Papers

High-dimensional data create challenges for causal effect estimation because identifying the covariates needed for correct model specification becomes increasingly difficult. Double/debiased machine learning (DML) facilitates the use of machine learning (ML) for causal inference by mitigating regularization and overfitting bias, but comparatively less attention has been given to covariate selection in relation to the double robustness (DR) property possessed by some DML estimators. In particular, ML-based covariate selection may result in differential covariate selection or in misspecification of both models, thereby limiting the practical utility of the DR property. To address these issues, we propose using the union of the covariates selected by the propensity score (PS) and outcome ML models to re-estimate both models. Simulation results show that using the union consistently reduces more confounding bias than using separate selected covariate sets. The results also show that ML-based estimation does not uniformly outperform conventional DR estimation, even under conditions favorable to the Lasso, and that post-Lasso reduces more confounding bias than standard Lasso. These findings demonstrate that successful use of ML for causal inference depends not only on the ML algorithm but also on how the information obtained through covariate selection is incorporated into causal effect estimation.

We investigate Empirical Bayes (EB) methods in the context of compound adaptive experiments, where the arm distribution in each experiment follows a normal distribution with an unknown mean that we seek to estimate. There are two main EB strategies: $g$-modeling, which estimates the prior by maximizing the marginal likelihood, and $f$-modeling, which derives posterior means directly from the empirical distribution of the observations. We show that $g$-modeling continues to be a valid EB procedure even when it incorrectly assumes that data are collected exogenously; its validity does not depend on the particular sampling algorithm or on whether sample sizes are endogenous. In practice, one can apply standard $g$-modeling techniques by acting as though the data were exogenously sampled. We extend regret guarantees from exogenous sampling to adaptively generated data. By contrast, naively applying the Tweedie formula based on the marginal density of the observed data, as in standard $f$-modeling, can produce biased rules under adaptive sampling. We corroborate the robustness of $g$-modeling through simulations with widely used adaptive algorithms and demonstrate its applicability using a real-world dataset consisting of multiple sequential experiments.

We propose Low-Rank Quantile Surfaces (LRQS), a bivariate causal model in which, in the causal direction, an unknown monotone transformation of the conditional quantile surface admits a low-rank functional decomposition. LRQS subsumes location-scale noise models and post-nonlinear heteroscedastic noise models, while allowing multiple quantile bases to represent changes beyond location-scale effects. We prove generic identifiability of LRQS: the transformed quantile surface is low rank in the causal direction, whereas reverse representability under the corresponding constraints occurs only for exceptional, fine-tuned cause marginals. We provide a simple-yet-powerful causal score using a nonparametric fitting procedure that alternates between rank-constrained approximation of discretized quantile surfaces and isotonic estimation of the unknown monotone transformation. Experiments on synthetic mechanisms with higher-rank distributional shape variation and strong nonlinear distortions, together with standard bivariate benchmarks, show that LRQS is especially effective when conditional distributional shape or observation distortion goes beyond existing location-scale assumptions.

Degree-sequence realizability is the combinatorial basis of configuration models, but degree constraints alone do not ensure the preservation of graph dynamics. Hence, configuration models are unable to recover centrality measures, unless these are strongly correlated with the degree sequence. To address this matter, we introduce EP-realizability, the analogue problem induced by an equitable partition (EP): given the EP of a graph, decide whether the partition is realized by a simple undirected loopless graph and therefore construct such a graph. After defining the problem, we solve it by reducing it to sub-problems related to Havel–Hakimi and the Gale–Ryser theorem. We also face the challenge of solving the problem with an Approximate Equitable Partition ($\varepsilon$-EP), so that it is possible to reconstruct a network starting from partial and more privacy-preserving information. We evaluate privacy with edge overlap, deriving also, for our proposed $\varepsilon$-EP-realizability solution, a predictor for this metric. Experiments on Karate, Cora, CiteSeer and PubMed datasets show that our algorithm achieves a favourable and tunable privacy–utility trade-off, comparing the results with Havel–Hakimi algorithm, Newman's configuration model and a stochastic block model. Finally, both with real data and random graphs, we show that our algorithm has approximately linear time complexity with respect to the number of edges.

Longitudinal continuous outcomes in clinical trials are commonly analyzed using mixed models for repeated measures (MMRM) under normality assumptions. However, many clinical outcomes are skewed, making mean-based treatment effects difficult to interpret and potentially reducing statistical efficiency. The Box–Cox MMRM (BCMMRM) approach accommodates skewness by enabling inference on model-based median differences via inverse transformation. However, BCMMRM typically assumes a common transformation parameter across treatment groups and time points. When distributional shapes differ between groups or evolve over time, this assumption may lead to biased treatment effect. Furthermore, when treatment affects not only central tendency but also distributional shape or tail behavior, treatment effects may not be adequately characterized by a single location summary such as the median. We propose the Box–Cox multivariate regression (BCMVR) framework for longitudinal data with skewed outcomes. BCMVR relaxes this restriction by allowing transformation parameters to vary across groups and time points. The framework enables inference based on interpretable summaries, including median differences and a probability-based treatment effect quantifying the probability that a randomly selected patient in one group has a better outcome than one in another group. This measure integrates information over the entire outcome distribution and provides a complementary summary when distributional shapes differ. Simulation studies demonstrate that BCMMRM can produce biased estimates when distributions differ in shape, whereas BCMVR provides nearly unbiased estimation. The probability-based measure achieves a favorable balance between robustness and statistical efficiency. The proposed framework provides a flexible and interpretable approach to treatment effect inference under distributional heterogeneity.

This work addresses a longstanding gap in the statistical foundations of marginal maximum likelihood estimation for high-dimensional latent variable models. Marginal maximum likelihood estimation is widely used to fit latent variable models across the social sciences, ecology, and machine learning. Despite its broad use, rigorous asymptotic theory for nonlinear models remains limited when both the sample size and the number of observed variables diverge. The gap arises largely from the fact that integration over the latent variables creates a nonlinear objective that tightly couples the high-dimensional model parameters. To address this issue, we first show that the marginal likelihood exhibits multiple nearly flat directions even at the true parameter, in contrast to the behavior in the fixed-dimensional case. Building on this geometric characterization, we develop new techniques to establish consistency and asymptotic normality for the marginal estimator of the high-dimensional parameters. For the latent variables, we provide frequentist and Bayesian uncertainty quantification, proving asymptotic normality of the maximum a posteriori estimator and a Bernstein-von Mises-type result for the plug-in posterior. Together, these results provide rigorous foundations for marginal estimation and latent-variable inference in high-dimensional models.

Model robustness analysis estimates an effect across a multiverse of specifications that pools control sets identifying the declared estimand with sets that condition on mediators or colliders. We propose stating rival assumptions about contested controls as a small set of candidate causal graphs, enumerating the adjustment sets each graph licenses, and reporting robustness metrics conditional on each graph. A finite-mixture identity splits the licensed multiverse's dispersion into within-graph and between-graph components; the between-graph share is a conditional descriptive summary whose reading depends on the candidate set, the weights, and a common estimand. Simulations examine misleading pooled robustness assessments and the limits of the decomposition. Applications to hurricane fatalities, job training, and union wages show fragility that survives every graph, instability produced by unlicensed specifications, and a fragility verdict concealing a significant premium in each adjustment-identified candidate world. An R package implements the workflow.

Causal discovery methods aim to determine the causal direction between variables using observational data. Functional causal discovery methods rely on structural and distributional assumptions to determine directionality but typically lack statistical inference. This paper reviews the statistical guarantees of existing functional causal discovery methods in theory, software, and applied use, highlighting a key gap: the absence of a unified inferential framework that applies broadly across model classes. As a first step toward addressing this gap, we formalize a test-based approach for bivariate causal discovery by repurposing goodness-of-fit and independence tests within a hypothesis-testing framework. Because directionality is determined through two disjoint hypothesis tests, corresponding to four causal discovery outcomes, the approach provides explicit uncertainty quantification and diagnostic insight into assumption violations. Resampling is further used to estimate the rates of causal discovery outcomes, offering an additional layer of inference. We demonstrate the use and behavior of our inferential framework through simulations that vary the degree of assumption violation, as well as through real-data applications. We conclude with practical lessons and recommendations for advancing statistical guarantees in functional causal discovery.

Reserving models increasingly rely on loss-based estimation, where the loss function encodes the assumed error structure. Mack demonstrated this for the chain ladder, showing that the volume-weighted average estimator minimises a volume-weighted squared-error loss function that is additive in successive claim developments. This paper instead considers a multiplicative error structure and proposes the corresponding volume-weighted squared log-error loss function. Adapting Mack's distribution-free framework, we show that this loss function is minimised by the volume-weighted geometric average of the individual development ratios. This provides practitioners with an alternative estimator of development ratios for chain-ladder-based models, and a candidate loss function for machine-learning-based reserving models. We further show that the same estimator arises from two independent arguments: a stability requirement on successive ultimate loss projections, and maximum-likelihood estimation under a log-normal model. The estimator thus admits three complementary justifications: loss minimisation, reserve stability, and parametric likelihood. An out-of-sample study of 362 Schedule P company-line datasets supports the use of the proposed estimator in place of the volume-weighted average for the chain ladder, by showing that it improves predictive accuracy and reduces a slight over-prediction bias.

The chain ladder's volume-weighted pattern minimises an explicit loss function, yet is rarely booked as such. Practitioners adjust the pattern and record the final adjusted ratios. This paper treats the chain ladder's pattern selection as a supervised-learning problem. Judgement on pattern adjustments becomes a framework of defined penalties and hyperparameters on the chain ladder's loss function, treated here as an objective function in machine learning. Data weights are generalised with a decay and a power parameter for recency and volume weighting. Benchmark shaping and smoothness enter through a reference penalty and Whittaker-Henderson smoothing. The assembled objective is strictly convex and minimised by a single linear system. Each hyperparameter becomes an interpretable adjustment in its own right, declarable by judgement and categorised as an experience or a prospective adjustment. Experience adjustments can be set more objectively by a proposed training loop and a reserve validation score on held-out calendar diagonals. Further hyperparameter-based adjustments are written as almost-everywhere differentiable penalties that re-time or reshape the pattern. A worked example carries one real Schedule P triangle through an incurred and then a paid training stage, demonstrating the workflow.

Single-cell perturbation experiments provide causal information on gene regulation, whereas population-scale single-cell studies characterize gene expression and phenotypes in human populations. We develop a framework that integrates these complementary data sources for causal path analysis. Rather than assuming that a perturbational gene network transfers directly to the target population, we use externally learned ancestral relationships to constrain the network topology and re-estimate its direct edges and effects from population data. To address latent heterogeneity and measurement error in multiscale single-cell measurements, we develop a surrogate-variable procedure operating at both the cell and subject levels, combined with errors-in-variables correction for network and outcome regressions. We establish theoretical guarantees for confounder recovery and high-dimensional estimation of network and gene-outcome effects. Simulations demonstrate the importance of jointly correcting confounding and measurement error. An application to acute myeloid leukemia identifies distinct regulatory pathways linking transcriptional regulators to blast count.

Local inference for spatial point distributions is dominated by Monte Carlo calibration. We develop an alternative based on the Tweedie–Miyasawa identities of empirical Bayes, which relate locally weighted moments of a point distribution under a Gaussian kernel to derivatives of its log-intensity in scale space. We first establish a rigidity theorem showing that the structure of these identities forces the Gaussian kernel. Under complete spatial randomness, we derive a closed-form null distribution for a bounded inter-scale contrast, yielding a calibrated simulation-free pointwise test. In experiments, the measured type I error is 0.070 at a nominal level of 0.05, with a calibration cost 199 times smaller than Monte Carlo for the same local statistic. We then derive a contamination law for structures of dimension m and width w embedded in a uniform background, together with an explicit detectability threshold. For a filament in three dimensions, the threshold is 16 pi. The resulting scale-resolved local dimension estimator has no free parameters. Applications to California seismicity, a trefoil knot, and 10,071 SDSS galaxies show that the method separates local structures across scales without a spatial mesh and reproduces published cosmic web fractions. All experiments are reproducible from a single public script.

Neighborhoods are multifaceted entities whose attributes span sociocultural, economic, and environmental dimensions. Clustering neighborhoods based on social determinants of health (SDoH) can inform the allocation of public health resources and interventions tailored to community needs. Continuous and bounded data, as seen in aggregated neighborhood-level SDoH data, can pose challenges for widely used clustering methods (e.g., k-means or Gaussian mixture models) that rely on Euclidean distances or normality assumptions. Moreover, not all SDoH variables contribute equally to meaningfully characterize neighborhood clusters, and the inclusion of irrelevant or weakly informative determinants can obscure the underlying structure. To address this issue, we propose a Bayesian Salient Multivariate Beta mixture (SAMBA-Mix) model that flexibly models proportional data with embedded feature saliency to identify relevant variables for clustering. Our model showed improved accuracy in cluster identification and structure, compared to existing models. Using data from the U.S. Agency for Healthcare Research and Quality(AHRQ) SDoH database, we demonstrate the utility of our model to derive neighborhood-level SDoH profiles in Massachusetts and identify key determinants that best characterize differences amongst the different profiles.

Neural networks are becoming popular in solving mathematical problems, but stochastic models do not provide mathematical exactness by themselves. This study introduces a discovery-to-certification framework in which high-dimensional variational trial functions are learned in a compact separable representation, spectrally diagnosed and pruned, and then certified exactly through multimodular evaluation. Exact certification makes the numerical proofs fully explicit and independently verifiable. This framework can be run on a standard personal computer. Across three extremal problems, we show that neural optimization can contribute to rigorous mathematics in three distinct ways: by discovering improved constructions, by exposing empirical invariants that lead to proofs, and by revealing optimization barriers whose geometry motivates new analytic or numerical representations. More broadly, these results suggest a path toward AI-assisted mathematics in which flexible computational discovery and exact certification become complementary components of a single rigorous workflow.

Bayesian clinical trials require a well-specified prior distribution, and regulators increasingly expect that specification to be documented, diagnosed for prior-data conflict, and shown to be robust to reasonable alternatives, yet few R tools connect the full workflow of prior construction, validation, and regulatory justification into a single package. We introduce bayprior, an R package and Shiny application that implements structured expert elicitation via quantile matching, moment matching, and the SHELF roulette method across six distribution families; linear and logarithmic expert opinion pooling with Bhattacharyya agreement diagnostics; derivation of meta-analytic-predictive (MAP) priors from historical trial data via random-effects meta-analysis; prior-data conflict assessment using the Box p-value, S-value (surprisal) surprise index, information divergence, Bhattacharyya overlap, and multivariate Mahalanobis distance; hyperparameter sensitivity analysis with tornado and influence heatmap visualisations; and robust, sceptical, and power prior alternatives. A regulatory reporting module generates self-contained HTML, PDF, or Word documents addressing expectations in the FDA's 2026 draft Bayesian methods guidance and in EMA guidance on incorporating external and historical information. The package is demonstrated on a synthetic oncology Phase II trial. bayprior is available on CRAN and includes a fully modular Shiny application for interactive use.

We develop two complementary Bayesian procedures for analytic inference under informative sampling. The first constructs a coherent likelihood by modeling the sample-level distribution of the design weight given the study variable and recovering the conditional inclusion probability through the identity of Sverchkov and Pfeffermann (2004); it is the Bayesian counterpart of a recently proposed conditional-likelihood estimator, attains the model-based efficiency bound under the correctly specified sample-level joint model, and can be biased otherwise. The second uses the same weight model only as input to a Neyman-orthogonalized analog of the design-weighted score and applies the loss-likelihood bootstrap; the resulting credible intervals are asymptotically sandwich-correct under Poisson sampling, and the posterior remains centered at the truth under misspecification of the weight model, although the working model can still affect the first-order variance. A beta regression on the population-level inclusion probability, inducing a beta prime sample-level weight distribution, serves as the parametric default. A data-adaptive implementation of the second procedure estimates the efficient factor $\bar\pi(x,y)=1/E_p(W\mid x,y)$ by a design-weighted Gamma/log-link regression and uses it in a joint one-step loss-likelihood bootstrap for the analytic parameter; its validity requires no rate conditions on the nuisance fit. We illustrate both procedures with simulations and Canadian Workforce data.

Characterizing longitudinal changes in region-specific distribution of environmental exposures, such as total nitrate (TNO$_3$) concentrations, is critical for understanding localized ecological risks that are otherwise obscured by standard mean-level modeling. However, modeling longitudinal distributional outcomes across spatial regions presents significant methodological challenges. The random objects are spatio-temporally dependent, and mathematical constraints are inherent to distributional representations, such as, monotonicity of quantile functions. To address this, we propose a novel spatially-indexed longitudinal distributional outcome regression model. The distributional coefficients corresponding to the fixed effects of covariates are modeled using Bernstein basis polynomials, while spatio-temporal random effects are flexibly captured via tensor product expansions of splines. We develop a scalable Markov Chain Monte Carlo (MCMC) algorithm to explicitly account for spatial dependencies, and introduce a fast two-stage projected-posterior approach to preserve the monotonicity of the predicted subject-specific quantile functions. Extensive simulation studies demonstrate that the proposed framework achieves superior estimation accuracy and predictive performance compared to standard non-spatial distributional outcome regression. We apply our methodology to predict monthly, site-specific distributions of TNO$_3$ concentrations across the contiguous United States. Accounting for spatial correlation provides substantially lower uncertainty in the estimated distributional effects and improves predictive performance over the non-spatial alternative, offering a robust, interpretable tool for spatio-temporal environmental monitoring.

We state general conditions under which the full-data law is identified in the presence of latent variables, leveraging key observed variables ("proxies") associated with unobserved variables. These assumptions extend those used in existing examples from the literature that recover the full-data law under relatively flexible model assumptions. We first describe graphical models compatible with our assumptions, and then consider target parameters that are functionals of the full-data law, developing estimating equations that give rise to consistent M-estimators using the observed data. Our approach replaces unobserved random variables appearing in full-data estimating equations with observed variables via a proxy-based weighting scheme. This strategy can be extended to construct observed-data influence functions, giving estimators with desirable properties such as multiple robustness and \(\sqrt{n}\)-consistency despite slower than parametric convergence of nuisance functions.

Statistical precision and scientific relevance operate on different scales. In regular problems, sampling uncertainty contracts at rate $n^{-1/2}$, whereas the magnitude below which an effect is scientifically negligible may be fixed or may vary with information. Let $\Delta_n$ denote a relevance threshold and $I_0$ Fisher information, and define $\lambda_n=\sqrt{nI_0}\Delta_n$. For separated negligible and meaningful parameter classes, we establish the minimax lower bound $\liminf R_n^*\ge 2\{1-\Phi(\varepsilon\kappa)\}$ when $\lambda_n\to\kappa$. If $\lambda_n\to0$, the experiments merge and consistent classification is impossible. If $\lambda_n\to\kappa\in(0,\infty)$, the problem converges to a Gaussian-shift decision problem. We characterize the exact minimax rule and risk in that limiting composite problem. As $\kappa\downarrow0$, the optimal cutoff converges to one statistical-error unit and the optimal improvement over trivial risk is $O(\kappa^2)$, while a simple relevance-boundary rule improves only at $O(\kappa^3)$; as $\kappa$ grows, that rule becomes asymptotically minimax. If $\lambda_n\to\infty$, consistent classification is attainable under a uniform estimation-resolution condition, verified for Gaussian and Bernoulli models. For $\Delta_n=dn^{-\gamma}$, the critical rate is $\gamma=1/2$. We also show that moving asymmetric relevance regions depend on standardized distances to their two boundaries rather than total width alone. For heterogeneous true effects, we derive a significance-saturation limit and show that point-null significance can be most selective for scientifically relevant effects at intermediate information. The framework characterizes when scientific relevance is statistically resolvable through a common information scale.

Likelihood-based network models are often fitted under links' independence and low-order constraints, while empirical networks frequently exhibit systematic higher-order structures such as triangles and wedges, characterizing the observed clustering patterns. Real-world core-periphery networks such as the interbank market or the air transportation system represent key examples, with cores displaying complex and nonlinear features. We formalize Penalized Likelihood with Structural Discrepancies (PLSD) as an inference-level correction that trades likelihood fit for agreement with targeted motifs. PLSD augments the negative log-likelihood with a penalty on standardized wedge and triangle discrepancies, yielding a controlled distortion of the likelihood surface that can be interpreted through a linear response analysis. A calibration approach for the unique tuning hyperparameter is introduced to turn off the penalization term when the model is correctly specified, thereby recovering maximum-likelihood estimation in that case. We then introduce a mixed-constraint maximum-entropy core-periphery Exponential Random Graph Model (ERGM), derive unconditional semi-closed motif formulas under Pareto-distributed core fitness, and interpret sparse-regime scaling through a big-jump mechanism for heavy-tailed distributions. We finally corroborate the PLSD inference methodology both with Monte Carlo simulations of a toy stochastic block model and by applying the novel core-periphery ERGM to weekly eMID interbank networks (2009-2015) and monthly US air traffic networks (1991-2000). We show that PLSD describes cores that are not only dense but also higher-order-rich and captures the observed heterogeneous degree distributions and the overexpression of wedges and triangles, at a link-level cost proportional to the model misspecification.

Although sequential decision-making is ubiquitous across domains, policy evaluation and learning with spatio-temporal data remain challenging due to spatial spillover and temporal carryover effects. We develop methods for evaluating and learning individualized dynamic policies under spatio-temporal interference. Under a semiparametric additive outcome model that allows for complex spillover and carryover effects, we consider a family of stabilized estimators for evaluating the performance of a given individualized policy. From this family, we select a data-adaptive optimal estimator that minimizes the asymptotic variance. We then derive the asymptotic distribution of the proposed policy evaluation estimator, and establish the finite-sample regret bounds of our policy learning estimator. We further propose a statistical test to select the complexity of the semiparametric additive model by determining the appropriate order of interactions. Through simulations, we assess the finite-sample performance of our estimators and the validity of the proposed test. Our motivating application examines the optimal allocation of economic aid in Iraq from February 2007 to July 2008. Drawing on declassified conflict data, we study the weekly assignment of aid projects across districts and find that reallocating aid away from regions with a persistently high level of violence can substantially reduce insurgent attacks.

Shared-parameter joint models for longitudinal and time-to-event data are powerful tools for analyzing repeatedly measured biomarkers, clinical events, and the complex relationships between them. Recent methodological advances have extended the basic framework, which was originally developed for a single event time and a continuous longitudinal biomarker, to more complex scenarios. This tutorial provides a step-by-step guide to fitting extended joint models for longitudinal and time-to-event data using the R package JMbayes2. We cover a range of applications, including models with competing risks, recurrent events, multistate processes, flexible association structures, and multiple longitudinal outcomes following different distributions. Each model is illustrated using simulated data that closely resemble a real-world dataset, with detailed explanations of data organization, model specification, fitting, diagnostics, and interpretation. The tutorial is designed for applied researchers who are interested in analyzing their own data with extended joint models using accessible and reproducible R code.

The microbiota is increasingly recognized as an active component of host biology, influencing various host phenotypes. Advances in high-throughput sequencing and the emergence of the holobiont perspective have raised expectations regarding hologenomic-informed prediction. Yet, whether and under which conditions integrating microbiota and genomic data meaningfully improves phenotypic prediction remains unclear. The biological characteristics of the microbiota, including but not limited to transmission mechanisms, environmental effects and interactions with host genetics, complicate their integration into classical evaluation frameworks. In addition, microbiota datasets are high-dimensional, highly dispersed, sparse and compositional. Finally, analytical choices such as the taxonomic granularity considered for aggregation or the similarity matrix used in prediction models may impact downstream inference and prediction accuracy. Here we explore these challenges using a comprehensive set of transgenerational hologenomic simulations. By generating controlled and contrasted biological scenarios across a broad parameter space, we examine how microbiota granularity, variance structure and host modulation influence (i) the estimation of variance components and (ii) the accuracy of phenotypic prediction. We show that the added value of hologenomic, compared to genomic prediction, is highly context dependent. Our results provide a structured framework to interrogate when and how integrating microbiota may enhance phenotypic prediction in breeding applications.

This paper studies the detection of multiple simultaneous (systematic) change points for high-dimensional nonstantionary economic and financial time series data. The analytic framework used is based on the standard and adaptive fused group lasso method, where the mixed L_{2,1} penalty is either uniform or re-weighted by data-dependent weights. This paper shows that, under appropriate conditions, this approach is L_2 consistent and, by adopting the data-dependent weights, could correctly select the change points with probability approaching unity (L_0 consis- tency). It quantifies the conditions on the interplay among the averaged minimum magnitude of structural changes, the number of change points and the number of observations for consistently discovering the change points. The performance of this approach is illustrated via an analysis of a large panel of U.S. economic and financial time series data over the past 50 years.

Many applications in public health, environmental science, and economics feature spillovers across connected units, violating the Stable Unit Treatment Value Assumption (SUTVA) underlying classical quantile treatment effect methods. We develop a general framework for defining, estimating, and conducting inference for quantile exposure effects (QEEs) under network interference, encompassing quantile direct and spillover effects as leading cases. Studying QEEs under interference faces three substantive challenges. First, because a single exposure level represents many neighborhood treatment configurations, the causal estimand must aggregate over these configurations in an interpretable manner. Second, quantile estimands are intrinsically non-smooth, placing them outside much of the existing network theory involving only Lipschitz or differentiable functionals. Third, in design-based, finite-population network settings, conventional smoothness assumptions on outcome densities cannot be imposed directly. Using conditional neighborhood dependence, we establish asymptotic normality under explicit network degree conditions and derive a locally uniform convergence rate for kernel density estimation. We also characterize the variance estimation bias arising from heterogeneous unit-specific score means and construct asymptotically conservative confidence intervals. Extensive simulations and an application to an educational intervention in school friendship networks demonstrate that the proposed framework reveals heterogeneous exposure effects, including tail-specific impacts, that are missed by analyses based solely on average treatment effects.

Longitudinal microsimulation models to evaluate policies and scenarios for chronic disease risk reduction typically involve simulating multiple risk factors for a synthetic population over time. Various statistical methods have been used to accomplish this, but the principles behind them have never been comprehensively reviewed or critically compared. We describe and review the range of methods that have been used to simulate multiple risk factors over time, given either longitudinal or repeated cross-sectional data, highlight those which are most practically applicable and flexible, and introduce some useful variants of them. We describe procedures that can be used to check and compare these methods in practice based on fit to data, and present a case study where the methods are used and compared, based on a microsimulation model to evaluate mid-life cardiovascular health checks. We conclude that a useful range of procedures are available, and this paper improves the knowledge base to support their use in models to inform health policy.

While homographies are fundamental to many computer vision tasks, the majority of conventional estimation techniques provide only point estimates without directly quantifying uncertainty introduced by noisy observations. Uncertainty, though, propagates to subsequent processing steps such as camera calibration and 3D reconstruction and is particularly relevant in safety-critical and socially relevant fields including medical imaging, autonomous driving, and defense. We present a fast Bayesian formulation for homography estimation from point correspondences that explicitly incorporates measurement uncertainty and prior knowledge while providing a posterior distribution over the homography parameters. A closed-form solution of the posterior mean of the homography is derived in homogeneous coordinates and supplemented by an iterative Bayesian approach to handle non-linearities. Synthetic experiments demonstrate the applicability to projective transformations and show improved estimation accuracy over DLT under varying noise conditions. Image stitching experiments further demonstrate applicability to real image correspondences while additionally providing uncertainty information.

Forecasts made at different levels of aggregation are often required to agree—for example, regional forecasts should sum to the national total. Forecast reconciliation imposes such relationships, but the meaning of agreement depends on whether the constraint is applied to a predictive distribution, a reported summary such as a mean or quantile, or a decision based on the forecast. We show that these operations are not interchangeable. Even when every possible outcome from a predictive distribution satisfies an aggregation rule, its separately reported marginal quantiles need not add up; under nonlinear relationships, even the coordinatewise means may violate the constraint. We characterise when linear reconciliation preserves marginal quantiles and show that nonmedian quantiles generally cannot be preserved in a genuine hierarchy. We also explain why conditioning on an exact nonlinear constraint requires specifying how that constraint is observed or approximated, and identify when the predictive mean contains enough information for a constrained decision. In an application to Australian tourism data with 28 rolling forecast origins, the median discrepancy between two natural constructions of the national 95th percentile is 159.9% of the reconciled 90% prediction-interval width under bottom-up reconciliation. Rankings of mean- and quantile-based forecasts also reverse when squared-error loss is replaced by asymmetric inventory loss. These results provide a framework for deciding what should be made coherent and how competing methods should be evaluated.

Long environmental records increasingly combine observations from successive observing or processing systems. Transitions between these systems create temporal seams that may reflect imperfect harmonization or changes in the observed process. We introduce the Temporal Seam Score (S-score, or S), a signed, robust measure for assessing continuity at a known transition time. The complete time series is fitted with a seam-blind model accounting for trend, seasonality, and optional covariates. The residual contrast between symmetric windows around the transition is compared with matched reference contrasts calculated within the contributing segments. The S-score is the standardized departure of the seam contrast from this reference. An S-score near zero indicates that the seam is consistent with ordinary temporal variability. Its sign indicates the direction of the discontinuity, while its magnitude (|S|) indicates how exceptional the discontinuity is. Simulation showed that |S| reflects the imposed discontinuity relative to residual variability: a 20% shift produced a median |S| of 2.58 at a residual coefficient of variation of 0.10, compared with 0.84 at 0.50. In a MODIS-to-Sentinel-3 vegetation record, 121 of 500 sites yielded finite S-scores, of which 90 met all reliability criteria. Among these reliable sites, median S was +0.217 and median |S| was 0.627, indicating little systematic directional displacement and a median seam departure below one reference spread. The S-score provides a general and auditable diagnostic for evaluating temporal continuity across generations of sensors, algorithms, and observing systems without requiring temporal overlap, thereby supporting harmonization quality assurance and more reliable attribution analyses based on long-term environmental records.

Regular-grid spatial functional datasets arise naturally in gridded environmental, oceanographic, climate, and remote-sensing applications, where each spatial location is associated with an entire curve. Existing spectral spatial functional principal component analysis methods provide an important frequency-domain approach for such data, but they do not directly target finite-neighbourhood least-squares reconstruction from an estimated latent spatial component field. To address this, we propose Spatial Functional Generalized Dynamic Principal Components (SFGDPC), a reconstruction-based dimension-reduction method for regular-grid spatial functional data. Each function is first represented by basis coefficients, and each coefficient vector is reconstructed from a scalar latent spatial field and its Chebyshev neighbourhood on the rectangular grid. The spatial neighbourhood radius is selected using a Bayesian information criterion (BIC)-type conditional reconstruction criterion. In the local-neighbourhood transfer simulation, SFGDPC reduced mean cumulative normalized mean squared error (NMSE) relative to spatial functional principal component analysis (SFPCA) by approximately 38-53% across the reported component counts and covariance conditions. In the Indian Ocean sea surface temperature (SST) application, one SFGDPC component produced lower whole-grid reconstruction error than both the boundary-safe and high-cap SFPCA benchmarks across all 33 annual fields. The results support SFGDPC as a local reconstruction-based complement to spectral SFPCA for regular-grid spatial functional data.