Papers

Population-level policies are introduced at a fixed time and evaluated from a single series of aggregate outcomes, and the interrupted time series design estimates the total shift in an outcome after the intervention. When the policy is expected to act through a measurable pathway, the total effect is less informative than its decomposition into direct and indirect effects. We formulate causal mediation for a single interrupted time series and study stabilized mediator weighting as the estimator of the natural direct and indirect effects. Because the intervention is a deterministic function, the exposure weight equals one and the exposure contrast is identified through the segmented-regression level shift, so only the mediator pathway is weighted. We add a cumulative mediator weight that carries the lagged confounder history, incorporate a concurrent event as a second interruption, and replace variance formulas that treat the estimated weights as fixed with a block-residual bootstrap that keeps the deterministic exposure timing intact and resamples the mediator and outcome residuals in moving blocks. In a simulation calibrated to daily data, the unweighted product-of-coefficients estimator is biased under mediator-outcome confounding, with an indirect-effect bias near $0.19$ and coverage of $0.003$, whereas stabilized weighting reduces the bias to about $0.03$ and improves indirect-effect coverage from near zero to about $0.83$. Applied to the 2019 termination of Ontario's Drive Clean vehicle emissions testing program, the method estimates a direct reduction in ground-level ozone of $2.113$ parts per billion (95% interval $-3.384$ to $-0.841$) that is robust across four Toronto regions, a positive but heterogeneous indirect effect through nitrogen dioxide, and a total effect near the boundary of significance; a pre-pandemic sensitivity analysis agrees with the primary results.

An increasing number of scholars use AI to measure variables they subsequently include in downstream analyses. Although AI-measured variables are often analyzed as if observed without error, ignoring prediction errors in automated measurement leads to substantial bias and invalid confidence intervals in downstream analyses, even if AI measurement accuracy is high, e.g., above 90%. Existing solutions, such as design-based supervised learning and prediction-powered inference, combine error-prone AI-based measurements with gold-standard labels, which may be costly and difficult to obtain in some application areas. In this paper, we propose debiased inference with multiple imperfect measurements (DMM), a framework that combines multiple error-prone AI measurements to enable valid downstream inference without gold-standard labels. Building on the established results on CP decomposition, DMM assumes that these measurements are independent conditional on the latent true label and observed unit-level features, such as text features represented by embeddings. This framework allows for unknown misclassification rates to vary across annotation methods (e.g., large language models) and across units of annotation (e.g., texts). Under this assumption, we use semiparametric inference theory to prove that the DMM estimator is consistent and asymptotically normal, enabling valid inference for a wide range of downstream statistical analyses common in the social sciences. Our simulation results show that DMM yields valid inference and that adding accurate, though imperfect, measurements can improve efficiency. Focusing on common applications of large language model annotations, we also develop diagnostics to assess the conditional independence assumption.

The spacing of data contains information about the underlying modality. Sections of consistent, similar spacing correspond to modes while it increases between them. We have defined parametric, runs-based non-parametric, and data driven tests to evaluate these features — flats and peaks — and determine the presence and location of multiple modes. This report will check the tests in two situations. By varying a bi-modal setup we can control the changes in spacing and determine the resolution and sensitivity of the tests. By applying them to the large number of test cases that exist in the literature from other modality studies we check the stability and consistency of the results. We will also evaluate the accuracy of the null-distribution models of the features. The results show that the spacing does reflect the data's modality, that the tests do screen marginal cases, and where the analysis begins to break down.

The spacing of a unimodal variate resembles a `U' with a flat bottom and rapidly increasing values in the tails. When combined into multi-modal setups, the transition between variates into their tails forms local increases in the spacing. These peak features signal the data is multi-modal while the flats locate the modes. We develop tests of the features, including parametric models based on an assumed null univariate distribution, the number of runs or longest run in the signed difference of the interval spacing, and feature reconstruction by means of permutations of the runs or bootstrap samples from a pool based on the difference of the signal. We also try combining existing changepoint detectors to look where the behavior of the spacing changes. This paper describes the processing of the spacing and models and tests in full, gives examples of their use, and summarizes the performance in general.

We study how fast experimental designs can approach the semiparametric efficiency bound in finite samples, as measured by the excess variance of unadjusted treatment effect estimation. We prove an impossibility theorem: under weak conditions, no design can approach the variance bound uniformly over smooth outcome models unless covariate dimension $d \ll \log n$. Even in experiments with thousands of units, this permits only a handful of covariates. Motivated by this, we propose new designs based on discrepancy minimization that instead attempt to control imbalances over restricted-complexity nonparametric function classes. Such designs achieve fast rates to their corresponding restricted efficiency targets, permitting $d \ll n$ covariates in an additive nonparametric specification. They can also be combined with matching to protect against unmodeled outcome variation. In simulations calibrated to 12 published experiments, our designs reduce variance relative to matched pairs randomization in every empirical setting.

We introduce Heteroskedastic Normalized Vecchia Gaussian Processes (HetNV), a scalable framework for Gaussian process regression with input-dependent observation noise. HetNV combines Vecchia likelihood approximations on normalized inputs with residual-based nonparametric variance estimation. The latent mean is estimated via a Vecchia GP with observation-specific nugget variances, while the log noise variance is obtained by smoothing stabilized log-squared residual pseudo-responses that account for kriging uncertainty and current nugget estimates, using LOESS in one dimension and thin plate spline generalized additive models in two dimensions. The method alternates between mean and variance updates, avoiding latent-variable inference for the variance process. For fixed neighborhood size ($m$) and number of observations ($n$), the dominant per-iteration cost is the Vecchia update, scaling as $O(nm^2)$. Simulation studies show improved recovery of input-dependent uncertainty relative to homoskedastic Vecchia models while maintaining competitive mean prediction accuracy, with additional gains in two-dimensional mean estimation. An application to spacecraft plasma measurements demonstrates how locally adaptive uncertainty estimates influence downstream signal-detection decisions in large, noisy, heteroskedastic settings.

Randomized trials provide internally valid treatment-effect evidence, but trial participants may not represent the target population. In contrast, observational studies are often closer to the target population, but their treatment assignment may be affected by possible hidden confounding. We develop a robust posterior-drift framework for estimating the average treatment effect in an observational target population when exact conditional-effect transportability may fail. The framework represents observational conditional potential-outcome regressions as their randomized-trial counterparts plus source-specific drifts. The randomized trial serves as an internally valid anchor, while the observational study supplies the target covariate distribution and partial information about the target causal contrast. To account for possible hidden confounding, we consider a Rosenbaum-type uncertainty set induced by a sensitivity parameter on the generalized propensity score and estimate the drift through a minimax worst-case risk criterion. We derive efficiency results in auxiliary regimes, establish uniform concentration and near-optimality guarantees for the minimax estimator, and handle general parametric and smooth nonparametric drift classes. Simulations and an ACTG 175–WIHS application show that the proposed analysis yields more cautious and interpretable target-population effect estimates than exact-transportability analyses.

Uncertainty visualisation is important for data transparency, especially for map visualisations where data is often aggregated. Despite the importance of this area, studies evaluating uncertainty visualisation lack consensus and produce conflicting results. This work introduces a new evaluation approach for uncertainty visualisation that attempts to assess uncertainty as noise, rather than signal. We evaluate five methods of visualising uncertainty: standard choropleth maps, value/variance bivariate maps, value-suppressing uncertainty palettes, overlaid sampling, and pixelated sampling maps. Built on principles of implicit testing, we put an 'uncertainty visualisation' spin on the classic Ishihara colourblind test to create a novel test that is able to evaluate uncertainty as noise. We compare signal visibility to conventional hypothesis tests at various levels of group separation. By building our experimental design on top of established graphics theory, we isolate the plot components that facilitate successful signal suppression and establish foundational theory for the perception of uncertainty visualisation.

Compositional predictors, such as microbiome abundances, pose unique challenges in variable selection due to their unit-sum constraint and inherent dependencies. Existing approaches often rely on fixed association graphs derived from phylogenetic or ecological distances, which may not reflect outcome-relevant relationships. We propose GRACE (GRaph-Adaptive horseshoe for Compositional rEgression), a fully Bayesian framework that enforces compositional constraints, performs variable selection, and adaptively learns an outcome-driven shrinkage graph. GRACE achieves compositionality through a novel linear reparameterization of regression coefficients, while a structured horseshoe prior induces sparsity and smooths coefficients along the learned graph. Graph learning is accomplished via scaled beta2 priors on edge weights, providing both outcome-specific adaptation and posterior uncertainty quantification. We develop an efficient Gibbs sampler incorporating elliptical slice sampling to ensure scalability in high dimensions. Through extensive simulations, GRACE demonstrates competitive predictive accuracy and improved graph recovery compared with existing methods, particularly under graph misspecification. Application to oral microbiome data from the ORIGINS study identifies taxa associated with insulin resistance and yields an outcome-driven graph summarizing how those taxa relate to the outcome, a structure that differs substantially from phylogenetic or co-occurrence networks. These findings highlight that fixed predictor graphs useful for regularization may not faithfully represent outcome-relevant feature relationships, underscoring the need for adaptive, outcome-informed approaches in compositional regression.

We develop blinded sample size re-estimation strategies for McNemar's test based on paired binary primary and secondary short-term surrogate endpoints. The development is motivated by a prospective randomized clinical trial on childhood glaucoma. A conditional power expression for McNemar's test given the primary endpoint at an interim analysis is derived and complemented by a sample size re-estimation rule. We show that this procedure preserves the type I error rate while allowing the second-stage sample size to be chosen to attain a prespecified target power. In the case where for some patients only a short-term surrogate endpoint is available at interim, we introduce a surrogate-based re-estimation approach that conditions on all possible numbers of primary-endpoint discordant pairs using transition rates from the surrogate to the primary outcome. We show how these transition rates can be estimated from data on a subsample for which both surrogate and primary endpoint are available. We derive the resulting surrogate endpoint-based conditional power and sample size rule and illustrate their use with the example of the motivating trial.

One-dimensional Gaussian processes with stationary, integrable kernel functions admit exact or arbitrarily accurate state-space representations, enabling linear-time inference through Kalman filtering and Rauch-Tung-Striebel (RTS) smoothing. However, the RTS smoother requires inversion of predicted state covariance matrices, which can become ill-conditioned and may therefore lead to numerical instabilities. In this work, we revisit the modified Bryson-Frazier (MBF) smoother as an alternative to the RTS smoother for Gaussian process regression in its state-space representation. In addition to reducing computational cost and memory requirements, the MBF smoother computes the same posterior distributions as the RTS smoother while avoiding the problematic covariance matrix inversion and the associated numerical instabilities. Furthermore, we demonstrate that the intermediate quantities computed by the MBF smoother can be reused to compute gradients of the negative log marginal likelihood, enabling kernel hyperparameter learning with minimal additional cost. Together, these results establish the MBF smoother as a unified and numerically robust approach to inference and kernel hyperparameter learning for one-dimensional Gaussian process regression.

Successive Difference Replication (SDR) is a replication based method of variance estimation introduced by Fay and Train (1995) for estimators based on complex multistage surveys, especially those including a final systematic sampling stage. The method has been used for many years as the primary variance-estimation methodology in large national household surveys administered by the Census Bureau, including the American Community Survey and also the Current Population Survey's monthly estimates based on self-representing strata. In settings where it is applied, generally no second method of variance estimation has been available, so the performance of SDR has been studied via simulation by various authors, for variances of survey totals and of nonlinear survey estimators. This paper begins with a thorough exposition of the SDR method and review of previously published results on the small-domain biases of SDR variance estimation. It is shown that the number D of cycles used in implementing SDR should be 3 or larger, in order to control the variability of SDR estimates, but need not be larger than 5. Beyond that, the value of D is virtually irrelevant to the occurrence of small-domain bias in SDR. The SDR method is shown via theoretical formulas and simulation to inflate average estimated variances in small domains by amounts that vary systematically with the patterns of attribute means and variances and survey weights in consecutively enumerated strata. The degree of average variance inflation is generally moderate, no more than 15 percent in domains with sample size 20, but can be larger in special settings. Moreover, SDR estimates are extremely variable in small domains, with standard deviations often far larger than any biases.

This paper develops an adaptive surrogate modeling method for problems with very high-dimensional spatio-temporal outputs. The analysis of spatio-temporal multi-physics systems is computationally expensive and consists of a large number of inputs and outputs. Surrogate models are often constructed to replace the physics-based model to achieve computational efficiency in analyses such as uncertainty quantification and optimization that require many function calls. In order to address the challenge introduced by the high dimensionality of spatio-temporal output, a dimension reduction method is first employed to map the high-dimensional output to a low-dimensional latent space. This is followed by the construction of the surrogate model in the low-dimensional space. The prediction error in the original space, which includes both the reconstruction error and surrogate model error, is evaluated using different error metrics. Based on the prediction accuracy of the surrogate model, new training points are identified for adaptive improvement of the surrogate model. We present a novel adaptive sampling technique that combines exploration and exploitation to improve the surrogate model accuracy with the fewest possible runs of the expensive physics-based model. Thermo-mechanical analysis of a gas turbine engine blade is used to analyze the effectiveness of the proposed method.

When computational models (either physics-based or data-driven) are used for the sensitivity analysis of engineering systems, the sensitivity estimate is affected by the accuracy and uncertainty of the model. This paper considers global sensitivity analysis (GSA) for situations where both a physics-based model and experimental observations are available, and investigates physics-informed machine learning strategies to effectively combine the two sources of information in order to maximize the accuracy of the sensitivity estimate. Two representative machine learning (ML) techniques are considered, namely, deep neural networks (DNN) and Gaussian process (GP) modeling, and two strategies for incorporating physics knowledge within these techniques are investigated, namely: (i) incorporating loss functions in the ML models to enforce physics constraints, and (ii) pre-training and updating the ML model using simulation and experimental data respectively. Four different models are built for each type (DNN and GP), and the uncertainties in these models are included in the Sobol indices computation. The DNN-based models, with many degrees of freedom in terms of model parameters and training options, are found to result in smaller bounds on the sensitivity estimates when compared to the GP-based models. The proposed methods are illustrated for additive manufacturing and lake temperature modeling examples.

Customer decline early-warning systems feed account-manager action lists, and every flagged account consumes intervention capacity. In a deployed business-to-business marketplace system, one action-list slot in three went to flags that dissolve under a seasonally aligned label. The standard target in non-contractual churn prediction compares an entity's next k months of activity with its trailing k months. The two windows cover different calendar months, so for seasonal entities the threshold-ratio construction confounds seasonality with decline, and the event rate depends on the label's anchor calendar month. We formalize the mechanism and measure it on three public panels and the production panel (the public arms pre-specified). Of the adjacent-window decay events, 37–69% on the public panels and 28–50% in production have no counterpart under a seasonally aligned definition. Pooling anchors, the standard remedy, balances the training mixture but corrects no individual label. Measured alternatives repair the curve only partially or change the detection horizon. Aligning the baseline to the same k calendar months one year prior – advice practitioners already state, here formalized, measured, and costed – flattens the curve at the source. With the classifier held fixed, production holdout ROC-AUC rises from 0.767 to 0.864 for decline (different targets; the gap closes on synthetic ground truth and a production hindsight referee). The served action list shrinks by a third, 119 to 79 accounts. The measured price is extra history, a blind spot to decline-then-stabilization, and a stricter cut under sustained growth.

This paper challenges the pessimistic meta-inductive argument against scientific realism by undermining its inductive step rather than its historical premise. Although related challenges already exist, I develop a new one. Drawing on a general epistemology of scientific inference developed in frequentist statistics, machine learning, and formal epistemology, I evaluate induction in terms of convergence to the truth. I argue that ordinary enumerative induction can achieve everywhere convergence, whereas meta-induction fails even to achieve almost everywhere convergence. Indeed, in the problem context where meta-induction arises, the failure is deeper: no inference method whatsoever achieves almost everywhere convergence.

This paper proposes a nonparametric estimation procedure for extropy and its extensions, namely the {\alpha}-Rényi and {\alpha}-Tsallis extropies, for finite discrete random variables. We establish almost sure rates of convergence and asymptotic normality for the plug-in estimators. The theoretical results are validated through a comprehensive simulation study. The findings provide a solid foundation for the use of extropy-based measures in practical applications, including forecasting, risk assessment, and decision-making under uncertainty.

Every team building Large Language Models (LLMs) faces a core challenge: offline benchmarks show performance gains and user engagement rises post deployment, but isolating cause from effect remains difficult. Simultaneous marketing, media coverage, and seasonal demand obscure whether model updates truly drive engagement gains. This paper presents a novel causal estimation approach that leverages non uniform quality improvements across capabilities within a single model version. Because capabilities improve unevenly (e.g., strong gains in coding versus modest gains in writing), users experience varied quality depending on their task distribution. This variation in experienced quality provides causal signal for estimation. We validate this approach on synthetic data with known ground truth. The raw estimator recovers 81% to 88% of the true effect, with the remainder lost to measurement error in usage estimates. Applying an errors in variables disattenuation adjustment (using a test retest reliability ratio mean correlation of 0.861) corrects the estimate to 1.017 (bootstrapped 95% CI: 0.915 to 1.109). By contrast, naive methods fail significantly, recovering only 63% without version controls and 62% using real time rather than frozen usage patterns. Permutation tests confirm the framework distinguishes true causal effects from noise. Sensitivity analysis indicates recovery improves monotonically from 78% to 87% as pre period length increases from 3 to 7 weeks, highlighting a clear tradeoff between sample duration and estimator precision. Seed sensitivity tests further confirm stability across random draws.

This paper studies the finite-sample bias of plug-in estimators for Shannon, Rényi, and Tsallis extropies for finitely supported discrete random variables. We derive explicit first-order bias formulas for all three estimators by analyzing the bias of the intermediate functional S_\alpha = \sum_{i=1}^r (1-p_i)^\alpha. Bias-corrected estimators are then proposed. We show that the uncorrected and corrected estimators are asymptotically equivalent, differing only by terms of order O(1/n). A simulation study validates the theoretical results and demonstrates the superior finite-sample performance of the bias-corrected estimators. The results justify the use of the simpler uncorrected plug-in estimators in asymptotic settings, such as those considered in the companion paper on almost sure convergence and asymptotic normality.

Online decision making often requires navigating a landscape shaped by both dynamic contexts and strategic interactions. In competitive pricing, for example, hotels must account for both dynamic contextual factors and rivals' strategic responses. Existing approaches address only part of this challenge: contextual bandits optimize single-agent decisions using observable features but ignore multi-player interactions, while online matrix games capture strategic behavior through Nash equilibrium but assume fixed payoffs, ignoring contextual information. How should agents act then when strategic payoffs evolve with contextual signals? We introduce online contextual matrix games to integrate contextual information into multi-player online games. We further propose OnGameLearn, an online learning algorithm that efficiently balances exploration and exploitation across both player actions and contexts. This approach comes with statistical guarantees: tail bounds for the estimated payoff matrix, the convergence of the estimated Nash equilibrium, the asymptotic normality of the parameter estimators, and the sublinear regret bound. We also develop the notion of policy value in matrix games and develop a doubly robust, $\sqrt{T}$-consistent estimator for it. Across simulated studies and a real-world hotel pricing application, we find that OnGameLearn effectively navigates the intertwined challenges of strategic and contextual decision-making.

Estimation of wildlife population size and spatial dynamics is central to ecology and conservation. Spatial capture-recapture (SCR) models estimate abundance, using detections at sensors such as camera traps, by linking detection probability to the distance between detectors and latent individual activity centres. However, standard SCR formulations assume detections are conditionally independent over time given activity centres without explicitly modelling movement between detection events. This assumption can be problematic when individuals exhibit movement-driven dependence in detections, potentially leading to biased inference on population size. We address this important issue by developing a continuous-time framework that integrates movement into spatial capture-recapture. Individual movement is modelled as a continuous-time Markov chain over a discretised landscape, and detections arise as state-dependent Poisson events. This yields a Markov-modulated marked Poisson process representation, in which detections provide information about an individual's latent location at the time of observation and allow likelihood-based inference in continuous time. We show through simulation studies that ignoring movement-driven dependence can lead to positively biased estimates of population size, whereas the proposed model recovers unbiased estimates and provides additional inference on space use. An application to camera-trap data of American martens illustrates how the framework yields new insights into movement and density. These results demonstrate that explicitly modelling movement is critical for reliable inference in spatial capture-recapture studies.

Electrophysiological brain signals are typically acquired through indirect and noisy measurements, providing transformed representations of the underlying neural activity. Source reconstruction—the inverse problem of resolving underlying neural signals from these measurements—is essential for mapping brain function but remains challenging because it is ill-posed and sensitive to noise. Deep learning methods have shown promise across a range of inverse problems, yet many do not explicitly incorporate the biophysical principles governing data generation, limiting data efficiency and adaptation across subjects. Here, we introduce DeepOp-Informed, a biophysics-informed geometric deep operator learning framework that embeds the biophysics of the sensing process into the model through a custom differentiable layer, enabling more efficient learning and improved reconstruction performance. This layer enables the neural network to adapt to subject-specific variations in the physics of signal generation, resulting from differences in brain anatomy and sensor positioning. In realistic magnetoencephalography simulations, DeepOp-Informed generalizes to forward models from held-out subjects, reducing reconstruction error relative to several neural-network and classical baselines. Applied to adolescent auditory-evoked recordings, it produces anatomically plausible reconstructions localized to the auditory cortex. While our application focuses on magnetoencephalography, the framework is general and may be adaptable to other imaging modalities.

Under the ICH E9 (R1) addendum, treatment policy strategies for intercurrent events target the treatment effect regardless of treatment discontinuation. Sequential multiple imputation (MI) models that condition each visit's imputation on discontinuation status or pattern reduce bias relative to mixed models and standard MI, but require every subject to contribute at least one post-baseline observation, an assumption violated by subjects who withdraw before any post-baseline assessment, a baseline-only early dropout pattern common in chronic-disease trials. We propose Extended Pattern-based Sequential Multiple Imputation (EPSMI), which reconstructs missing data for baseline-only early dropouts using covariate-matched, same-arm donors before applying an extended discontinuation-pattern indicator within eight sequential MI models. Two strategies were evaluated: EPSMI-Full, imputing the entire post-baseline trajectory from a donor, and EPSMI-Y1, imputing only the first visit and leaving later visits to the pattern-extended MI engine. A simulation study grounded in published Sjogren's syndrome trials evaluated bias, coverage, precision, power, and Type I error across 24 scenarios, comparing EPSMI against MMRM, standard MI, and sequential MI after excluding early dropouts (No Early). Under random early dropout, both EPSMI strategies reduced bias relative to No Early. Under informative early dropout the strategies diverged: EPSMI-Y1 remained robust, matching or exceeding No Early coverage with only mild Type I error inflation, whereas EPSMI-Full's deterministic reconstruction produced larger bias, narrower intervals from underestimated variance, lower coverage, and clear Type I error inflation. EPSMI-Y1 is recommended as the primary analysis strategy for baseline-only early dropout, keeping estimation faithful to the treatment policy estimand over the full randomized population.

Bayesian dynamic borrowing (BDB) methods leverage historical data to reduce treatment effect uncertainty, yet existing approaches rely on parametric outcome models susceptible to misspecification. We propose the nonparametric latent exchangeability prior (NP-LEAP), an outcome-agnostic, assumption-lean framework to borrow information from historical data. The NP-LEAP performs individual-level exchangeability assessment, inducing Bayesian model averaging over all possible partitions of the historical data into exchangeable and nonexchangeable subsets. Although applicable to a variety of data types with choice of appropriate kernel, the NP-LEAP is particularly well-suited for studies with time-to-event outcomes, where parametric BDB is potentially triply misspecified - imposing a parametric baseline hazard, the proportional hazards structure, and blanket exchangeability. We establish posterior consistency under mild regularity conditions. Simulation studies demonstrate favorable operating characteristics relative to parametric borrowing methods and nonborrowing semiparametric frequentist methods. We illustrate the method by augmenting the control arm in a randomized trial of patients with non-small cell lung cancer.

Generalised Bayesian inference uses weights of the form $\exp\{-\beta_n\ell_n(\theta)\}$ even when the loss is only estimated. Exponentiating an unbiased loss estimate changes the target, and when $\beta_n\asymp n$ an ordinary Monte Carlo loss estimate with variance of order $M^{-1}$ requires a per-proposal budget $M$ of order $n^2$ to keep the leading log-weight variance bounded. We introduce Sign-Corrected Bessel Debiasing (SCBD), a signed pseudo-marginal method based on independent block estimates of the loss, and study its ordinary-MC and independently randomised quasi-Monte Carlo (RQMC) implementations. Under an i.i.d. Gaussian block model, a Bessel factor constructed from the block sample variance exactly removes the Gaussian exponential inflation despite the variance being unknown. For general non-Gaussian finite blocks, the method targets a posterior differing from the intended posterior by a parameter-dependent multiplicative factor. Under regularity conditions, the uncorrected and corrected ordinary-MC targets have total-variation errors of orders $\beta_n^2/M_n$ and $\beta_n^3/M_n^2$. If an RQMC block estimator has variance $\mathcal O\{B^{-\alpha}(\log B)^{d-1}\}$, the corresponding errors are of orders $\delta^{\mathrm{RQ}}_{n,M_n}$ and $(\delta^{\mathrm{RQ}}_{n,M_n})^{3/2}$, where $\delta^{\mathrm{RQ}}_{n,M_n}=\beta_n^2M_n^{-\alpha}{\log(2+M_n)}^{d-1}$. The same variance rate gives a sufficient budget of order $n^{2/\alpha}$, up to logarithmic factors, for bounded leading log-weight variance when $\beta_n\asymp n$. The numerical examples show that favourable RQMC representations can inherit this budget scaling and that variance reduction and Bessel correction are complementary. Compared to existing exact corrections, Bessel debiasing is essentially "for free". It is generic, easy to code and supported by theory.

Seasonal infectious-disease interventions are commonly evaluated with interrupted time-series or pre–post designs that align epidemics by calendar week. When epidemic onset, speed or peak timing differs between seasons, such comparisons confound a shift in epidemic phase with a change in disease burden. We propose a Bayesian causal count model in which season-specific affine transformations map calendar time to a latent epidemic clock, and intervention effects are estimated on that clock rather than on the calendar. The alignment is a model component rather than a preprocessing step, so uncertainty about epidemic timing propagates into every causal contrast. The model uses a negative-binomial observation distribution, hierarchical area, season and area-season effects, a shrunk Fourier epidemic curve, and a continuous programme-intensity exposure. Posterior g-computation yields prevented cases, prevented fractions, peak attenuation and epidemic displacement, under both a controlled contrast and a dynamic contrast that propagates disease history within each arm. A two-tier simulation study evaluates bias, root mean squared error, interval coverage and parameter recovery under stable timing, epidemic-clock variation, intensity-dependent ascertainment and area-level confounding. We illustrate the framework using open Catalan primary-care surveillance and respiratory syncytial virus immunisation data, with explicit attention to the overlap in programme intensity that identifies the effect.

The log-rank test and Kaplan–Meier plot are standard tools for analyzing time-to-event data in randomized clinical trials, yet neither provides a summary of the magnitude of the treatment effect. Practitioners typically fill this gap by reporting a hazard ratio from a Cox proportional-hazards model or an acceleration factor from an accelerated failure time (AFT) model, but both require assumptions beyond those needed for the log-rank test or Kaplan–Meier estimator. We propose two nonparametric confidence intervals for scalar effect-size summaries, an additive shift c and a multiplicative factor $\rho$, obtained by inverting the log-rank test under sharp null hypotheses of constant treatment effects. Building on the randomization-inference framework of Li and Small (2023), both intervals are valid under the randomization distribution alone, requiring no assumptions for the event-time distribution. We evaluate the proposed multiplicative interval via simulation, finding that it maintains nominal coverage across a range of censoring rates and sample sizes, including under data-generating processes that misspecify a parametric AFT model, while incurring only a modest efficiency loss compared to parametric AFT inference under correct specification. We illustrate the approach using data from a randomized trial of rhDNase for cystic fibrosis and provide R code and a Shiny application for ease of implementation.

Dataset alignment is a central step in data analysis across science and engineering, where the goal is to match observations between datasets. Entropic Optimal Transport (EOT) offers a computationally tractable framework for this task by encoding cross-dataset affinities in a transport plan. However, when two datasets are sampled from geometrically similar low-dimensional structures with substantially different sampling densities, the EOT plan may match points by relative sampling density rather than geometric proximity, yielding geometrically misleading correspondences. To address this issue, we propose a density-reweighted EOT framework in which the influence of sampling density on the transport plan can be discounted to a desired degree, ranging from standard EOT to alignment driven purely by underlying geometry. Under suitable regularity conditions, we establish convergence of the reweighted EOT plan to a family of population-level plans whose dependence on sampling density is made explicit. Through simulations, we show that our approach recovers geometrically faithful correspondences, improving over related EOT-based frameworks when datasets exhibit substantial sampling density disparity.

Bayesian optimal experimental design (BOED) aims to collect informative data by optimizing an expected utility reflecting the goals of an experiment. However, this optimization is computationally challenging for common utilities and complex models. This is especially so for sequential or adaptive designs, where design and data collection alternate, so that feedback from already observed data must be taken into account. Most existing BOED research employs information gain as the utility, leading to the expected information gain (EIG) criterion. While EIG is widely useful, it may not always adequately reflect experimental goals. EIG can be viewed as rewarding experiments that produce large positive evidence for the truth on average, but it does not directly control the risk of an experiment producing misleading evidence. Here we consider an alternative criterion, which we call bias against (BA), that prioritizes such control. To address computational challenges when applying this criterion for adaptive design, we consider a policy-based deep adaptive design framework, which has previously been used for the EIG criterion. Minimizing a tractable upper bound on the BA objective is equivalent to maximizing a variance-penalized EIG criterion, and we optimize the latter by approximating it by Monte Carlo and learning design policies using stochastic gradient methods. The differences between BA and EIG designs are demonstrated in several examples including the adaptive design of a complex discrete choice experiment.

Ornstein-Uhlenbeck processes with flexible multivariate drift matrices are powerful models for capturing coupled, asymmetric, and damped-oscillatory mean reversion. However, likelihood-based inference is challenging because the drift matrix must remain Hurwitz stable, while likelihood and gradient evaluations require repeated, costly computation and differentiation of the drift matrix exponential and of solutions to the associated Lyapunov equation. We introduce the Hurwitz smooth spectral block parametrization (H-SSBP), which represents the drift as a change of basis applied to independent one- and two-dimensional stable blocks. Simple scalar constraints enforce Hurwitz stability, while the two-dimensional blocks vary smoothly between real- and complex-eigenvalue regimes, avoiding discrete model selection. The H-SSBP represents every real Hurwitz matrix diagonalizable over the complex numbers and has dense, full-measure support within the Hurwitz cone. Its block structure reduces the OU transition matrix, stationary and innovation covariances, and their reverse-mode derivatives to constant-size block or block-pair computations plus change-of-basis multiplications. Numerical experiments demonstrate dramatic speed-ups over alternatives, particularly for matrix-exponential adjoints and Lyapunov-equation kernels. Real-data analyses of asynchronous financial data and multivariate phylogenetic traits illustrate the proposed framework in practice.