Papers

Missing data in social network studies routinely affects both node-level attributes and the network ties themselves. Standard multiple imputation software such as mice (van Buuren and Groothuis-Oudshoorn, 2011) handles the former well but has no notion of network structure, while dedicated network-imputation procedures typically treat tie imputation and attribute imputation as separate problems. This paper introduces netimpute, an R package that (a) computes a broad battery of node-level structural and attribute homophily measures across one or more networks, (b) can reduce these to a manageable set of principal component predictors while optionally preserving specific raw measures that are themselves part of substantive hypotheses, (c) provides a dyadic (cell-level) regression for network ties in the spirit of MR-QAP (Krackhardt, 1988), and (d) combines both into netmice(), a chained-equations routine that jointly imputes missing node attributes and missing network ties by cycling between them, using network-derived predictors for attributes and attribute-derived (and other-network-derived) predictors for ties. Network ties are updated tie-wise by default: a sequential Gibbs step redraws each missing tie one at a time, conditional on all previously imputed ties, refreshing the endogenous statistics (reciprocity, shared contacts) after every single draw via change statistics. The package additionally supports structural zeros, logical constraints between networks, social-relations-model random intercepts in the tie model, custom imputation models with interactions among any internally created terms, and network-aware per-target predictor selection (netquickpred()). We describe the package's design choices, the measures it computes for binary and non-negative weighted networks, and illustrate its use with a reproducible example

Aygün et al (2026, https://doi.org/10.1038/s41586-026-10658-6) claim that their AI-driven Empirical Research Assistance (ERA) system produces COVID-19 hospitalisation forecasts which outperform the state-of-the-art CDC ensemble by a considerable margin for the 2024/25 season. We demonstrate that the observed performance gain is attributable to information leakage in the retrospective forecasting setup, which resulted because data revisions were not taken into account. As similar mechanisms are at play in many other forecasting fields, our cautionary tale applies not just to epidemic forecasting, but is relevant to the entire emerging field of AI-assisted predictive modelling.

We provide limit theory for the trace of the squared sample correlation matrix $\mathbf R$, constructed from $n$ observations of a $p$-dimensional random vector with iid components. If the entries have finite fourth moment and $p$ and $n$ grow proportionally, it is known that $\operatorname{tr}({\mathbf R}^2)$ satisfies a central limit theorem (CLT) and the centering and scaling sequences are universal in the sense that they do not depend on the entry distribution. Under symmetry and regular variation assumption with index $\alpha$ and any growth rate of the dimension, we prove that the universal CLT remains valid for $\alpha >3$. For $\alpha<3$, we identify a critical dimension growth at which the fluctuations of $\operatorname{tr}({\mathbf R}^2)$ become non-Gaussian. Moreover, if the dimension $p$ grows faster and $\alpha\le 3$ we establish a non-universal CLT with norming sequences depending on the value of $\alpha$. Our findings are illustrated in a simulation study.

The one-sided microstructure noise model for high-frequency quotes from a limit order book is generalized to capture asset-specific noise tail behaviour. Estimation of a noise tail parameter becomes the key step for inference. This is possible based on moments of the high-frequency returns when specifying a parametric noise model. For a Gamma noise distribution, we establish a central limit theorem for 1-dependent observations from the resulting Gamma difference distribution and prove that it is valid also in the convolution model with general semimartingale log-price dynamics. We highlight that the noise tail parameter has important implications for estimating the efficient price and its volatility. An empirical analysis of recent NASDAQ limit order book data demonstrates that asset-specific noise tail parameters are relevant in practice.

We introduce a fuzzy network jump model for clustering time-varying observations indexed by the nodes of a weighted graph. The framework allows flexible graph representations with spatial and temporal regularization promoting smooth soft cluster assignments across connected nodes and consecutive time points. Estimation is performed through an efficient alternating optimization scheme that exploits the quadratic structure of the regularization terms. A simulation study covering different levels of spatial dependence and cluster overlap shows that the proposed method accurately recovers the true membership probabilities and outperforms competing clustering methods. An application to traffic-network data for the city of San Francisco identifies interpretable traffic regimes and reveals their evolution over time and across connected road segments.

Distinguishing True Progression (TP) from Pseudo-Progression (PsP) after chemoradiotherapy remains a major diagnostic challenge in GBM, as both entities present near-identical appearances on conventional contrast-enhanced post-treatment MRI. This distinction carries substantial clinical weight, since TP and PsP demand divergent management yet cannot be reliably separated on routine imaging alone. We investigated whether radiomic features derived from a parsimonious, voxel-wise pharmacokinetic model of dynamic contrast-enhanced (DCE) MRI, combined with MGMT status, could discriminate between the two. The cohort comprised 82 adults with IDH-wildtype GBM who developed a new contrast-enhancing lesion within six months of chemoradiotherapy; classification (53 TP, 29 PsP) was established by histopathology where available (n=52) and modified RANO criteria otherwise (n=30). At every voxel, contrast-concentration time courses were fitted to five candidate pharmacokinetic models, and the best fit was retained by AIC minimisation, yielding parsimonious Ktrans, Ve, Vp, and taui maps adapting to local heterogeneity rather than a single fixed model across the tumour. Following segmentation, 1,073 radiomic descriptors were extracted and reduced via Mann-Whitney U filtering and Elastic Net, then used to train five classifiers across four feature configurations. A Random Forest classifier combining parsimonious DCE-MRI radiomics with MGMT status achieved the best discrimination (mean AUC 0.89, sensitivity 0.93, specificity 0.76, F1 0.90), outperforming features without MGMT (0.84), a T1-post-contrast baseline (0.72), and a single-model extended-Tofts analysis (0.68). Shape and textural descriptors of the Ktrans map, with tumour volume, were the strongest predictors, MGMT contributing a smaller, independent effect. Allowing the model to vary voxel-wise improves non-invasive discrimination.

Base-rate neglect is usually treated as one mistake: giving the prior too little weight. But turning co-occurrences into a judgment means correcting for two base rates, not one – the prior (how common the outcome is) and the cue's own frequency. Under-correcting the prior is classical base-rate neglect; under-correcting the cue is the cue-density effect, long studied but not usually framed as base-rate neglect's cue-side analogue. We write both corrections as two weights in one Bayesian equation. Response format fixes which weight a study can measure: a graded rating carries the cue-frequency weight in full; a forced choice between two outcomes cancels it and measures a companion weight in odds space instead, the same correction as it acts on the posterior odds rather than on the judged magnitude. The cancellation is exact, so a same-cue choice carries no information about the cue-frequency weight, not even its direction; a choice between two cues rather than two outcomes keeps the term and identifies the weight, and differing cue frequencies is necessary and sufficient for a choice to see it. The same weight appears in six standard learning-and-memory models, some as an exact identity and some only as a limiting or constructed correspondence; when an experiment keeps only the four cells of a cue x outcome contingency table, every model family rich enough to fit them projects onto one scalar coordinate, which alone cannot separate the accounts free to sit anywhere along it. The two neglects should be separately identifiable: an experimenter can move the regressor driving one weight without moving the regressor driving the other – a two-coefficient separation a one-parameter account cannot produce. This paper lays out the framework and the rating experiment that tests the coefficient separation; a companion paper fits the two weights to an existing colour-flavour dataset.

Background: Deep brain stimulation of the subthalamic nucleus (STN-DBS) is an established PD treatment that improves motor symptoms and quality of life, but long-term survival and mortality risk remain poorly characterized. This study evaluated long-term survival and mortality-associated factors after STN-DBS. Methods: A retrospective survival analysis of 214 PD patients who underwent STN-DBS used Kaplan-Meier methods to estimate survival probabilities and median survival, with log-rank tests comparing survival by gender and age at implantation. Cox proportional hazards (Cox-PH) models identified mortality-associated factors in both univariate and multivariate analyses, and were validated using accelerated failure time (AFT) models. Results: Mortality rose progressively, with 8.0%, 42.5%, and 56.0% of patients dying within 5, 10, and 15 years, respectively; median survival was approximately 134 months. Survival did not differ by gender (p = 0.63) but was significantly lower for patients aged 60 years or older at implantation (p < 0.0001). At least one post-implantation revision reduced mortality risk (HR = 0.296, p < 0.001), while implantation at age 60 years or older increased it (HR = 4.689, p < 0.001); both remained significant after adjustment and were confirmed by AFT models. Patient satisfaction was high, with 97% of 52 surveyed patients reporting satisfaction and 96% would recommend STN-DBS. Conclusion: STN-DBS is linked to long-term survival and high patient satisfaction in individuals with PD. Older age at implantation increased mortality risk, whereas revision surgery and mortality likely reflect confounding by indication rather than a direct causal effect. These findings support age-stratified patient selection and highlight the importance of continued long-term monitoring following STN-DBS.

Bayesian model selection couples a discrete model indicator with a model-specific continuous parameter space. We introduce structured dimension-matched variational transdimensional inference (SM-VTI) for finite enumerable model spaces. A rooted construction graph expresses a model as a sequence of local stop/child decisions. Each typed edge compiles a declared scientific parent-child edit into an exact native-coordinate dimension-matching lifting; an edge-conditioned flow then learns the residual continuous transport. The resulting local policy and conditional flow define one direct joint variational distribution, without embedding every model in a saturated maximum-dimensional surrogate. We derive its exact path density and optimize the joint reverse-KL objective. On a controlled 15-model target, SM-VTI-Joint recovers terminal masses, local actions, and nonlinear conditional geometry. On a 128-model misspecified robust variable-selection problem, a 10-data-set nearly parameter-matched affine comparison with AVTI shows stronger early model-mass recovery and competitive final joint accuracy under the same target-evaluation budget.

Design-stage power and sample-size evaluation under biased-coin minimization can be computationally intensive when a prespecified randomization test is reproduced within every simulated trial. We develop a reusable stratum-imbalance Gaussian approximation (SIGA) framework by exactly decomposing a fixed-score statistic into joint-stratum imbalance and orthogonal within-stratum components. Under explicit allocation-copy limit conditions for the same absolute-imbalance rule, the sampling-calibrated procedure, SIGA-S, consistently estimates the repeated-sampling variance at a marginal mean- or risk-difference boundary. At a nonsharp boundary, the conditional variance of a fixed-score randomization test can differ because the score contains the observed allocation path. To characterize this distinction, we express the first-order variance gap as a quadratic form involving pair-path covariance and introduce the randomization-calibrated procedure, SIGA-R, based on a reusable paired allocation-only calibration to approximate the conditional reference distribution. Separate comprehensive benchmarks showed close agreement between each SIGA procedure and the corresponding reference randomization test. A trial-inspired simulation based on published aggregate planning characteristics likewise produced similar power for SIGA-S, SIGA-R and the reference randomization test, while both reusable calibration procedures substantially reduced computation relative to nested rerandomization.

Autonomous agents now carry out entire data analyses, selecting cohorts, joining tables, and fitting models with little step-by-step supervision. When such an analysis turns out to be wrong, someone must determine which operation caused it. A recent approach does this without any labelled mistakes, learning instead from analyses known to be sound and flagging operations that depart from what that model predicts; how reliable such audits are has not been studied. This paper supplies that analysis. The choice of score determines whether an error can be localized at all. If each operation is scored by how surprising it is given the operation immediately preceding it, then operations that merely inherit an earlier error are indistinguishable from correct ones, so one mistake produces one flag; scores computed against a longer reconstruction of the intended analysis instead spread a single mistake across many operations. We quantify how far they spread, and how to choose the comparison length when an error accumulates gradually rather than at once. We then give procedures that control the proportion of falsely flagged operations within a single audited analysis, requiring only that sound analyses be exchangeable rather than that the fitted model be correct, and we quantify how much the guarantees weaken when the model is imperfect or when the analysis was selected for review in a way that depends on its content. Finally we establish a limit on what any such audit can report: errors below a certain magnitude cannot be attributed at all, being indistinguishable from ordinary variation among sound analyses. This limit falls so slowly as more sound analyses are collected that at the representation sizes now in use a hundredfold increase reduces it by under two percent, so the dimension of the representation rather than the volume of training data is the binding constraint.

Knowledge distillation (KD) is widely used to transfer the capabilities of large language models (LLMs) to smaller students, but existing objectives often struggle to balance faithful imitation and robust generation. In particular, existing methods mainly combine FKL and RKL, overlooking that RKL itself provides a mechanism for adjusting the student's imitation strength. Motivated by this, we revisit on-policy Reverse Kullback-Leibler (RKL) distillation and decompose its objective into a teacher-fitting term and a student-entropy term, without introducing an explicit FKL branch. We show theoretically that the token-level optimal student distribution corresponds to a tempered variant of the teacher distribution, where the adaptive weight controls the trade-off between mode-seeking and uncertainty preservation. Guided by this insight, we propose Adaptive Entropy Distillation (AED), which uses the teacher's entropy to dynamically calibrate token-level imitation strength. Experiments on instruction-following and mathematical reasoning benchmarks demonstrate that AED achieves superior overall performance and generally improves teacher–student distributional and entropy alignment.

Real-world time series inherently intertwine global periodic structures with localized non-stationary variations. Existing approaches process these heterogeneous dynamics within a single computational domain, incurring fundamental limitations: time-domain models suffer from periodic misalignment over long horizons, while frequency-domain models over-smooth transient spikes. We argue that the optimal computational domain is not a property of the model, but of the data itself. Based on this principle, we propose RouteTS, a unified forecasting framework that partitions the frequency spectrum via amplitude routing and delegates components to their mathematically optimal domains. Dominant frequencies are processed by a complex-valued linear predictor in the frequency domain to preserve periodic structure, while residual spectral energy is reverted to the time domain and modeled by a lightweight MLP for local variations. Extensive experiments demonstrate that RouteTS achieves competitive prediction accuracy across diverse real-world datasets, with routing decisions guided by the underlying spectral signature. Furthermore, the lightweight design of RouteTS provides significant computational efficiency advantages, offering a principled solution to the longstanding dilemma between global periodicity and local transience.

Objective: Routine third-trimester examination yields fetal biometry, maternal, Doppler and fetal-cardiac measurements, acquired at clinical discretion and therefore often incomplete. We show that these four measurement blocks are close to mutually uninformative, and that this single property determines what a representation of them can impute, what it can audit, and what fetal size alone cannot indicate. Methods: A linear-Gaussian factor model (K = 8 by parallel analysis, VARIMAX-rotated) was fitted to 25 measurements in four blocks from 977 fetuses (169 SGA, 61 severe; 77 LGA). Posterior precision sums contributions from observed measurements only, so missing values are marginalized rather than imputed. Data quality was screened using the standardized residual between each measurement and its reconstruction. Results: Predicting any one block from the other three gives an out-of-fold R2 of 0.023. The representation is a continuous growth spectrum with no cluster structure (Hartigan dip p = 0.99, gap statistic k = 1, three-cluster silhouette 0.07) ordering fetuses by birthweight centile (Spearman rho = 0.55). Among 169 SGA fetuses the haemodynamic redistribution axis separated the 25 adverse outcomes (AUC 0.70, 0.585-0.808) where measured size did not (0.60, 0.451-0.738). With Doppler censored, the marginalized interval covered held-out measurements in 97% and 93% of cases against nominal 95% and 90%. The reconstruction residual flagged 38 of 977 records, 36 confirmed transcription errors in the registry. Conclusion: Marginalizing missing measurements yields a representation whose uncertainty reflects the available data, and whose reconstruction residual doubles as a data-quality screen. Because the blocks are nearly independent, confirmed flags are within-block errors, and a synthetic benchmark gives the coupling needed before cross-block detection becomes available.

Predicting fatigue failure in steel components experimentally is costly, requiring testing across multiple compositions and processing conditions, spurring research on data-driven prediction models. Studies using the NIMS MatNavi steel fatigue dataset often report high point-prediction accuracy but rely on aggregate error metrics, leaving uncertainty about the reliability of individual predictions and whether accuracy is consistent across the fatigue-strength spectrum. This paper is the first to apply conformal prediction to steel fatigue strength, comparing seven interval-construction methods across 50 independent data splits and distinguishing marginal coverage from coverage within specific sub-regions of the predicted property. A gradient-boosting point model achieves an R^2 of 0.976 +/- 0.009 and a mean absolute error of 18.3 +/- 2.3 MPa. Split-conformal prediction provides valid marginal coverage (0.918) but drops to 0.758 in the highest-strength quartile, where design margins are most critical, a pattern also observed with a Gaussian process baseline. Two locally-adaptive methods correct this: a cross-fitted normalised conformal method holds 0.872-0.940 across quartiles at no cost in average width, and Mondrian group-conditional conformal prediction holds the tightest band of any method (0.917-0.939) at a 12% width premium, part of which traces to the more conservative finite-sample quantile level implied by per-group calibration at this sample size. Conformalized quantile regression, by contrast, restores marginal validity but inflates intervals in every quartile without closing the conditional gap. Marginal coverage claims for ML-based fatigue-strength predictions can conceal systematic unreliability precisely where engineering decisions are most risky; therefore, conditional coverage should be routinely assessed alongside marginal coverage.

Multi-agent LLM systems route among model-backed advisors, yet a deployer rarely knows before shipping whether routing will help at all. Prevailing routers optimize a gate's AUC and presume that advisor complementarity suffices. We show that neither determines the deployable gain. We introduce RouteGuard, a deployment-certification framework. Routing gain decomposes as $G = \pi \Delta_E$, and the achievable gain is governed by a conditional-regret functional $\Phi$, not by AUC. A finite-sample certification bracket comes with a matching Le Cam lower bound, constant-sharp over the fixed-activity class, and a robustness phase transition. On two benchmarks the framework acts as a guardrail. On RouterBench (11 cross-family models) the verdict depends on the sampling unit: the protocol certifies a gain over GPT-4 under prompt-level sampling and withholds it under workload-cluster resampling, because the gain rests on 3 of 86 workload cells. On OpenRCA (three Gemini advisors) the advisors are statistically redundant: the realized oracle sits at or below the independence baseline in all pools we tested (221 RouterBench pools and three OpenRCA distributions), so the protocol correctly refuses to certify. A pre-registered semi-synthetic control confirms calibration: the protocol certifies a genuine gain once $m \ge m^\star$ and does not certify a true null. Code and frozen artifacts will be released with the published version.

Generative models can reproduce an observational distribution while encoding an incorrect causal structure. We study a sequential game in which a structural causal generator proposes observational and interventional distributions, while an adversarial experimentalist selects interventions intended to maximally falsify the generator. The discriminator is therefore not merely a real-versus-synthetic classifier: it is indexed by an intervention and tests whether the generator reproduces the corresponding post-intervention law. We introduce Adversarial Causal Intervention Falsification (ACIF), formulate oracle and implementable versions of the game, and distinguish three objects that are often conflated: observational fit, interventional equivalence over an admissible query class, and point identification of a structural causal model. For finite model and intervention classes, we prove: (i) an exact reduction of the adversarial objective to a worst-intervention integral probability metric; (ii) identification up to interventional equivalence, with point identification under a separating intervention family; (iii) existence of mixed-strategy equilibria; (iv) finite-sample uniform convergence and margin-based model-selection guarantees; and (v) a logarithmic elimination guarantee for a disagreement-driven sequential design under a balanced-separation condition. We also give a complete linear-Gaussian example in which two observationally indistinguishable causal directions are separated by a single well-chosen intervention. The framework clarifies what an adversarial causal discriminator can and cannot certify, and provides a principled bridge between causal generative modeling, active causal discovery, and experimental design.

E-scooters have emerged as an important micromobility mode for short urban trips, yet evidence on route choice behavior remains limited. This study examines e-scooter route choice in Washington, DC using GPS trajectory data and a Path Size Logit model. In addition to roadway and infrastructure characteristics, the model incorporates visual streetscape features extracted from Google Street View imagery using computer vision techniques. The results show that the effectiveness of cycling infrastructure depends strongly on roadway context. On major roads, only protected bicycle facilities significantly increase route attractiveness, whereas on minor roads both protected and designated lanes provide utility gains. Sidewalks constitute the most frequently used riding environment, yet only asphalt-paved sidewalks are associated with positive utility, suggesting that sidewalk riding may reflect the absence of attractive on-street alternatives rather than a preference for pedestrian infrastructure. Tree coverage, particularly during summer, as well as building and wall coverage, are positively associated with route choice. Likelihood ratio tests and value-of-distance analysis indicate that roadway infrastructure exerts a stronger influence on route choice than visual streetscape features, although the latter provide additional explanatory power. These findings support targeted infrastructure investment and the integration of streetscape improvements as a complementary strategy for enhancing micromobility route attractiveness.

Probabilistic prediction heads in neural networks typically output either a Gaussian mixture or a single conformal region. Neither separates the distinct sources of uncertainty often present in real prediction tasks: a discrete choice among modes, bounded systematic drift within the chosen mode, and irreducible stochastic noise. We introduce the Hybrid Probabilistic Zonotope (HProbZ), an output head that represents these three sources as binary, bounded, and stochastic generators of a zonotope, and admits a closed-form likelihood by convolution. Sharing the bounded generator across prediction steps couples future predictions algebraically, so observing one step refines the predictive distribution at every remaining step in a single forward pass. We establish that the three generators are identifiable from the likelihood up to permutation, and that an HProbZ density is representationally distinct from any finite Gaussian mixture. The same shared structure provides analytic per-mode risk and distribution-free multi-modal conformal sets at inference time. Empirical analysis on representative prediction benchmarks supports the effectiveness of the design relative to same-encoder mixture baselines, while offering structural properties that mixture or convex-conformal predictors do not jointly provide.

Understanding e-bike route choice is essential for developing effective cycling infrastructure, yet empirical evidence remains limited. This study investigates shared e-bike route choice in Washington, DC, using Global Positioning System (GPS) trajectory data from the Capital Bikeshare system. A Path Size Logit model is estimated using a hybrid choice set consisting of observed routes and corresponding shortest paths, integrating Geographic Information System (GIS)-based infrastructure variables with computer vision-derived street-level visual features extracted from Street View images (SVI). The results indicate that e-bike riders tend to choose routes that minimize conflicts with both motor vehicles and pedestrians while maintaining travel continuity. Roadway hierarchy substantially moderates the influence of bicycle facilities, with the presence of bicycle facilities having a much greater impact on route choice along major roads than along minor roads. Longer trips also exhibit stronger preferences for cycling infrastructure. Incorporating street-level visual features improves model performance, although their effects are generally smaller than those of road infrastructure, with trees being the only greenery component showing a consistently positive effect. Standardized effect sizes further identify the most behaviorally important route attributes. These findings provide practical evidence for cycling infrastructure planning in the e-bike era.

Sequential clinical decision-making often involves more than maximizing average efficacy. Clinicians may need to simultaneously optimize clinically relevant tails of the outcome distribution, control treatment-related risk, and choose among multiple treatment options. Existing quantile dynamic treatment regime (DTR) methods capture distributional features of treatment outcomes but remain largely restricted to efficacy-only objectives and binary treatments. To address these limitations, we propose Risk-Aware Quantile Dynamic Treatment Regimes (RQDTR), a unified framework that optimizes a prespecified quantile of the cumulative potential outcome while explicitly incorporating treatment-related risk. We also develop an angle-based formulation for jointly learning decision rules across multiple treatment categories. Our framework includes three interpretable subclasses: efficacy-only quantile learning, constraint-based learning with population-level risk control, and utility-based learning through a composite benefit-risk utility. Theoretically, we establish identification and oracle equivalence, Fisher consistency of the smoothed surrogate, consistency of the estimated regime, and finite-sample performance error rates. Extensive simulation studies and applications to All of Us major depressive disorder and MIMIC-III sepsis data demonstrate that RQDTR improves tail-oriented efficacy and achieves more favorable benefit-risk trade-offs than existing quantile DTR methods.

We study the independence between an order statistic and its corresponding rank indicator for independent nonnegative random variables. A general characterization is established through a probability measure obtained by reweighting the distribution of a single observation according to its conditional probability of occupying a prescribed rank. This framework yields explicit expressions for the associated weighting functions and conditional distributions, as well as distribution-free measures of departure from independence based on Kolmogorov and Wasserstein distances. Special attention is devoted to the minimum and maximum order statistics, leading to new characterizations of independent right- and left-censoring under both single and multiple censoring mechanisms. We also establish sufficient conditions based on proportional hazards and proportional reversed hazards models and derive complete characterizations in the classical single-censoring setting. Discrete and continuous examples, together with numerical illustrations, are presented to demonstrate the applicability of the proposed methodology.

Gradient-based Markov chain Monte Carlo methods are often introduced as a catalog of algorithms: Hamiltonian Monte Carlo (HMC), the Metropolis-adjusted Langevin algorithm (MALA), the No-U-Turn Sampler (NUTS), and several underdamped variants. This presentation obscures the common structure of the methods and, more importantly, the reasons why a sampler that is correct in principle may be ineffective in practice. We develop a unified account, beginning with exact continuous-time dynamics that represent idealized sampling methods and for which Metropolis adjustments are not required. Numerical discretization makes the dynamics computationally feasible but introduces bias. Metropolis adjustment removes the asymptotic bias by converting numerical errors into rejection, leading to HMC, MALA, NUTS, and the Metropolis-adjusted kinetic Langevin algorithm (MAKLA). The second half of the paper presents geometric design choices that determine practical performance, namely, although MAKLA and NUTS have nice theoretical properties, their sampling efficiency may be slow in practice. Importantly, a fixed mass matrix can whiten globally anisotropic targets, often fixing sampling inefficiency in Bayesian posteriors with large data. Whereas hierarchical posteriors introduce their own problem, causing state-dependent variation in the Hessian (e.g., Neal's funnel). We explain how a randomized step size can be used effectively to sample from such a distribution. The resulting paper is both a tutorial on the mechanics of gradient-based sampling and a set of practical recipes to improve sampler performance.

In this work we develop statistical methodology to estimate and perform inference on subgraph densities using time-indexed, or dynamic network sequences. These estimates explicitly adjust for observation errors for the network edges, and have good theoretical properties as the size of the network grows. By specifying a stochastically evolving hidden Markov network model, we address two important directions for further investigation identified by Chang et al. (2022): robustness to non-identical network replicates, and efficient aggregation of multiple available network snapshots. These new methods vastly expand the analysis of noisy networks to new data settings, as network replicates are commonly observed dynamically. The methodology is also extended to consider joint inference for subgraph densities at multiple time points, to facilitate formal statistical comparison of dynamic network snapshots.

The large volume of data and concerns about data privacy have motivated the development of techniques for distributed data, a problem also known as federated learning. In this scenario, sub-samples of the data are divided across different machines, and statistics must be computed over that data without direct access to the full sample. Johnstone & Lu (2009, JASA) show that principal component analysis (PCA) is statistically inconsistent in the high-dimensional regime, and propose a way to recover consistency through wavelet-based sparsification and variable selection. Fan et al. (2019, AoS) show a way to perform this same estimation – specifically, to estimate the eigenspace that would be obtained if all the data were pooled together, even though it remains effectively distributed – without addressing the high-dimensional regime. This work incorporates the wavelet-based sparsification of Johnstone & Lu (2009) into the distributed PCA framework of Fan et al. (2019), aiming to reduce communication cost without compromising the quality of the eigenspace estimation. Simulations across $d \in [52, 5000]$ show that the proposed method overtakes Fan et al. (2019) in estimation error beyond a clear dimensional threshold ($d \geq 152$ for $\lambda=25$, $d \geq 252$ for $\lambda=50$), while transmitting systematically fewer coefficients throughout the entire range studied. This study was financed by the Sao Paulo Research Foundation (FAPESP), Brazil. Process Number #2023/02538-0 and Number #2025/21250-2.

We present a statistical method to reconstruct the vertical thermohaline conditions in the Indian Sector of the Southern Ocean, where temperature and salinity profiles are partially sampled by female southern elephant seals. Datasets collected by biologgers provide unprecedented spatial and temporal coverage of ocean conditions. However, the maximum recorded depth varies with the animals' behaviour, offering only a partial view of the vertical environment. Using multivariate functional Principal Component Analysis (PCA), a parametric estimation of the covariance structure and mean function from a set of complete bivariate profiles allows the construction of an eigenfunction basis. By accounting for measurement error variance, partially sampled temperature and salinity profiles can be projected into the eigenspace of the complete profiles through conditional estimation of their functional principal coordinates and then reconstructed over the defined domain. For simulated snippet profiles truncated at depth $z_{\max} = 250$ m and reconstructed over $\mathcal{Z} = [20,500]$ m, reconstruction accuracy increases by 30 % for temperature and 33 % for salinity when incorporating geographical covariates. We then reconstruct ~90,000 incomplete profiles from the multivariate functional PCA of ~10,000 profiles reaching 500 m, covering approximately 3 million km$^2$ around the French subantarctic islands.

Generalized dissimilarity models (GDMs) have emerged as a valuable tool for formal statistical analysis of biodiversity. In particular, beta diversity, measured using dissimilarity measures, e.g., the Bray-Curtis dissimilarity in our case, provides a statistical summary of the difference in species composition between sites. It also provides novel data for spatial and spatio-temporal modeling as it resides over the product space of one space-time pair and a second space-time pair. In earlier work we developed the spatial generalized dissimilarity mixed model (spGDMM) to remedy some of the stochastic issues concerned with the foundational GDM in the literature. Here, we extend that work to include dynamics. We find much richer modeling opportunities as we consider beta diversity with regard to change in time as well as space. We illustrate with a dataset from the Cape Floristic Region (CFR) in South Africa.

Sequential hypothesis testing offers flexibility over fixed-sample designs, but stopping rules coupled to decision criteria risk confirmation bias through early peeking. The HDI+ROPE algorithm exemplifies this: it stops as soon as the posterior Highest Density Interval (HDI) falls entirely outside a Region of Practical Equivalence (ROPE) around the null (rejecting it) or entirely inside, which enables positive acceptance of the null, something Null Hypothesis Significance Testing cannot do. However, this coupling means a wide HDI can satisfy the criterion on early, unrepresentative samples, incurring a systematic false-positive cost. Fully decoupled methods, such as “Precision is the Goal” (PitG), eliminate this bias by halting only once a target HDI width $\omega$ is reached; yet, by divorcing the stopping rule from the decision criterion, PitG frequently yields inconclusive outcomes, particularly when the null hypothesis is true. We propose “Decisive Precision is the Goal” (DPitG), which requires both the precision target and a conclusive verdict to be satisfied simultaneously. In fair coin simulations ($\omega=0.08$, ROPE$=0.5\pm0.05$), DPitG reduces the PitG inconclusive rate from 62% to 2% at a median cost of only 5% more samples, with zero false positives; HDI+ROPE achieves comparable conclusiveness only at the cost of false positives. Across the $\omega$ range tested, DPitG conclusiveness remains above 97% while PitG's varies widely. We provide a closed-form planning formula $N\propto V/\omega^2$ (where $V$ is the observation variance), an online interactive calculator, and open-source code. Demonstrated on single-group binary data, the framework extends readily to continuous outcomes and two-group comparisons. DPitG's fully pre-specified stopping rule is compatible with pre-registration standards and is the method of choice whenever a reliable verdict is required.

Baseline covariate adjustment can enhance the efficiency of randomized trials by improving precision of treatment effect estimates. However, the precision gain depends on how strongly the baseline covariates are prognostic for the primary outcome. In randomized trials of infectious disease prevention interventions (e.g., vaccines or passively administered antibodies), an individual's exposure to the pathogen is a leading prognostic factor but is rarely measurable at baseline. Hence, conventional covariate adjustment offers limited precision gain in prevention trials. We propose adjusting for a negative control outcome (NCO) event time, which is causally unaffected by the intervention but shares overlapping exposure mechanisms with the primary outcome. We formalize assumptions under which adjustment for the NCO event time is valid, and show that right-censoring of the NCO event time further complicates adjustment. We derive the efficient influence function for the treatment-arm-specific survivor function of the primary outcome when both the primary outcome and the NCO event time are right-censored, and use it to construct a cross-fitted, one-step estimator that is multiply robust to nuisance misspecification and asymptotically efficient when the nuisances are estimated accurately. In numerical experiments, our estimator compares comparably to benchmarks when the NCO event time is uninformative, and gains precision as the NCO event time is more prognostic for the primary outcome. We apply our method to HVTN 704/HPTN 085, a randomized, double-blinded trial of VRC01, a broadly neutralizing antibody against HIV-1. Adjusting for the time to a bacterial sexually transmitted infection — a negative control outcome for HIV-1 acquisition — reduced the estimated variance of the prevention efficacy estimate by approximately 27%, compared to roughly 2.5% for baseline covariate adjustment.

Eighteenth-century Italian opera seria was dominated by soprano voices. Although masculine roles were typically performed by castrati and feminine roles by women, cross-casting was common, producing four soprano configurations in which performers of either sex could portray characters of either gender. We hypothesize that composers tailored their writing both to the singers premiering their arias and to the characters' gender. Using statistical models built on approximately 1,700 arias, we analyze relationships between vocal typology, characters' gender, and stylistic choices, comparing supervised learning methods and selecting ridge logistic regression as our primary model, whose performance is competitive with that of the best-performing alternative while allowing for interpretation and uncertainty quantification of its coefficients. Results reveal an asymmetry: character gender is consistently encoded in the writing, while the singer's sex is barely recoverable. Masculine-character arias feature large melodic leaps, intervallic variability, and wider ranges; feminine-character arias favor higher maximum pitches, minor intervals, and melodic stability. Female singers sang higher pitches than male sopranos, but this correlates more with character portrayal than with physiology.