Papers

Medical imaging provides rich information for predicting Alzheimer's disease progression, but existing imaging-based methods typically focus on a single survival endpoint and treat transition times as exactly observed or right-censored. Motivated by the Alzheimer's Disease Neuroimaging Initiative (ADNI), we develop a predictive framework that represents disease progression as an intermittently observed multistate process with interval-censored transition times and predicts future progression from any current disease state. We incorporate imaging biomarkers as functional covariates in a semiparametric proportional intensity model and combine functional principal component analysis with nonparametric maximum pseudo likelihood estimation. We further develop a profile score test for assessing the overall association between the imaging covariate and the multistate process. We establish the asymptotic properties of the proposed estimators and test statistic, and simulation studies demonstrate satisfactory finite-sample performance. In the ADNI application, baseline lateral ventricular morphology is strongly associated with Alzheimer's disease progression. The proposed functional multistate model also achieves the best overall predictive performance among the competing methods.

Latent space models represent network nodes as points in a geometric space, with connection probabilities determined by distances between latent positions under a fixed metric, typically Euclidean, spherical, or hyperbolic. We generalize the classical formulation by introducing nodal multiplicative effects motivated by a local deformation of the latent metric. This modification approximates a conformal deformation of the metric tensor while preserving the logistic predictor and the geometric interpretability of the model, thereby capturing additional structural heterogeneity without altering the global reference geometry. We study the generative behavior of the proposed model through simulation experiments and develop an optimization-based inference scheme derived from a hierarchical Bayesian formulation with parameter regularization. Applications to eight real networks show that the proposed approach increases the generative flexibility of classical latent space models and more accurately reproduces several topological properties observed in real networks.

Statistical inference on individual activity networks has been a historically difficult task due to the lack of available data at the appropriate granularity and the complexity of modeling individual mobility patterns. The recent availability of GPS data from individual devices, combined with highly detailed demographic information, suggests that one of these challenges can now be addressed. We introduce a new model which we call the Symmetric Matrix-Variate Normal Mixture Model (STRUCTURED) to estimate how demographic traits influence changes in human activity networks, using sociomatrices that capture the probabilistic spatial overlap between individuals over time. We exploit the commutativity constraint inherent in the symmetric matrix-variate normal distribution to parameterize the column precision matrix as a polynomial of the row precision matrix, reducing the effective parameter space by an order of magnitude. We develop two variants of STRUCTURED: STRUCTURED-FP, which estimates the full polynomial, and STRUCTURED-RJ, which uses reversible-jump MCMC to select a reduced-order parameterization. Simulation studies demonstrate that STRUCTURED-RJ outperforms existing methods in sparse-data regimes, whereas STRUCTURED-FP is preferred when sample sizes are large. We apply the model to GPS-derived sociomatrices of 293 individuals in King County, WA, finding that local crime environments and youth employment density are the dominant demographic factors explaining variation in weekly activity overlap patterns.

Studying consequences following baseline exposures has become increasingly important for advancing comparative effectiveness research using real-world data. This case study evaluates the impact of hospital-acquired conditions (HAC) during hospitalization for hip fracture on post-discharge recovery trajectories among older adults living with Alzheimer Disease and Related Dementia, a population particularly vulnerable to high post-hospital mortality. To appropriately account for truncation of recovery trajectory due to death and to explore heterogeneity in effect modification by patient demographics, we introduce a novel pseudo data-based robust (PD-Robust) analysis strategy, accompanied by an R package and detailed usage guidance to inform real data analysis. Grounded in an interpretable estimand via principal stratification under principal ignorability and a structural working model, PD-Robust accommodates truncation by death, provides model diagnosis and robustness check against assumption violation, and facilitates the characterization of patient profiles among the principal stratum. Applied to Medicare claims data, where better recovery is defined as more days at home (DAH) over six months post-discharge, PD-Robust reveals heterogeneity in HAC effects, with males under the age of 85 years as a high-risk subgroup experiencing up to 23 fewer DAH, comparing HAC to no HAC. This exceeds the 8-day threshold regarded as clinically meaningful difference in DAH due to any exposure. Moreover, simulation studies further demonstrate that PD-Robust achieves low estimation bias and accurate statistical inference, supporting its utility in real-world data applications.

Classical likelihood-ratio tests and $\Delta$AIC exacerbate the statistical significance crisis by scaling with sample size, often flagging negligible improvements as highly significant. While causal estimands like the average treatment effect (ATE) quantify practical magnitude, their reliance on the expectation operator ties them to the data's original coordinate scale. Furthermore, existing pseudo-$R^2$ metrics are inadequate: variance-based measures ignore higher-order distributional changes, and current formulations lack invariance to monotone transformations. We resolve these limitations by introducing Entropic Variance (EV) as a rigorous, scale-independent generalization of error variance in ordinary least squares. We define the population EV-based parameter, $\rho^2_V$, which projects unbounded cross-entropy onto a standardized $[0,1]$ scale, and establish that the EV-based $F_\text{V}$ statistic asymptotically follows an $F$-distribution. Building on these distributional properties, we propose two estimators: the empirical population $R^2_{\text{SV}}$ and the out-of-sample predictive $R^2_{\text{SVP}}$. Both are derived by exponentiating per-observation cross-entropy and incorporate a degrees-of-freedom correction for training optimism. Leveraging the $F_\text{V}$-distribution, we derive refined $p$-values and confidence intervals for $\rho^2_V$ without requiring intractable Fisher information matrices. Simulation studies and a Parkinson's disease microbiome application demonstrate the superiority of variable selection via these EV-$R^2$ metrics. Notably, evaluating the $R^2_{\text{SVP}}$ of a LASSO path via data-splitting reduced false discovery rates from 80% to 6% in simulations while fully preserving signal recall.

Hidden Markov models (HMMs) are widely used probabilistic models for discrete sequential data but can be limited when hidden dynamics are complex. Hidden quantum Markov models (HQMMs) generalize HMMs by replacing probability vectors with density matrices and stochastic transitions with quantum operations, enabling richer latent representations. However, existing HQMM learning methods have not consistently outperformed Expectation–Maximization (EM)-trained HMMs on data not generated by quantum processes, limiting their practical applicability. We introduce NS-RIS, Newton–Schulz Retraction-based Inference on the Stiefel manifold, a scalable algorithm for learning trace-preserving HQMMs. NS-RIS uses Newton–Schulz orthogonalization to compute a polar-factor search direction while preserving Stiefel-manifold feasibility, avoiding costly matrix decompositions. We further establish a finite-time stationarity guarantee under standard assumptions on smoothness, stochastic gradients, and finite Newton–Schulz accuracy. Empirically, NS-RIS provides the first benchmark evidence that an HQMM can significantly outperform an EM-trained HMM on data not generated by a quantum model. On synthetic HMM-generated benchmarks, NS-RIS outperforms both EM and the state-of-the-art HQMM method COSM, improving the evaluation metric by an average of 38.5% and by up to 50.6%. On a synthetic HQMM benchmark, it improves the test metric over COSM by 18.9% while reducing runtime by 12.0%. On the real-world Splice classification benchmark, NS-RIS also surpasses both EM and COSM in higher-dimensional latent regimes, reducing mean classification error by 17.9% for latent dimension 6 and 14.9% for latent dimension 8 relative to COSM. These results move HQMMs beyond a theoretical generalization of HMMs and establish them as practical and expressive models for scientific sequence data.

Random-projection tests for functional data depend on the probability law used to generate projection directions. A measure has to be selected to generate the random directions in which the data is projected. In $L^2$, probability measures defined by their moments can be discriminated using Gaussian measures. The covariance operator of the Gaussian projection law determines which regions and structures of the functional space receive appreciable probability, and consequently affects finite-sample power. We show that mixtures of non-degenerate Gaussian measures preserve the almost-sure separation property and induce a metric between functional probability laws. A concentration argument further makes explicit that the power of projection tests is governed by the integrated projected distance associated with the chosen law. As a concrete construction, we combine Haar and Fourier Gaussian components, which emphasize localized and oscillatory departures, respectively. The resulting permutation test retains consistency, while component labels and upper-tail separation scores provide a descriptive indication of the geometry of the detected discrepancy. Simulations illustrate the specialization of the two components and the robustness of their mixture, and an ECG5000 application identifies a predominantly localized difference between two classes. We also compare with a pooled functional principal component analysis covariance operator. This finite-rank, data-adaptive projection geometry preserves permutation validity through its label-invariant construction and improves power in several simulated settings, particularly under a change in covariance structure.

Multinational HIV cohort studies face regulatory barriers to cross-border sharing of individual participant data, limiting centralized pooled analyses. Federated statistical methods, which exchange only aggregated information, offer a privacy-preserving alternative but have rarely been examined in real-world distributed environments for HIV research. Here, we evaluate the feasibility and analytical performance of a communication-efficient federated framework within the Caribbean, Central, and South America Network for HIV epidemiology. Virologic failure and major regimen change after antiretroviral therapy initiation were analyzed as separate outcomes; for each, we estimated cumulative incidence functions (CIFs) and fit stratified cause-specific Cox proportional hazards models via a surrogate likelihood-based federated implementation. Each site imputed missing data, conducted local analysis, and shared only summary statistics according to a coordinated computation protocol. The federated approach exactly reproduced centralized CIFs and closely approximated centralized Cox regression estimates, outperforming conventional meta-analysis for both outcomes. These findings demonstrate that authentic federated analysis is feasible for multinational HIV research and can yield results closely aligned with centralized analysis while preserving data privacy. Post-hoc feedback from local analysts, however, indicated that broader adoption will require managing the logistical and coordination overhead and ensuring harmonized data collection and quality control across sites.

Latent trajectory analysis is a statistical method for explaining heterogeneity by partitioning patients into homogeneous subgroups based on similarities in outcome variables. In the context of clinical work, patients often do not follow the same course of illness or treatment response, and traditional analyses often average across patients, masking important subgroups. This work proposes a novel latent trajectory model for multivariate longitudinal outcomes with mixed types and uses the expectation-maximization algorithm as an estimation strategy. The proposed model can identify individual-level, time specific latent class memberships and a latent trajectory membership that describes how the latent class memberships change over time. By capturing these dynamic changes, we can highlight patients at higher risk of poor outcomes, reveal early indicators of improvement or decline, and ultimately support more individualized treatment planning. We present an application of our methodology to the Alzheimer's Disease Neuroimaging Initiative (ADNI), a longitudinal, multi-center, observational study to validate biomarkers for Alzheimer disease (AD) clinical trials.

Randomized experiments are often run in one population to guide decisions in another. Allocating by experimental proportions wastes budget on groups that rarely appear in deployment, whereas allocating by deployment proportions under-samples groups that are hard to measure precisely. We propose TWNA (Target-Weighted Neyman Allocation), a two-stage stratified design that uses pilot estimates of group–arm outcome variances to allocate final-stage sample sizes and treatment probabilities for target-weighted group average treatment effect (GATE) precision. The oracle rule has a closed form and balances deployment importance with statistical difficulty; the plug-in rule recovers it as pilot variance estimates stabilize. We also extend TWNA to handle uncertainty about deployment composition, remaining robust whether the target mix is roughly known or entirely unknown. Finally, we distinguish this weight robustness from a pilot-robust variant for skewed, rare-event, or contaminated outcomes. Simulations and real-covariate benchmarks show the largest gains when groups are both deployment-important and difficult to measure.

Latent subgroup analysis is central to fields such as genomics, precision medicine, and social science, where the goal is to identify heterogeneous populations with distinct covariate structures or response behaviors. Mixture models provide a natural probabilistic framework for this task, representing the data-generating distribution as a weighted combination of subgroup-specific laws with unobserved labels. In high-dimensional regimes, these analyses face significant challenges. Often, only a small subset of covariates drives meaningful subgroup separation; the remaining variables may introduce noise or redundancy. Standard clustering methods typically treat all dimensions as equal, but in high-dimensional spaces, irrelevant coordinates can distort distances and obscure the low-dimensional structures defining latent classes. This paper introduces a Bayesian distilled clustering framework for high-dimensional mixture models. We propose that clustering should occur within a statistically justified subspace rather than the full ambient space. Our method utilizes a Bayesian variable selection model to estimate posterior inclusion probabilities, quantifying the evidence that each covariate contributes to subgroup separation or response behavior. A "distilled" covariate set is then identified by controlling the expected false-discovery proportion. Clustering is performed on this reduced subspace, followed by conditional independence diagnostics to examine subgroup-specific dependencies among selected variables. Critically, this framework is model-based: the distillation step is tied directly to the mixture structure and response model rather than a generic dimension-reduction criterion. This ensures the resulting subspace remains aligned with the scientific objective: identifying latent subgroups that differ in both distributional structure and behavior.

The autocorrelation function (ACF) and partial autocorrelation function (PACF) are foundational tools for identifying autoregressive moving-average (ARMA) models, yet they are often introduced in ways that appear disconnected from the regression concepts students already know. This paper develops a unified, regression-based instructional framework for the ACF, PACF, Durbin–Levinson recursion, and one-step-ahead prediction for weakly stationary time series. We show that the ACF is the coefficient from a simple linear regression of a mean-zero stationary process on one of its lagged values, while the PACF is both the coefficient of the newest predictor in an expanding multiple regression and the corresponding partial correlation. Using partial regression, we derive the Durbin-Levinson updates for the newly added coefficient, the existing regression coefficients, and the prediction-error variance from familiar ordinary least-squares principles. Worked MA(1) and AR(1) examples show how the characteristic cutoff and tailing-off patterns of the ACF and PACF emerge naturally from this regression perspective. The same recursive regression coefficients also determine the optimal linear one-step-ahead predictor. The resulting framework provides a coherent instructional pathway from regression to model identification, recursive estimation, and prediction and suggests practical ways to connect introductory regression and time series courses.

We propose a new unit of analysis for longitudinal data: the Latent Memory Table. The scientific contribution is not the encoder. It is that table, treated as a reusable statistical object on the same footing as a matrix of principal-component scores, a table of estimated random effects, or a table of predicted probabilities. We estimate a statistical table that summarizes recent longitudinal history and is intended to be stored, queried, analysed and reused throughout the statistical workflow. A memory operator maps each masked windowed history to a finite-dimensional state; collecting those states with uncertainty yields the Latent Memory Table. Validation is organized around six properties—recoverability, personalization, temporal coherence, interpretability, stability and reusability—summarized by a composite quality index \(Q\); the Transformer, the SoccerMon case study and the simulations exist to argue that this table deserves that status. Classical exponentially weighted moving averages and related short- and long-horizon scalar summaries arise as restricted, typically univariate special cases of the same operator class. A simulation study with known memory mechanisms shows that \(Q\) and rotation-invariant recovery scores discriminate genuine multivariate or personalized memory from negative controls and from misspecified windows, whereas regime classification accuracy alone does not. SoccerMon serves as an empirical case study: a constructed Latent Memory Table attains \(Q\approx 0.73\) versus about \(0.40\) for classical and lagged principal-component baselines, with incremental held-out value for some wellness targets and Procrustes ensembles for row-wise reliability.

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

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.

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.

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.

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.

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.

We developed a unified covariate-adjusted causal inference framework for estimating the desirability of outcome ranking (DOOR) probability for benefit-risk evaluation in randomized trials and observational studies. The framework expresses the DOOR probability as a bilinear functional of the marginal ordinal outcome distributions under the two treatment strategies, estimates conditional ordinal distributions through sequential risk-set hazards, and derives the efficient influence function (EIF) of the DOOR probability. The point-estimation simulations compared G-computation, normalized inverse probability weighting (IPW), augmented IPW (AIPW), and targeted maximum likelihood estimation (TMLE), with nuisance functions estimated using generalized linear models or Super Learner (SL). TMLE-SL showed the strongest and most consistent point-estimation performance, with AIPW-SL ranking second. EIF-based inference was then evaluated for AIPW-SL and TMLE-SL, with and without cross-fitting, across settings varying in overlap, treatment-effect heterogeneity, and treatment allocation. CVTMLE-SL showed the strongest overall performance across DOOR-scale bias, recovery of the underlying ordinal distributions, standard-error accuracy, and confidence-interval coverage. We illustrate the methodology using data from the multidrug-resistant organism network of the Antibacterial Resistance Leadership Group.

Micro-randomized trials (MRTs) provide a framework for evaluating the marginal and moderated effects of mobile health (mHealth) interventions. In many applications, treatments take the form of categorical variables with multiple levels, such as different message contents or delivery strategies. Many scientifically meaningful longitudinal outcomes in mHealth studies are binary, such as whether a participant opens an app, engages with content, or completes a target behavior following a decision point at which treatment is randomized. This paper focuses on MRTs with categorical treatments and binary proximal outcomes. We define the causal excursion effect, propose an estimator called EMEE-catA, and derive a sample size formula for comparing categorical treatment levels that controls the type I error rate and guarantees power under working assumptions. We conduct extensive simulation studies to evaluate the operating characteristics of the proposed sample size formula, including robustness to violations of these assumptions. We further provide practical guidance for implementing the proposed approach to ensure adequate power in real-world MRTs. The methods are illustrated using data from the Drink Less MRT.