Papers

Research on modelling peer effects has predominantly relied on linear-in-means models. However, averaging peer responses prevents these models from capturing the effects of extreme peer behavior. To address this limitation, we propose a quantile social autoregressive model based on a novel quantile social norm, which uses empirical quantiles of peer responses. By treating the quantile level as an unknown parameter estimated directly from the data, our approach identifies which segment of the peer response distribution most strongly influences individual behavior. To estimate the model, we introduce new moment conditions using pseudo-response instruments. Because the quantile social norm is nonsmooth, we apply kernel smoothing to the instruments and residuals, ensuring valid statistical inference. Additionally, we establish equilibrium existence and uniqueness and derive the identification conditions. Furthermore, we prove the consistency and asymptotic normality of our proposed estimator. Finally, Monte Carlo experiments examine the finite-sample performance of the estimator, and an empirical application illustrates the interpretation of the estimated quantile levels and their corresponding peer effects.

Researchers frequently study interactions between two distinct types of actors, represented as bipartite networks. These networks exhibit dependence patterns that differ from those in one-mode networks and therefore require models tailored to their structure. This paper develops an additive and multiplicative effects (AME) framework for longitudinal bipartite data. First, I distinguish the dependence structure and specify the corresponding modeling assumptions. Second, I introduce the bipartite dynamic AME model and develop an estimation procedure based on block coordinate descent. Third, I incorporate a squared iterative method to improve computational efficiency. Using simulations and an application to global production networks, I show that the model improves coefficient estimation, more accurately recovers the data-generating process, and better captures the multiplicative latent structure. The model reveals evolving patterns in countries' global production engagement that are not captured by observed covariates or static specifications. I provide an R package, RAMEN, to facilitate implementation.

We consider the problem of scalar-on-function regression. Most existing methods implicitly assume that the functional covariates are observed exactly, but in practice, they are often contaminated by measurement error. Our goal, therefore, is to deal with the problem of scalar-on-function regression when the regressor functions are observed with error. In this paper, we propose a simulation-extrapolation method to correct for the attenuation of estimated coefficient functions caused by the error. The method first estimates the error variance, establishes the relationship between a sequence of added error variance and the corresponding estimates of coefficient functions, and then extrapolates to the zero-error. We describe three methods to extrapolate the sequence of estimated coefficient functions. In a simulation study, we compare the performance of the simulation-extrapolation method with two pre-smoothing methods based on smoothing splines and functional principal component analysis. Next, we discuss the extension of the method in several directions, allowing for more complex noise covariance structures, multiple replications of functional predictors, generalized responses, and 2D and 3D functional predictors. Finally, we illustrate the methods by an application to diffusion tensor imaging data.

Factor modeling provides a framework for extracting common components from high-dimensional time series. We develop an estimator of the factor loading space that combines contemporaneous covariance with lagged autocovariance information. Under cross-sectionally heteroskedastic white noise, the contemporaneous covariance contains heterogeneous diagonal noise contributions. We apply the existing HeteroPCA algorithm to the combined estimation matrix to correct this contamination while retaining information from serial dependence. The framework also accommodates noise contamination on a known set of entries subject to sparsity and incoherence conditions. Under regularity conditions for dependent observations, we establish consistency and derive convergence rates, identifying regimes in which incorporating contemporaneous covariance improves the rate relative to the lagged-autocovariance estimator. Simulations evaluate loading-space estimation error and the effects of contemporaneous covariance inclusion and diagonal correction. An application to S&P 500 stock returns illustrates the method.

Consideration of frequentist type-I error or power based on certain fixed conditions may not fully embrace the aims of a Bayesian analysis; this is particularly true in settings where informative priors are involved. Calderazzo et al. consider adaptations of a testing procedure involving Bayesian borrowing from external control data. Particular caution may be necessary here in order not to condition on parameters and data simultaneously. We consider their example case and argue that (a) the conditioning scheme may have limited practical implications, and (b) if the main concern are assumption violations, these might be better addressed by adapting the likelihood function.

Dynamic borrowing can improve efficiency in clinical trials using external information, but existing methods may not offer transparent, prespecified control over borrowing. We introduce Standardized Dynamic Borrowing (SDB), which combines a source-informed component with a no-borrowing component and updates their relative odds using a Bayes factor standardized by its supremum over admissible target data. The posterior density under the no-borrowing component is obtained by normalizing the target-data likelihood. The prespecified source-component initial weight is a sharp uniform upper bound on its posterior weight, providing an interpretable borrowing constraint. When source and target models belong to the same one-parameter canonical exponential family, posterior expected local-information-ratio effective sample size equals target sample size plus borrowed source-prior effective sample size minus a nonnegative heterogeneity penalty. For normally distributed outcomes, borrowing depends on a standardized source-target conflict $Z$-score and decreases according to a standard normal kernel. We also jointly select the initial weight and target sample size to meet prespecified power and Type I error requirements. Normal and binomial illustrations demonstrate how SDB translates source-target compatibility into data-adaptive borrowing and how the calibration procedure prespecifies the source-component initial weight and target sample size under operating-characteristic constraints. These results provide a transparent framework for prespecifying, controlling, and interpreting dynamic borrowing.

Time-series foundation models such as Google's TimesFM-3 forecast series they were never trained on, but whether they should replace classical methods such as ARIMA and exponential smoothing is hard to settle on public benchmarks, because few benchmark datasets are absent from every model's pre-training corpus. This exploratory study compares TimesFM-3 with classical methods on data generated from nine known processes, which the model cannot have seen. Across 7200 series and a pre-registered protocol with a 12-step horizon, neither family dominates. TimesFM-3's error is never more than 1.31 times that of the best method in a scenario, whereas every classical method's is at least 2.2 times somewhere; the largest classical failures occur with only two seasonal cycles, where the automatic methods fall back to non-seasonal models. With four or more cycles automatic ARIMA is 21-24% more accurate than TimesFM-3 on seasonal ARIMA data. Among five foundation models this robustness is specific to TimesFM-3, and it holds only at short horizons: at steps 25 to 48 the three foundation models tested there forecast a decline on a saturating process whose level stays flat, and automatic ARIMA has the smaller worst case elsewhere. On intermittent demand TimesFM-3 shows no advantage over simple benchmarks built from the history. Randomised parameters, heavy-tailed noise and outliers leave these patterns qualitatively unchanged; on the official test period of 1000 M4 monthly series TimesFM-3 is level with the fifth- to seventh-ranked M4 entries, behind the four best, and on 101 macroeconomic series observed after the models' documented training data it is statistically level with the classical methods. The study characterises the behaviour of a black-box model, not the reasons for it, and its findings are conditional on the processes and horizons examined.

Principal component analysis and factor analysis are foundational to the study of high-dimensional data, yet their efficacy depends entirely on correctly identifying the latent dimension $r$. While parallel analysis (PA) is widely regarded as the gold standard for this task, its performance suffers in high-dimensional regimes consisting of mixed signals and/or heavy-tailed error distributions. This arises because under the preceding conditions, column-wise permutation mechanism (or any modern variations) applied to the data matrix $\textbf{X}$ fails to destroy the signal, leading to an inflated null spectrum. To address this, we propose a nonparametric solution. We show that the latent dimension is uniquely preserved in the degree of order within the rank-transformed data matrix, which restores spectral exchangeability under permutation. We prove the consistency of Rank PA under relaxed conditions, requiring neither the pervasiveness of factors nor restrictive fourth moment assumptions. We establish that Rank PA can consistently estimate the number of factors up to the maximum of $O(n^{1/3 - \tau})$ where $\tau >0$. The robust performance of our remedy is demonstrated through numerical simulations and an analysis of the FRED-MD dataset.

Probabilistic record linkage identifies records belonging to the same entity even when identifiers are incomplete or imperfect, and is increasingly used to conduct population-level inferences from administrative data at scale. Linkage produces noisy pairwise links that must then be resolved into distinct individuals. The standard approach, transitive closure, applies a fixed threshold to each link independently and assigns clusters from the resulting connected components. However, the risk of merging distinct individuals grows with population size, motivating approaches that use graph structure to improve linkage accuracy. Clustering algorithms from adjacent fields solve the same graph-clustering task in other domains, yet have never been systematically evaluated for entity resolution. We evaluated eleven clustering algorithms – five established in entity resolution and six from adjacent fields – across three simulated datasets and one real-world dataset, and propose an adaptation tailored to linkage graphs. Cross-field algorithms – Leiden, Louvain, label propagation – were among the most accurate, reducing linkage error by up to 66% relative to transitive closure. The three algorithms also ran up to 40 times faster than Markov clustering (a leading approach in the entity resolution literature) and integrate directly into existing pipelines at scale.

Tests for heteroscedasticity in linear regression lose their level or power in three situations: when the data contain outliers, when the variance is not monotone, and when it changes along a variable outside the regressors, such as time. The proposed tests sort the observations by any chosen variable, split them into three equal parts, fit the regression in each part and compare the largest with the smallest error scale. With least squares fits and normal errors, the ratio follows Hartley's maximum F distribution with three groups exactly. With least trimmed squares fits, the ratio resists outliers spread along the ordering. Its square is approximately a maximum F ratio with effective degrees of freedom, whose limit we derive in closed form from the influence function of the trimmed variance. A factorial simulation covered 72 settings of variance shape, ordering variable, number of regressors, contamination and sample size. The robust test had the highest mean size-adjusted power, 67%, against 45% for the next test; when the variance changed along a regressor, which all tests were given, it led White's test after an outlier screen, 67% against 56%. With heavy-tailed t3 errors its lead was similar, 64% against 35%. Unlike the tests built on the regressors, it can follow a variance changing along time, and it identifies the part of the data where the variance changes. Two published robust versions of the Goldfeld-Quandt test, as implemented from their descriptions, did not hold their nominal level. The R package KOTORY implements the methods.

When minimizing the squared-error loss, the popular CP decomposition can be interpreted as parameter inference in a Gaussian model with a low-rank mean tensor and constant variance across the tensor entries. We introduce heteroskedastic-CP (HCP), which models entrywise variability with a non-constant, low-rank precision tensor, and develop an alternating block-coordinate ascent method to recover both the low-rank mean and precision tensors from noisy observations. Our procedure is computationally competitive, with the same leading-order factor-update complexity as CP-ALS. We demonstrate HCP on synthetic experiments and an EEG application.

Classical variance-based Global Sensitivity Analysis (GSA) assumes that the input–output mechanism can be repeatedly evaluated under a designed sampling scheme, which is infeasible when only a given sample of observations is available. We propose MM–GSA, a metamodel-based approach to GSA from observational data, in which supervised learning approximates the systematic input–output relationship. MM–GSA combines two complementary perspectives on input relevance: a model-agnostic estimator of the first-order Sobol' index, quantifying the contribution of an input to the variability of the systematic response, and a new trigger-based structural index, quantifying how predictive performance depends on the availability of a predictor across alternative predictor subsets. We establish consistency for both estimators and a variable-selection property for the structural index under input independence. Monte Carlo experiments and an NHANES application illustrate their finite-sample behavior and show that the two measures provide complementary information on input relevance.

Extreme events are often studied through regression models describing how covariates modify tail parameters. In many applications, however, interest lies directly in identifying the parts of the covariate space associated with tail events and with elevated exceedance probabilities. We formalize these ideas through tail halos, covariate-defined regions associated with extremes. Risk halos, when they exist, are minimum-mass covariate regions accounting for a prescribed fraction of exceedance probability, while favorable halos collect covariate values where conditional exceedance probability exceeds its marginal level. To make these set-valued objects interpretable beyond low dimensions, we introduce halo-induced covariate laws and, when densities exist, corresponding halo densities. We develop a Bayesian structured additive distributional regression framework based on extended generalized Pareto marginals, covariate-dependent copulas, and spike-and-slab effect selection to learn marginal and joint halo-induced covariate laws while propagating posterior uncertainty. The approach extends Bayesian shrinkage methods for conditional tail modeling to multivariate bulk-and-tail modeling, nonlinear effect selection, and covariate-region inference. Simulations show recovery of relevant nonlinear effects and increasingly accurate finite-sample halo representations as sample size grows. An application to PM2.5 and NO2 extremes in Edinburgh reveals distinct environmental and temporal configurations associated with high pollution.

Estimating causal effects from observational data is central to science and policy, but the effects are not identified when confounders are unmeasured. Proximal causal inference addresses this problem with proxies of the unmeasured confounders. However, existing proxy-based approaches either designate proxy roles and solve an inverse problem, which is ill-posed and hard to estimate with high-dimensional proxies, or use a latent-variable model, which assumes that the learned latent variable matches the hidden confounder and leaves bias when it does not. To address these challenges, we introduce proximal balancing. It carries the classical idea of covariate balancing to confounders that are observed only through proxies: it learns a low-dimensional summary of the covariates and proxies that makes the treatment groups comparable, and then adjusts for this summary. It needs no designated proxy roles, inverse problem, or latent model. We give identification theory, finite-sample guarantees, and a practical algorithm, PROBE. We demonstrate the method on low-dimensional, high-dimensional, and image proxies and on real-world data.

In this work, we revisit estimation and variable selection in sparse Gaussian regression, possibly under affine constraints. We adopt a middle-ground approach between optimisation and fully hierarchical Bayesian methods, preserving much of the computational efficiency of the former while adding posterior uncertainty quantification. In particular, we develop an empirical Bayes framework that separates shrinkage calibration from posterior-informed selection while using the same log-concave model throughout. The resulting workflow is modular: different methods can be used for noise-variance estimation, shrinkage calibration and posterior sampling. At the same time, these tasks are linked, and numerical choices made at one stage can propagate through the workflow and ultimately affect the decision about which variables to retain. We investigate in detail one instance of the framework based on a Laplace prior, with the amount of shrinkage determined by stochastic approximation proximal gradient. The proximal machinery used for this calibration also supports posterior simulation. We further show how the empirical Bayes calibration should be modified when homogeneous constraints reduce the number of free parameters. Nonhomogeneous affine information is instead incorporated softly; when this information is strong, posterior sampling can become poorly conditioned, and we develop a preconditioning strategy to improve mixing and posterior exploration. Synthetic experiments examine how scale calibration, posterior run length and sampler conditioning affect estimation, uncertainty quantification and the final sparse decision. On a diabetes dataset, posterior uncertainty agrees closely with established Bayesian analyses, while the final decision provides a sparser practical summary.

Density estimation is a fundamental problem in statistics and machine learning. In this work, we introduce BayesNDE, a neural density estimator based on Bayesian generative modeling. BayesNDE learns a Bayesian generative model and evaluates its density without requiring invertible networks or Jacobian-determinant computation. For each observation, it infers a sample-specific latent posterior to construct an adaptive proposal that focuses computation on regions contributing most to its density. Bridge sampling then combines samples from this proposal with separate posterior samples to estimate the density. Experiments on nonlinear and multimodal synthetic datasets show improved estimation of density values and better recovery of the density structure compared to the state-of-the-art neural density estimators. Applications to real-world datasets further demonstrate improved anomaly detection. Together, these results highlight BayesNDE as a flexible and effective neural density estimator, demonstrating how posterior inference can turn generative models into tools for density estimation. The code and tutorials are available at https://github.com/liuq-lab/BayesNDE.

In platform trials, model-based approaches typically estimate treatment effects conditional on calendar time. However, scientific and regulatory interest often lies in treatment effects defined for a target population spanning multiple enrollment periods, requiring explicit consideration of how effects should be averaged across time. This raises two fundamental challenges. The first is the definition of the appropriate target estimand when combining data across multiple periods. The second is the selection of the estimator to be used. In this work, we examine conditional and marginal estimands in platform trials with time trends, and describe target populations of interest. To address the second challenge, we evaluate model-based, G-computation and augmented inverse probability weighting estimators, comparing their bias and variance. We discuss how the choice of estimand, target population and trial data used for estimation affects estimator performance.

We consider simulation-based Bayesian inference (SBI) for the parameters of models with intractable likelihoods but tractable forward simulation. Building on Gaussian mixtures-of-experts surrogates, as a first contribution we develop a sequential procedure to estimate the posterior, incorporating an importance sampling step that introduces a locally amortized likelihood-to-evidence ratio estimator. The local amortization allows the ratio estimator to be evaluated at new parameter–data pairs from a local (data-dependent) design, without re-estimation, which is particularly convenient for our second contribution. The second contribution is localized simulation-based calibration (SBC). Localized SBC provides a graphical diagnostic of calibration over neighborhoods that are deliberately broader than the available posterior, at low additional computational cost. Rather than repeatedly running the full inference procedure for each simulated pseudo-observation, localized SBC fits the local surrogate and ratio estimator only once for each local design, and reuses them across all pseudo-observations. This approach is particularly appealing for SBI applications. We evaluate both contributions on three case studies, including a real-data epidemiological application.

Days Alive and Out of Hospital (DAOH) and Days Alive at Home (DAH) are increasingly used as patient-centred primary outcomes in perioperative trials, and a recent editorial has advocated DAOH for its simplicity and reliance on routinely collected data. We argue that the choice between these endpoints affects power, treatment effect estimation and missing data, and should be made at the design stage with these consequences in mind. By treating days in nursing homes or rehabilitation facilities as equivalent to days at home, DAOH assumes that being out of hospital is a valid surrogate for good recovery, an assumption that patient perspectives, including those from the NOTACS trial, call into question. Choosing DAH over DAOH therefore involves a trade-off between measuring what matters to patients more accurately and the added burden of tracking discharge destination, including a greater risk of missing data. If an intervention affects only length of stay, readmission or mortality, the two endpoints yield the same expected treatment effect, and the extra burden of tracking discharge destination brings no benefit. If it instead enables more patients to return directly home rather than to a care facility, DAOH may conceal this benefit and lose statistical power. We propose a baseline-adjusted DAH, which counts only days spent in a setting representing an escalation of care relative to the patient's baseline, as a better proxy for recovery that also accommodates hospital-at-home and virtual ward services.

Casting Bayesian inference as a neural network optimization problem targeting an amortized posterior is attractive, as it extends to otherwise intractable statistical models and offers near instantaneous inference for new datasets after prepaying the training cost. Although theory guarantees faithfulness under ideal convergence, practical amortized inference still requires iterating over architectures and optimization choices and ultimately “satisficing” under finite simulation, compute, and time budgets. Even the best-performing solution may thus retain avoidable representation gaps that typically require problem-specific fixes. Here, we propose a generic alternative which improves training dynamics with auxiliary guidance losses applied to internal representations. Specifically, we show how such guidance leads to faster convergence when training data is abundant and to better performance when it is scarce. We formalize representation gaps as getting stuck in a local optimum at the information bottleneck between the parts of the network tasked with feature learning and those tasked with conditional distribution learning, and offer a generic diagnostic to separate summary failures from inference failures. Finally, we demonstrate that auxiliary supervision improves convergence speed and accuracy on a range of challenging real-world inference problems.

We present B-GRASP (Bayesian GRAph inference with SPDE priors), a Bayesian framework for inferring uncertain edge weights in stochastic dynamical systems on graphs from noisy observations of nodal states. The unknown edge weights parameterize the graph differential operator and therefore directly govern the evolution of the graph process. Motivated by connections between differential operators in PDEs and SPDEs and their graph counterparts, we construct stochastic graph models incorporating diffusion, reaction dynamics, and stochastic forcing. The resulting hierarchical formulation jointly represents uncertainty in the graph structure and stochastic forcing. Latent graph variables determine positive edge weights and the corresponding graph Laplacian, while latent Brownian variables represent the stochastic forcing. Conditional on these variables, the graph dynamics define a deterministic forward map from which the likelihood and posterior distribution are constructed. We characterize the posterior using maximum a posteriori estimation and the No-U-Turn Sampler, enabling both point estimation and uncertainty quantification. We demonstrate the framework on a one-dimensional inverse heat-conduction problem, stationary and nonstationary graph reaction-diffusion systems with nonlinear dynamics, and state-level COVID-19 data in the United States. The numerical results show that posterior uncertainty provides information not captured by point estimates, particularly for weakly identifiable or highly conductive edges, and enables uncertainty in both graph connectivity and stochastic forcing to be quantified within a Bayesian framework.

Algorithms are increasingly being used to help automate and improve data-driven decisions, but care must be taken to prevent such algorithms from learning discriminatory patterns from historical data and perpetuating their biases. Statistical notions of fairness aim to mitigate either a model's disparate impact on disadvantaged groups (thus ensuring group fairness) or the resulting disparate treatment of individuals with similar features (thus ensuring individual fairness). Simultaneously mitigating disparate impact and disparate treatment is generally impossible for non-trivial models, necessitating a compromise. In this paper, we introduce the Fair Lasso and Fair Posterior as methods for selecting fair covariates in generalised linear models. By targeting variables that are simultaneously strong predictors of the response and weakly dependent on the sensitive group memberships, we aim to achieve favourable trade-offs between disparate treatment and disparate impact. Additionally, our selected set of fair features can be used as the conditioning set of legitimate features in the paradigm of Conditional Demographic parity (CDP) when no prescriptive legal framework exists.

Reinforcement learning and contextual bandit algorithms have become increasingly common in sequential decision-making applications. When these methods are deployed in high-stakes domains, there is growing interest not only in learning effective policies, but also in conducting statistical inference for quantities learned under adaptive data collection. However, classical procedures applied naively in these settings can fail: even when estimators are unbiased, their variance becomes path-dependent and as a result may not be asymptotically normal. A growing literature has emerged to ameliorate this problem, but solutions tend to be problem specific and often rely on correct specification of a working model. In this work, we develop a unified framework for constructing asymptotically valid confidence intervals to cover smooth functionals of nonparametric M-estimands under adaptive sampling. Under Neyman orthogonality, we provide two novel methods for performing inference: (1) a self-normalized statistic based on the realized quadratic variation of the influence function and (2) a statistic using a plug-in estimate of the conditional variance based on reweighted influence function increments. Our results allow for flexible nonparametric estimation of nuisance parameters and remain valid under model misspecification. Our theory is supported by a simulation study for a dynamic pricing application which demonstrates that this method can produce asymptotically valid confidence intervals where standard methods fail.

This paper develops a framework for estimation and inference on the volumes of sets that are projections of critical function sets, focusing particularly on the convex body beneath the optimal receiver operating characteristic (ROC) surface. Specifically, we propose a volume calculation method that first uses an Aumann expectation representation and then applies Minkowski mixed volumes. Using this framework, we show that the population volume under the ROC surface (VUS) is proportional to the expectation of a symmetric U-statistic kernel. We then propose a double/debiased machine learning estimator of the VUS, derive its asymptotic properties, and develop an inference procedure. Further applications of this framework include an analysis of the feasible error set across pre-defined groups and a natural generalization of the Gini coefficient for measuring inequality.

Policy evaluation and learning aim to assess and optimize treatment assignment rules based on individual characteristics. A fundamental challenge arises when outcomes are truncated by death, rendering conventional policy utilities undefined. To address this challenge, we study policy evaluation and learning under truncation by death within the principal stratification framework. We propose the survivor average utility and subgroup survival rates for evaluating treatment policies. Under treatment ignorability and monotonicity, the subgroup survival rates are point identified, whereas the survivor average utility is only partially identified through sharp bounds. We then develop semiparametrically efficient estimators for the subgroup survival rates and hybrid estimators for the survivor average utility bounds. Building on this evaluation framework, we formulate a constrained minimax optimization problem for policy learning that minimizes worst-case regret relative to a benchmark policy while requiring the learned policy to achieve a survival rate no lower than that of the benchmark. We show that the optimal policy admits a threshold representation based on two priority scores. We develop an estimation procedure for the optimal policy and establish regret and feasibility guarantees. Simulation studies and an application to the MIMIC-III clinical dataset demonstrate the practical performance of the proposed methods.

The Bayesian optimal phase II (BOP2) design accommodates simple and complex endpoints but does not address biomarker-guided enrichment or multiplicity control across pooled and subgroup claims. We propose BOP2-ENR, which monitors biomarker-negative (NG) and biomarker-positive (PG) cohorts separately, permits interim enrichment to PG, and calibrates pooled and PG-restricted claims. Strong family-wise error rate (FWER) control is defined over a prespecified monotone-activity parameter space. Under the mixed configuration in which NG is inactive and PG is active, the probability of a false joint claim is bounded by the probability that NG survives futility monitoring. This exact single-cohort bound does not involve the final efficacy cutoff and also yields a ceiling on joint-claim power. For efficacy-toxicity monitoring, subgroup inactivity is defined by a union null and safety is established separately within each subgroup. Across the scenarios considered and binary, co-primary and efficacy-toxicity endpoints, all selected designs met the prespecified exact-bound and Monte Carlo verification criteria; in sensitivity analyses over odds ratios between component outcomes assumed independent in calibration, point estimates of the error-control quantities remained below the nominal level, although power was association-sensitive. The bound was nearly attained as PG efficacy approached the boundary of the nuisance space, whereas disabling enrichment produced mixed-configuration error rates near one. BOP2-ENR therefore extends the BOP2 framework to adaptive enrichment while clarifying that the NG futility gate governs the mixed-configuration component of strong error control and the attainable power of a joint claim.

Generative AI has dramatically accelerated the rate at which new treatments—from novel pharmaceuticals to online marketing campaigns—can be conceived and deployed. As a result, modern experimentation platforms often run continuously, with treatments added as they are ready and removed when they underperform. We formalize this "Always-On" experimental setting, in which treatments can be dynamically generated, added to, and removed from a running experiment, and study the statistical problem of deciding whether to accept or reject each treatment while controlling for the false discovery rate. We develop sequential tests that achieve time-uniform Type-I error control under arbitrary stopping times and "predictable" treatment schedules. Our approach builds on the testing-by-betting framework: we construct test supermartingales for testing the average treatment effect of each treatment, and show that the construction of these test supermartingales is growth-rate optimal in an almost-sure sense.

Batting average factors exactly as BA = c times f, where c = (AB - SO)/AB is the rate of avoiding a strikeout and f = H/(AB - SO) is the rate at which non-strikeout at-bats become hits. Using the 256 major-league hitters with at least 300 at-bats in 2025, we show that the two factors behave very differently. Strikeout avoidance is highly repeatable, with a median year-to-year correlation of 0.86 over 19 consecutive-season pairs from 2004 to 2025. The finishing rate is not: its median correlation is 0.44, and batting average itself (0.44) is no more repeatable than its noisier factor. A bivariate logistic-normal random-effects model fit to the 2025 season estimates the correlation between the two talents at -0.68 (95% profile interval -0.85 to -0.50), far stronger than the raw correlation of -0.44, and implies single-season reliabilities of 0.91 for c and 0.37 for f. The model also yields a closed-form bivariate shrinkage estimator in which a hitter's strikeout rate informs the estimate of his finishing rate. Applied to decades of American and National League data, the decomposition revisits Gould's explanation for the disappearance of the .400 hitter. Since the dead-ball era, the talent variance of strikeout avoidance has grown roughly 4.6-fold while that of finishing has halved, and the correlation between them has moved from near zero to about -0.53. That emerging trade-off, rather than a general narrowing of talent, accounts for the reduced spread of modern batting averages.

We develop a three-stage adaptive procedure for principal component analysis (PCA) when high-dimensional observations are collected sequentially and additional sampling incurs a cost. The procedure balances PCA compression loss against sampling cost while selecting the retained dimension through a prescribed explained-variance criterion. Starting from a pilot sample, an intermediate stage updates the PCA quantities before determining the final sample size, thereby avoiding reliance on unknown population eigenvalues. Under suitable regularity conditions, we establish both first- and second-order efficiency relative to the population oracle. Comparison with the corresponding two-stage rule shows that the additional recalibration yields sharper second-order control and reduces the influence of the pilot stage on the final sampling decision. The theory allows the ambient dimension to exceed the sample size under appropriate covariance and spectral conditions. Simulation studies demonstrate the strong finite-sample performance of the procedure across increasing dimensions and several dense covariance structures. As a real-data application, we conduct a retrospective study of gene-expression data from 32 cancer-type cohorts in The Cancer Genome Atlas, illustrating both cost-effective early stopping and settings in which additional observations are recommended.

Modern experiments increasingly produce rich post-treatment objects—such as text, images, and video—that may provide early surrogate signals for outcomes that are delayed, expensive, or observed only for a subset of participants. A pretrained encoder can turn such an object into a strong generic embedding, but the embedding is not trained for the estimation tasks required by a causal estimator and may emphasize information irrelevant to the causal target. We propose SIRNET, a Surrogate-Informed Representation adaptation framework for neural-NETwork-based causal estimation in the presence of unstructured post-treatment surrogates. Starting from pretrained surrogate embeddings, SIRNET learns a shared adapter jointly for outcome prediction, treatment propensity, and arm-specific surrogate marginalization, beyond the generic pretraining objective. The resulting covariate and surrogate representations provide a common interface for these nuisance tasks. The final treatment-effect estimate and confidence interval are obtained from cross-fitted orthogonal scores that attain the semiparametric efficiency bound under the stated nuisance-rate conditions. We also validate SIRNET's performance in synthetic and semisynthetic experiments, as well as the Anti-Amyloid in Asymptomatic Alzheimer's Disease (A4) trial, using frozen pretrained brain-MRI embeddings as surrogates for a long-term outcome.