Papers

Data assimilation estimates a dynamical state from partial and noisy observations. Classical ensemble filters are efficient but restrict analysis updates through finite sample covariance and affine Gaussian distribution. We introduce the Flow Ensemble Filter (FlowEF), which uses conditional flow matching to transport the forecast ensemble from a classical baseline filter to an analysis ensemble. FlowEF uses a localized Gaussian source during training, transports forecast ensemble members from a baseline filter at deployment, and conditions its velocity field on ensembles from that baseline filter and the observation. The proposed model therefore learns a nonlinear update while mapping each baseline ensemble independently. For sparsely observed dynamical systems, FlowEF improves both deterministic and probabilistic metrics over all four classical ensemble filters. It also achieves the best performance among the state-of-the-art generative data assimilation models.

Bayesian Federated Inference (BFI) estimates statistical models from multicenter data when individual-level observations cannot be combined across centers. We present \pkg{BFI}, an \proglang{R} package that implements this methodology for Gaussian, binomial logistic, and survival regression models. Each center performs a Bayesian maximum a posteriori analysis and sends only parameter estimates and curvature information to a central server, where these summaries are combined to approximate the analysis of the combined data. The package supports prior specification, structured forms of between-center heterogeneity, several parametric and flexible baseline-hazard models for survival analysis, and treatment-effect estimation for observational and randomized studies. We describe the software design and the information exchanged between centers, give reproducible workflows for these analyses, and compare the federated results with pooled-data analyses for Gaussian, logistic, and survival models.

When computer codes model complex physical systems, calibration alone is insufficient; one must also assess whether a discrepancy term is needed. In this paper, we study computer code validation through a Bayesian mixture approach that compares a pure-code model with a discrepancy-corrected model. The method relies on the posterior distribution of a mixture weight, which measures the relative support of the two competing distributions. Under the assumption that the code is linear in the calibration parameters, or can be well approximated by a linear surrogate, we show that mixture component-shared parameters can be used to combine flexible modeling, even when noninformative priors are assigned to some common parameters. Inference is performed using a Metropolis-within-Gibbs algorithm. In addition, we introduce a thresholded allocation rule that complements the global mixture weight by providing a local diagnostic of where the discrepancy-corrected component is truly needed along the input domain. Beyond global model comparison, the proposed approach is also able to perform local model discrimination by identifying where the discrepancy-corrected component is truly needed along the input domain.

We develop a model-agnostic framework for noise reduction in high-dimensional time series that explicitly targets optimal recovery of a low-dimensional latent dynamic component contaminated by observational white noise. Under the assumption that the latent dynamics live in a low-dimensional linear dynamic subspace, we characterize the optimal linear projection onto the dynamic subspace and provide a geometric description of the residual error in terms of the relative orientation of the signal and noise spaces. We propose estimators for the dynamic subspace and the optimal projection based on lagged covariance matrices, bootstrap dimension selection, and a low-rank representation of the structured noise. Under mild conditions, the resulting denoised series is shown to converge to its population target at the usual parametric rate. Simulations show that the proposed method can substantially improve subspace estimation, reconstruction error, and one-step-ahead forecast accuracy compared with both orthogonal projection-based denoising and the raw data. The approach is illustrated by empirical applications to high-dimensional stock returns and to a 20-variate time series of macroeconomic indicators.

In observational time series, statistical inference for dynamic causal effects of a one-time intervention across horizons is complicated by high-dimensional observed pre-treatment information, unmeasured confounding, and serial dependence. To address these challenges, we develop a semiparametric framework for inference from a single serially dependent time series, integrating debiased machine learning with instrumental variables through buffered block cross-fitting. Under geometric beta-mixing, we derive non-asymptotic bounds on estimation error, asymptotic normality at each fixed horizon, and feasible inference that accommodates serial dependence. We further show how learner-specific prediction guarantees under temporal dependence can be used to verify the nuisance-rate conditions required for orthogonal inference. In a monetary-policy application with 468 months and 1464 lagged FRED-MD controls, we show an instrumented policy tightening lowers housing starts at medium horizons, with sensitivity analyses that support the finding.

Biometrical sciences and disease diagnosis in particular, are often concerned with the analysis of associations for cross-classified data, for which distance association models give us a graphical interpretation for non-sparse matrices with a low number of categories. In this framework, usually binary exploratory and response variables are present, with analysis based on individual profiles being of great interest. For saturated models, we show the usual linear relationship for log-linear models is preserved in full dimension for the distance association parameterization. This enables a two-step procedure to facilitate the analysis and the interpretation of associations in terms of unfolding after the overall and main effects are removed. The proposed procedure can deal with cross-classified data for profiles by binary variables, and it is easy to implement using traditional statistical software. For disease diagnosis, the problems of a degenerate solution in the unfolding representation, and that of determining significant differences between the profile locations are addressed. A hypothesis test of independence based on odds ratio is considered. Furthermore, a procedure is proposed to determine the causes of the significance of the test, avoiding the problem of error propagation. The equivalence between a test for equality of odds ratio pairs and the test for equality of location for two profiles in the unfolding representation in the disease diagnosis is shown. The results have been applied to a real example on the diagnosis of coronary disease, relating the odds ratios with performance parameters of the diagnostic test.

We study sequential testing of a fixed family of hypotheses when observations are costly and a sampling horizon is specified in advance. The challenge is to pool evidence for earlier decisions when the number and identities of false hypotheses are unknown, while controlling the probability of any false rejection at level $\alpha$. Existing merges attain the pooled growth rate at a single number of false hypotheses: averaging when one is false, multiplying when all are. Under an independent-stream model with common simple null and alternative distributions, we test each intersection with a prior-weighted mixture of products of marginal likelihood ratios. Closed testing combines these elementary-symmetric-polynomial mixtures to identify individual false hypotheses. Design-specific boundary calibration gives finite-horizon family-wise error control, with exact finite-state guarantees or a confidence qualification for Monte Carlo calibration. The prior-matched mixture uniquely maximizes expected log evidence at each horizon. Mixtures assigning positive weight to every nonempty subset of streams attain log-growth rate $lD$ when $l$ streams follow the alternative. Here $D$ is the mean log likelihood ratio per alternative observation, and a round supplies one observation per stream. This rate attains the first-order intersection-delay lower bound as $\alpha\downarrow0$ at fixed dimension, configuration, weights, and a long enough horizon. Power for an individual hypothesis cannot exceed the best single-stream power at a given deadline, but closure removes the multiplicity penalty when all are false. Gaussian, basket-trial, language-model and advertising studies illustrate both. The primary basket boundaries are 40-52% below $1/\alpha$. Across 41 simulated configurations, the median reduction in capped mean patient outcomes relative to prespecified interim-look Bonferroni tests is 31%.

We consider $K$-dimensional Bayesian vector autoregressions (BVARs) with Cholesky stochastic volatility (SV), in which the innovation covariance matrix is a lower-triangular linear transform of $K$ independent univariate SV processes. Such models are widely used in empirical macroeconomics to capture time-varying uncertainty and improve forecast accuracy, but the cost of posterior simulation is the binding constraint on the size of the system, and a major bottleneck for empirical work. We introduce a Markov chain Monte Carlo (MCMC) kernel that mixes better than existing samplers at the same computational complexity. It rests on a reparametrisation that makes the $K$ volatility trajectories conditionally independent, and on Particle Gibbs to update each trajectory. The kernel targets the exact posterior, rather than an approximation of it, and in an application with $K = 15$ it raises the mean effective sample size per second, relative to the benchmark corrected triangular algorithm, by a factor of approximately $14$ for the VAR coefficients and $3.4$ for the volatilities. We also introduce a a Sequential Monte Carlo squared (\smcsq{}) sampler, which used our MCMC kernel as a building block, and which delivers at every $t$ the one-step-ahead predictive density and the marginal likelihood of the data up to $t$, and hence on-line forecasting and model choice. To our knowledge, this is the first algorithm that delivers sequential marginal likelihoods for Cholesky-SV BVARs with static contemporaneous coefficients and a non-conjugate prior. We illustrate both on US monthly macroeconomic data, with $K=15$ for posterior inference and $K=6$ for the sequential sampler and model choice.

Information systems (IS) researchers increasingly use quasi-experimental methods such as difference-in-differences (DiD) and instrumental variables (IV) to recover causal effects from observational panel data. Power calculations that justify these designs assume i.i.d. errors, but the deeper problem is what even a cluster-robust calculator cannot see. We report a Monte Carlo study over 9837 parameter conditions (approx 9.8 million datasets) and decompose the planned-versus-achieved power gap. The serial-correlation component is recoverable by an AR(1)-aware calculator when rho is known, and partially when rho must be estimated from short pre-periods, but panel attrition, staggered-adoption bias, and parallel-trends pretesting are captured by no closed-form formula; exogenous attrition alone costs approx 8 to 11 percentage points at the few-hundred-to-thousand sample sizes IS studies use. Treatment-correlated, outcome-dependent attrition instead induces bias, not just power loss. For IV, holding first-stage F fixed, larger N neither raises power nor curbs exclusion bias, though with a fixed instrument more data does sharpen the first stage, so identification rests on instrument strength, not sample size.

We study causal discovery where each node is a random function. Previous studies on this topic rely on structural assumptions, e.g., linearity or non-linearity, and distributional assumptions, e.g., Gaussianity or non-Gaussianity. In contrast, we make use of covariance operators to avoid these assumptions. Under functional additive noise models, we propose a new sufficient condition to identify a valid topological ordering based on comparing norms of conditional covariance operators. Taking advantage of this identifiability condition, we develop a new mixed regression model that subsumes linear and non-linear models. Together with variable selection, our procedure yields an estimation of the causal directed acyclic graph (DAG) for functional variables. In theory, we develop the least-squares-type theory of this regression model, and derive asymptotic consistency of order determination, sparse regression, as well as identifying the DAG. Computational algorithms based on discrete observations are provided. Applied to simulated data, our approach performs satisfactorily among existing approaches. A real data example of brain effective connectivity is also presented.

We develop a general framework for model specification testing in stationary functional time series. The approach is based on an autoregressive approximation that represents a broad class of stationary functional processes through coefficient kernels whose dimension and autoregressive order may increase with the sample size. Different model assumptions induce different structural restrictions on these kernels, and our tests are constructed by measuring deviations from the corresponding restrictions. We illustrate this principle for three problems: testing a prescribed order of a functional autoregressive model, testing a functional autoregressive moving-average specification, and testing separability of autoregressive coefficient kernels. The resulting statistics are based on weighted $\mathcal{L}^2$-distances, and the critical values are obtained by a multiplier bootstrap. We establish a quantitative bootstrap approximation that is uniform over a class of weight functions and prove asymptotic validity and consistency of the proposed tests. The methodology allows for data-adaptive weighting and is illustrated by simulations and a data example.

We study distribution-free sequential changepoint detection for independent observations with unknown and unrestricted pre- and post-change laws. We build on the conformal test martingales and associated e-detectors of Vovk(2021), which control the probability of false alarm (PFA) and the average run length (ARL) respectively. The majority of these works focus on validity, with statistical efficiency usually left for simulations. We develop a comprehensive theory of how conformal p-values behave under non-exchangeable data with a changepoint at an unknown time $T$. We use this to analyze the post-change growth and resulting detection delay of conformal martingale methods, and prove that the standard existing methods are suboptimal for PFA and ARL control, and can lead to delays that are $\Omega(T)$ and $\Omega(\sqrt{\text{ARL}})$ respectively. We propose different conformal e-processes and e-detectors that are provably minimax optimal, with delays $\Theta(\log T)$ and $\Theta(\log \text{ARL})$ respectively, and have much shorter delays in simulations.

Bayesian calibration of functional-output computer models typically relies on dimension reduction techniques, such as functional principal component analysis, which assume that differences among simulator realizations arise only from amplitude variation. When simulator output also exhibits phase variation such as shifts in the timing or location of key features, this assumption is violated. Recent work has addressed this issue through elastic calibration, which aligns functional computer model realizations with observed experimental data prior to dimension reduction. Separately, multi-fidelity methods reduce the cost of calibration by supplementing a small number of expensive high-fidelity simulator runs with a larger ensemble of cheap low-fidelity runs. This is typically done through either a mapping strategy, which corrects low-fidelity predictions toward high-fidelity output, or a fusion strategy, which builds a shared basis across both fidelities. This paper combines these two lines of work, introducing elastic multi-fidelity Bayesian model calibration, which aligns high- and low-fidelity functional output to a common reference before applying multi-fidelity mapping or fusion. On a synthetic two-dimensional calibration problem and a dynamic material properties equation-of-state problem, both elastic multi-fidelity strategies match or improve on the leave-one-out predictive accuracy of a mono-fidelity elastic emulator, with the fusion approach achieving the lowest error. Both strategies also produce tighter calibrated posteriors than the mono-fidelity baseline, with the fusion approach providing the best coverage and parameter estimates closest to the true values.

Density-valued time series are common in practice. However, since these functions are non-negative and must integrate to one, they do not form a linear vector space, which complicates the direct application of standard time-series methods. To address these constraints, we introduce two transformations, based on the centered log-ratio transformation and the cumulative distribution function, for modeling and forecasting balanced panel data represented by multiple densities. Both transformations map densities bijectively into an unconstrained function space in which cross-sectional and serial dependence can be modeled directly. Within the resulting unconstrained space, we consider two approaches: multi-population functional time-series modeling to account for correlations among populations, and gap modeling between gender and region. Using Japanese subnational age-specific life-table death counts from 1973 to 2024, we evaluate and compare the one- to 20-step-ahead point and interval forecast accuracy of the two approaches for each transformation, and offer some general recommendations.

Large language models (LLMs) can give reliable labels under one setup yet change those labels when researchers make other reasonable design choices. We tested seven LLMs, 12 task designs, three independent runs, and 3,000 tweets labeled for offensive language and hate speech. Repeating the same model and task design produced high agreement (median Fleiss' $\kappa = 0.91$). Agreement fell when we changed the task design for the same tweets (median Cohen's $\kappa = 0.76$). Task design and model choice increased the variance of estimated prevalence by factors of 76.7 for offensive language and 110.6 for hate speech compared with sampling variance alone. Variation across LLM task designs reached 560-572 basis points, compared with 270-331 basis points across five human instrument versions. Confidence scores did not solve this problem. They tracked repeated model outputs more closely than agreement with human labels, and grouping six tweets in one prompt lowered mean offensive-language confidence by 660 basis points. We call the variation caused by task design and model choice instrument uncertainty. Researchers can measure it only by comparing reasonable task designs. Repeating one setup or relying on confidence scores cannot replace that test.

Data observed over space and time can exhibit dependence across both dimensions, and datasets can grow very large in both the number of locations and the number of time periods. This dependence and data size mean that many statistical models cannot be fit at a reasonable computational cost as a result of dense matrix inversions, large parameter spaces, or memory and storage challenges. When the data are ordinal, this only adds to the computational complexity of model fitting. Many ordinal models rely on a latent continuous variable designed to capture dependence in a computationally efficient manner, and then partitioned according to cutoff parameters to yield the observed ordinal response data. A very common choice is a latent Gaussian distribution, which can accommodate different dependence structures and permits Gibbs sampling in a Bayesian framework. Unfortunately, this model can be overly restrictive and fails to provide the flexibility needed to capture a range of ordinal outcomes. In this paper, we demonstrate the use of Bayesian nonparametric (BNP) methods to enhance the model flexibility of a Gaussian latent model for ordinal drought data observed over space and time, with Dirichlet process priors inducing clustering among time periods within each spatial location. In this work, we model ordinal drought data separately at each spatial location while accounting for temporal dependence, but we do not model spatial dependence across locations. We show that these BNP models often outperform Bayesian parametric approaches at a reasonable computational cost.

We propose a Bayesian framework for uncertainty quantification from the perspective that the working model is mis-specified in settings of a multilevel data-generating process. We focus on settings in which the mis-specification fails to match the functional form of the mean structure, and discuss Bayesian estimation of target parameters under dependence induced by a mismatch between working and data-generating models. The proposal represents a Bayesian semi-parametric procedure aimed at estimating population-level parameters while accounting for cluster- and unit-level variation in the estimating function. The proposal extends the regular Bayesian bootstrap to account for cluster- and unit-level variation using multilevel weights from an enriched Dirichlet model. Simulation studies indicate that the proposed approach has good frequentist properties when the data-generating process and the proposed model induce a partially exchangeable sequence associated with the unknown quantity of interest. Applications to radon (Gelman and Hill, 2007), Programme for International Student Assessment 2022 (OECD, 2023), and tuberculosis (Nobre et al., 2023) datasets are presented for illustrative purposes. The results demonstrate that the proposed method is competitive with variations of multilevel models, with major differences observed in the range of credible intervals, which are justified by the nonparametric assumptions underlying the proposed method.

In causal mediation analysis, natural direct and indirect effects are defined through nested counterfactuals that combine the outcome under one exposure level with the mediator value under another and are therefore inherently cross-world. Their canonical identification additionally relies on cross-world independence assumptions. Consequently, both the estimands and their identifying assumptions remain controversial. In this paper, we ask what additional single-world structure would be required to re-express cross-world estimands as single-world quantities, identifiable under single-world assumptions. We show that these quantities can be written as mixtures of controlled single-world effects under assumptions involving a susceptibility marker, a possibly latent baseline variable that encodes the "would-be" mediator value under a reference treatment arm. If observed, the marker would make several implications of the marker restrictions empirically testable. These results provide a transparent single-world formulation of cross-world mediation effects while making explicit the assumptions required. Although these conditions clarify how cross-world estimands can be interpreted within a single-world framework, their practical relevance depends on whether such susceptibility markers can be justified in specific applications. We discuss implications for principal stratification and show in the Supplementary Material how the formulation extends to ordered mediators and settings with exposure-induced mediator-outcome confounding.

We study prediction in new environments when training data contain rare, large shifts. Anchor regression penalizes the average of the squared mean residual across environments. It protects against shifts in an ellipsoid determined by the second moment of the training shifts. Covering rare shifts may therefore require a large penalty, expanding the ellipsoid in every direction and reducing accuracy on common environments. We propose CVaR anchor regression, which replaces the average of the squared mean residuals with a tail average. Unlike CVaR or GroupDRO applied directly to prediction risks, it does not give environments more weight solely because their noise levels are high. We prove an exact worst-case risk guarantee under a linear structural model that allows for heteroscedastic noise. For discrete environments, decreasing the CVaR tail fraction expands the robustness set from an ellipsoid to a scaled convex hull of the training shifts and their negatives. A separate parameter controls its scale. Examples show how the method can improve protection against rare shifts while retaining accuracy on common environments. We illustrate the method on New York City taxi data.

We introduce Rolling Conformal Prediction (rolling-CP), a distribution-free predictive inference method for the setting of sequential model training. Specifically, given a data stream $(X_1,Y_1),(X_2,Y_2),\dots$, at each time $n$ the trained model may depend on the observed history $\{(X_i,Y_i)\}_{i<n}$. This setting arises naturally in modern sequential training, including one-pass training over massive datasets and continual fine-tuning or test-time adaptation of language models during deployment. Rolling-CP first calibrates each incoming observation against the current predictor and then rolls it into future training. In this way, we avoid the need for data splitting. Remarkably, although the models at times $n=1,2,\dots$ may have entirely different properties and accuracy levels, for exchangeable data it is nonetheless possible to establish a guarantee of marginal coverage, with a familiar universal factor-two guarantee (a worst case guarantee of $1-2\alpha$ coverage, as compared to the target level $1-\alpha$), without any assumptions of stability or any restrictions on the model training process. For i.i.d. data streams, we further prove high-probability training-conditional validity uniformly over time; under stability conditions, coverage guarantees sharpen towards $1-\alpha$. Numerical experiments on sequential regression, multiclass SGD, and one-pass neural-network training further demonstrate the practical effectiveness of rolling-CP.

This article is motivated by an imaging application from the Adolescent Brain Cognitive Development (ABCD) study, aiming to predict task-based brain activation maps from t-fMRI using cortical metrics from structural MRI (s-MRI) and brain connectivity data from resting-state fMRI (rs-fMRI). Hierarchical Bayesian modeling is well-suited for integrating diverse imaging data and quantifying prediction uncertainty. However, progress in this field is limited due to challenges in designing joint priors that capture the structures and interconnections between different imaging modalities, along with computational complexity and lack of theoretical assurances. To address these challenges, the article introduces a novel regression framework that treats t-fMRI and s-MRI images as functional data, incorporating additive non-linear effects of both network and functional predictors on the functional response. Specifically, we employ Gaussian process (GP) priors on coefficients related to the functional predictors to capture their intricate functional dependencies with the response. Furthermore, a GP prior is assigned to encapsulate the non-linear nodal effects of the network predictor on the response function. The method is supported by theoretical results on predictive accuracy for the functional response, and is empirically validated through simulation studies and analysis of multi-modal neuroimaging data from the ABCD study.

We consider simultaneously testing hypotheses about thousands of units, e.g., genes or proteins, where each unit yields a handful of replicate measurements and we test whether its mean is zero. A widely used approach in genomics, implemented in the limma software, borrows strength across units to learn the distribution of the unit-specific variances, then computes moderated t-statistics. Here we develop the first procedures using moderated t-statistics that (i) control the false discovery rate (FDR) in finite samples under independence across units and null group invariance, without assuming limma's hierarchical model, and (ii) match the power of an oracle local false discovery rate procedure in a sparse asymptotic regime under limma's working model. Benjamini-Hochberg (BH) with standard t-test p-values has asymptotically zero power in the same regime. Our approach learns the variance distribution from statistics that depend on each unit's data only through its orbit under a compact group of transformations that preserves the null distributions, such as sign flips or orthogonal rotations. We then calibrate the resulting moderated t-statistics against group-transformed statistics pooled across units to obtain compound p-values, which we use with BH and a close variant. For small finite groups, we also construct a Selective SeqStep+ procedure using the same learned scores. Our approach extends to two-sample tests and tests of linear model coefficients.

Clustering is an unsupervised learning technique that partitions unlabeled data into groups. Most existing methods require user-specified parameters, such as the number of clusters or neighborhood size. Conversely, we propose automatic depth-based local center clustering (A-DLCC), a fully data-driven method that eliminates numerical parameter tuning. A-DLCC uses the $\beta$-integrated local depth to identify stable exemplars, points consistently central across multiple locality levels, termed local centers, which are ranked by their representativeness. Each local center induces a group of similar points, with group-level similarity measured by a proposed nonparametric metric called group-level local similarity. To guide merging, we incorporate the bottleneck path idea from graph theory, which forms the basis of our adaptive merging criterion. Based on this criterion, we design a single agglomeration rule in which a group is either absorbed by a neighbor it reaches better than itself or bonded to a neighbor that both sides find more reachable than their own background, every merge being additionally required to be carried by a contact stronger than a configuration-model null expects. The rule automatically estimates the number of clusters and decides when to stop merging. Experiments on synthetic and real data show that A-DLCC produces interpretable clustering results without parameter tuning.

With the rapid advancement in data collection devices and storage capacities, we have access to increasing amount of spatial point pattern data where each event location is augmented by multiple, potentially non-scalar marks. Therefore, there is need for efficient analysis techniques to investigate the structural relationships between the marks. In this paper, we recall the distance covariance and distance correlation and adjust them to the marked point process setting. As a result, we introduce a novel class of mark characteristics for single real-valued marks as well as multivariate combinations of marks, including mixtures of integer- and real-valued quantities, and non-scalar marks.

Offline reinforcement learning and off-policy evaluation evaluates dynamic treatment rules based on retrospectively collected data prior to deployment. In recent AI applications, state and reward information is recorded as complex text or image, which recent AI advancements such as LLM-as-a-judge can label with unknown bias. Expert annotation may be available but at a higher cost. For example, safety classification via cheap but imperfect classifiers vs. expensive expert review. We show how a limited budget for ground-truth data-annotation can be used via doubly-robust OPE with missing rewards, and we optimize variance-optimal annotation probabilities for sequential off-policy evaluation, where the target policy value is estimated from annotated data. We characterize the optimal annotation probabilities for sequential forward-monotone annotation protocols, and provide a feasible batch-adaptive implementation. Our work is motivated by a collaboration with a homelessness services nonprofit that writes casenotes for individuals over time. Our method can be used to unlock trustworthy inference from casenote data and answer new inferential questions such as: how does expanding outreach effort over time affect progress towards a housing application and improvement in housing placement? In simulations and on two real datasets - casenotes from the nonprofit and human-preference votes from LMArena - we see reductions in RMSE of 34-65% for housing placement and 17-68% for progress towards a housing application at budgets of 40% of full annotation and above, and by 55-62% at every budget on LMArena.

This paper studies adaptive experimental design for multiple testing, where an experimenter sequentially chooses which hypothesis to sample. We propose the e-value-based posterior sampling (e-PS) procedure, which uses the empirical average of log e-value increments to guide randomized sampling and applies e-BH to construct rejection sets. Under conditionally valid e-value increments, the procedure controls the false discovery rate at arbitrary stopping times and produces nested rejection sets. We establish high-probability bounds on the number of samples needed to discover all nonnull hypotheses in terms of the growth and concentration of the underlying e-processes. We specialize these bounds to simple-versus-simple, composite-versus-simple, and simple-versus-composite testing. Simulations and experiments using joke ratings and watermarked text illustrate the procedure's power under limited sampling budgets.

Let X1,...,Xn be independent exponential random variables with arbitrary positive, not necessarily equal, rates, and let Y1,\ldots,Yn be independent and identically distributed exponential random variables. We prove that, for every order statistic, the homogeneous order statistic is smaller than its heterogeneous counterpart in the convex transform order. Our results show that, relative to the homogeneous benchmark, heterogeneity stretches upper quantiles more strongly than lower quantiles, while the homogeneous order statistic ages faster in the convex-transform sense. We further extend the comparison to a proportional-hazards family that includes Weibull, Lomax, and Burr XII distributions. We give explicit conditions under which the comparison is preserved and show that the shape restriction is sharp within the Weibull family. These results characterize how component heterogeneity changes the distributional shape of order statistics beyond effects on location or scale.

In archaeological chronology building, stratigraphic constraints arising from the excavation context are commonly incorporated into Bayesian models through order-constrained priors. However, these models suffer from well-documented artifacts: estimated durations are inflated, and the bias worsens as more samples are dated. First, we prove that this phenomenon is intrinsic to the prior: when all true ages coincide, the posterior duration converges to the prior support's width. We then propose an unconstrained posterior that does not include stratigraphic knowledge and project it onto the space induced by the stratigraphic order. The projected posterior is the Wasserstein-closest constrained distribution; it can be computed via isotonic regression on a directed acyclic graph and corrects duration inflation unlike constrained priors. Simulation studies and two archaeological case studies demonstrate substantial bias reduction and precision gains.

We propose a novel and flexible nonlinear approach for dimensionality reduction of large-scale multiview network data and derive its theory. The (linear) predictor incorporates observed covariates (edge-specific, layer-specific, and global) and Gaussian latent factors. Inference is conducted via the graph Laplace approximated maximum likelihood estimator. Letting $K$ denote the number of network layers and $n_V$ the number of nodes, we derive asymptotic theory under two regimes: (i) $K \to \infty$ with fixed $n_V$, and (ii) double asymptotics $K, n_V \to \infty$, establishing consistency and asymptotic normality for local and global parameters, with distinct convergence rates. In an application to the gravity model for commodity trades, we use a zero-adjusted Gamma distribution with latent factors and observable covariates (e.g.\ distance, tariffs, common language) to capture excess zeros, skewness, and unobserved heterogeneity. Synthetic and real-data exercises show that our approach outperforms the routinely applied Poisson pseudo-maximum likelihood estimator with fixed effects. We complement our theoretical and empirical contributions with open-source R/C++ routines and a novel strategy for starting values selection.

This paper reviews advances over the last decade in the field of computational structural reliability modelling. The discussion is focused on problems of time-variant/time-invariant reliability at the component level. Three broad classes of problems are considered: (a) time-invariant reliability problems involving static problems, (b) problems of time-variant reliability analysis for deterministically parametered dynamical systems driven by random excitations, and (c) time-variant reliability analysis of randomly parametered dynamical systems subjected to random excitations. Four classes of approaches are discussed: (a) analytical methods based on first/second order reliability analyses (for time-invariant reliability analysis) and level crossing based approaches for time-variant reliability problems, (b) methods based on importance sampling strategies (including the Girsanov transformation based method for dynamical systems), (c) particle and trajectory splitting based methods, and (d) methods that employ machine learning based tools (primarily involving development of surrogate models and active learning strategies) in tackling reliability problems. The focus of the discussions is on methodological advances, and questions related to specific applications are not addressed. The review presents critical discussions on the relative merits of alternative approaches (in terms of computational efficiency, accuracy, scalability, treatment of rare events, ability to handle geometric complexities linked to failure surface, and suitability for high-dimensional problems) and identifies several directions for future research.