KSA can also be combined with ACSA to obtain online-calibrated prediction intervals. In experiments designed to reflect real-world markets, conventional scenario analysis can substantially understate risk, including for portfolios that appear safe under standard stress tests. Our proposed methods achieve better calibration and sharper intervals than empirical-quantile baselines. Overall, the framework moves scenario analysis beyond point estimates by quantifying predictive uncertainty and providing tools for statistically validating scenario gains.

Bilateral data from paired body parts are common and correlated in clinical studies. Classical frequentist methods perform poorly in small or sparse datasets. This paper develops a Bayesian framework for bilateral data with multiple groups under Dallal's model. We derive three objective priors (uniform, Jeffreys', and Bernardo's reference priors) and propose a range-based posterior testing procedure, combined with a decision rule, to test the homogeneity of risk differences, with the equivalence margin calibrated. Monte Carlo simulations evaluate empirical Type I error rates, powers, and interval estimation properties. Results show that the Bayesian methods achieve accurate coverage probabilities, narrower confidence intervals, and better Type I error control than the frequentist Wald approach, especially in small-sample and sparse-data settings. We illustrate the methodology with two real datasets. The proposed framework provides a robust and flexible tool for multi-group bilateral data analysis.

The paper introduces the R package CovEsts, which implements several nonparametric estimators for the autocovariance function. First, it presents the theoretical foundations of the implemented estimators, their properties, assumptions, and potential limitations. Next, it outlines the structure of the package and its key functions, including several methods for estimating autocovariance functions, constructing corresponding bootstrap confidence regions, and correcting the provided estimators. The package also includes diagnostic tools, such as several metrics for comparing estimators, and additional functions for broader use. The article illustrates a high degree of flexibility of the package in the selection of function parameters and the tuning of the estimators. Applications of selected estimators and package functions are illustrated using simulated data, yearly sunspot counts, and US unemployment increments data.

Schmelzer and Hastie prove that Markowitz's Critical Line Algorithm and the LASSO path trace the same curve. This companion note checks that result numerically with a stock LASSO solver, lars\_path from scikit-learn, and no portfolio software. It covers long–short portfolios under a leverage cap, fixed leverage with varying risk appetite, and the classical long-only, fully invested frontier. Every corner the path returns meets its own optimality conditions to about $10^{-13}$ and agrees with independent quadratic-programming solvers, on factor models of up to 500 assets, on the Fama–French size and book-to-market portfolios, and on daily returns of 494 S&P~500 stocks. Called naively, the long-only path stops at the maximum-Sharpe portfolio. One shift of the response, by an amount computed in advance, lets a single call reach the minimum-variance portfolio. The script, its checks, the Fama–French returns and an R cross-check are published, with a locked environment, so that anyone can repeat them.

AI models trained on the same data can disagree about patient risk, with disagreement potentially concentrated in clinically important subgroups. We propose V(S), a statistically grounded vulnerability index combining an observable lower-bound witness of model disagreement with clinical severity, and develop inference and multiplicity-adjustment procedures for auditing prespecified subgroups. We applied the framework to two large critical-care cohorts, MIMIC-IV (n = 65,078) for model development and eICU-CRD (n = 188,230 admissions, 208 hospitals) for external validation, comparing a random forest with logistic regression across 158 prespecified subgroups. The two primary models did not both satisfy the prespecified epsilon = 0.02 Rashomon-set tolerance: the logistic-regression AUC was 0.0488 below the best candidate-model AUC. The RF-LR discrimination gap is thus interpreted as disagreement between two specific models, not as a guaranteed lower bound on the full Rashomon set. Nine subgroups had discrimination gaps distinguishable from a prespecified clinical floor. The age >=80 and cardiac subgroup had the largest point estimate of V(S) (0.307), but was underpowered and did not meet the full high-priority decision rule. The univariate cardiac subgroup (V(S) = 0.193, 95% CI [0.163, 0.223]) was the only statistically distinguishable subgroup with adequate power. Post hoc analyses identified lactate as important for both models but did not establish a causal explanation for the disagreement. Four simulation studies quantified operating characteristics of the proposed procedures, including inflated small-sample detection rates and imperfect Wald-interval coverage. The framework offers a reproducible approach for ranking subgroup vulnerability to model disagreement while separating exploratory signals from adequately supported findings.

Interpretable prediction models are important in biomedical research, where predictive accuracy must often be balanced against the ability to examine predictor-outcome relationships. Automatic Binary Logistic Estimation (ABLE) provides interpretable rule-based representations by constructing additive models using threshold rules. However, the original method is restricted to binary outcomes, and its greedy forward construction follows a search path, making candidate rules dependent on earlier selections and potentially excluding alternative structures. We extended ABLE to binary, continuous, and time-to-event outcomes using outcome-specific fitting criteria, yielding Generalized ABLE (GABLE). We then propose bootstrap rule pooling for GABLE (BRP-GABLE), which applies GABLE rule generation to bootstrap samples to explore alternative search paths, pool distinct rules, and perform a single global LASSO selection over the pooled rules and truncated linear terms. Unlike conventional bagging, bootstrap-specific models are not averaged, and resampling is used to diversify the candidate rule space before constructing a final model. Simulations showed that BRP-GABLE consistently improved predictive performance compared with GABLE and provided competitive prediction with relatively simple rule structures. Application to overall survival demonstrated its use for clinically interpretable prediction. BRP-GABLE provides a flexible framework for constructing sparse and interpretable predictive models across multiple outcome types.