Papers

Operational evidence, i.e., evidence of operation without failure is an important component of confidence in the safety or reliability of a system in service, but it is costly to collect. When the context of operation changes, the relevance of previously collected operational evidence becomes unclear. This problem arises, for example, when an autonomous vehicle that has operated safely in one operational environment (the Target Operational Domain, TOD) is deployed in a different but related TOD. Existing practice often treats such evidence in an all-or-nothing manner: either it is fully reused, or it is discarded. Neither position is satisfactory when there are good reasons to believe that the new context is no worse than the previous one, but that belief is itself uncertain. This paper studies how to make post-change reliability claims by combining evidence from two TODs using Conservative Bayesian Inference (CBI), which combines the evidence from the new context with a weighted amount of previous context and partial prior knowledge through constraints on a set of admissible priors. This yields conservative posterior bounds on quantities of interest. A numerical example illustrates how pre-existing evidence from a previous TOD can be transferred, conservatively and transparently, to support reliability claims in the changed TOD.

Fractional Ornstein–Uhlenbeck (fOU) processes model temporal dependence and memory, including long-range dependence, while retaining the classical Ornstein–Uhlenbeck process as a special case. We extend the integral fractional Ornstein–Uhlenbeck (ifOU) process to a multidimensional setting for animal telemetry. Longitude, Latitude, and Altitude velocities are represented by coordinate-specific fOU processes driven by a multivariate fractional Brownian motion, allowing each coordinate to retain its own damping, scale, and Hurst parameters. We establish covariance validity, characterize the admissible cross-correlation region, and derive the asymptotic behavior of cross-covariances and separated increments. We develop procedures for finite-dimensional simulation, Gaussian likelihood inference, and conditional velocity reconstruction. Replicated simulations examine estimation of cross-coordinate correlations, while joint estimation of the complete parameter vector is illustrated for one three-dimensional trajectory. The proposed model is applied to telemetry records from five common noctule bats migrating in Germany, including three trajectories with Altitude measurements.

Latent growth models (LGMs) have been widely used to describe individual trajectories of change, average change patterns, and individual differences in change within a group. Structural equation model tree (SEM Tree) partitions samples through recursive partitioning using external covariates and characterizes between-group differences via parameters of prespecified SEM template models. An SEM Tree with an LGM as its template model may therefore serve as a useful classification method for longitudinal data. However, current SEM Tree implementations may face important practical obstacles, including high computational cost and frequent improper solutions caused by model misspecification or data characteristics (e.g., a limited number of measurement occasions). In the present study, we developed a matrix decomposition LGM tree (MDLGM Tree), which applies the matrix decomposition factor analysis (MDFA) approach, an eigenvalue-decomposition-based method for model estimation. Previous studies on MDFA and its extensions to SEM have shown that this approach can reduce the risk of improper solutions while yielding estimates highly similar to those obtained by maximum likelihood estimation. Through a series of simulations, we demonstrated that, compared with conventional SEM Tree, the MDLGM Tree greatly reduces the occurrence of improper solutions and is also highly efficient in terms of computation time.

We introduce the local quasi-linear (LQL) model, a differential equation-constrained local polynomial regression framework for the general first-order linear ordinary differential equation (ODE) $g'(x)=a(x)g(x)+b(x)$, extending prior work on differential equation-constrained local polynomial regression (DE-constrained LPR) for the exponential growth model. We derive closed-form DE-constrained local polynomial (DE1-$k$) estimators for arbitrary Taylor degree $k$, establish their asymptotic conditional bias and variance, and propose two approaches for estimating $a(x)$ and $b(x)$ when they are unknown. A simulation study across two structurally different ODEs shows that DE1-$k$ estimation with automatic degree selection reduces both estimation error and ODE-consistency error relative to unconstrained local linear regression. We then apply the framework to the firebrand burning-rate experiment of Albini (1979), modelling the density-loss curve of wind-driven firebrands with a physically motivated forced-convection ODE; the DE-constrained estimator outperforms local linear regression in the sparsest species-diameter groups, where physical structure is most valuable in compensating for scarce data. We further examine the robustness of the LQL model to misspecification against a local quasi-exponential alternative. Together, these results extend the DE-constrained regression paradigm to a broad class of physically motivated linear models and provide a practical estimation tool for fire science and other application areas where mechanistic knowledge is available but data are sparse.

Group testing is an established, highly cost-effective strategy for population-level disease surveillance that identifies positive individuals by pooling biological specimens. Originally introduced during World War II for large-scale screening and heavily utilized in modern high-throughput public health infrastructure, traditional group testing methods are restricted to purely associational analyses. Consequently, they lack the capacity to infer the direct causal effect of an intervention when individual-level data are subject to baseline confounding. In this work, we bridge this fundamental gap by introducing a causal inference framework tailored specifically for group testing designs. We integrate the principles of inverse probability weighting (IPW) directly into a pooled pseudo-likelihood formulation to construct an unbiased pseudo-score function. Under standard regularity conditions, we prove the consistency and asymptotic normality of our proposed plug-in estimator. Extensive numerical simulations demonstrate that our framework successfully purges severe selection bias, accurately recovering the true average treatment effect where traditional unweighted pooling models fail. Finally, we illustrate the practical utility of our method as both an estimation and a diagnostic tool using real-world observational surveillance data from the CDC's U.S. Influenza Vaccine Effectiveness Network.

Estimating causal effects in observational studies requires adjustment for confounding, a task that becomes challenging when the exposure is a function observed over a continuous domain rather than a scalar variable. We develop a functional propensity score weighting framework that achieves covariate balance by removing dependence between time-varying treatments and observed confounders, thereby enabling estimation of marginal causal effects in settings with functional treatments, covariates, and outcomes. We propose a dual formulation of the weight estimation problem that yields a smooth unconstrained optimization and improves computational scalability. The proposed framework extends naturally to settings with time-varying covariates and to longitudinal outcomes via a function-on-function marginal structural model, allowing estimation of causal effect surfaces. The proposed method improves covariate balance, estimation accuracy, and computational efficiency compared to the existing approach and retains these properties when extended to functional covariates and outcomes. We apply the method to data from the UK Biobank to estimate the causal effect of body mass index trajectories on the risk of Type 2 Diabetes and on subsequent glycated hemoglobin trajectories, a functional measure of metabolic status.

In early 2022, FIA mandated the change to the technical regulations for Formula 1, requiring to design cars around ground effect aerodynamics to mitigate the performance loss incurred by driving in the turbulent "Dirty Air" of another car. The reduction of the penalty was subsequently claimed, but never formally evaluated on a per lap basis. We gathered 100486 racing laps for the years 2021-2025 using the FastF1 API, built a compound-specific physics correction for Dirty Air to account for fuel and tyre wear, and evaluated the change introduced by the 2022 regulation using both OLS regression with clustered standard errors and Causal Forest Double/Debiased Machine Learning. We repeated the analysis using season as a categorical variable, applying a generalized circuit filter to account for a changing calendar. Both methods produced similar results, demonstrating no statistically significant change to the Dirty Air penalty when combining 2022-2025 data together (OLS interaction term beta = -0.0025, p = 0.803; Causal Forest mean effects of 0.019s and 0.018s per second of following distance in 2021 and 2022-2025). We tested the hypothesis, that the penalty reduction may have been concentrated in 2022 and partially eroded through 2023-2025. We found no season for which the change was different from the one observed in 2021 in the OLS analysis, while several seasons were significantly different from zero in the Causal Forest analysis, in a non-monotonic pattern, not following the theorized erosion timeline. We conclude there was no statistically significant change to the Dirty Air penalty under the new regulation, both in pooled and season-specific analysis. By evaluating the real-world racing results, we demonstrate that even if an aerodynamic advantage exists, it did not translate into a measurable improvement over following distance, where other factors can swamp such an effect.

Matrix decomposition SEM (MDSEM) is a data-matrix-based alternative to conventional covariance-based SEM, but its theoretical relationship to covariance-based SEM and the statistical properties of its estimator have remained unclear. We first reformulate MDSEM using a single loss function that integrates the measurement and structural models. We then prove that minimizing this loss over the model parameters is equivalent to minimizing the squared Bures-Wasserstein (BW) distance between the observed and model-implied covariance matrices, and use this equivalence to establish the estimator's theoretical properties. Specifically, the equivalence identifies the proposed estimator as both an MDSEM estimator and a covariance-based SEM estimator within the minimum discrepancy estimation framework, from which consistency, asymptotic normality, and standard errors are derived. Simulations show that its finite-sample performance is comparable to that of conventional estimators, including maximum likelihood, and that confidence-interval coverage is close to the nominal level. The estimator is also more numerically stable than conventional SEM estimators in small samples and under model misspecification. Thus, the BW formulation provides a theoretical foundation for MDSEM and a practically useful discrepancy function for covariance-based SEM.

The conditional forecast-revision scale $\It=\{\Var(\E[X_{t+1}\mid\F_t]\mid\F_{t-1})\}^{1/2}$ measures the history-specific size of the forecast update induced by observing $X_t$. Because it is a conditional second moment built from two unknown conditional means, it is not directly observed. We study which estimator of $\It$ should be used under different structural assumptions and computational budgets. The comparison includes a block bootstrap, a conditional-variance model, a fitted state-space model, two $O(1)$ streaming smoothers, and the forget gate of an already-trained recurrent network. An error decomposition separates one-step-prediction error from conditional-second-moment tracking error. We show that externally tuned lag-only smoothers can be inconsistent when $\It$ changes at the sampling scale, although they attain the usual $T^{-2/3}$ mean-squared-error rate ($T^{-1/3}$ for $\It$) under slow variation; a correctly specified state-space estimator escapes this limit by using the current state. In volatility-driven designs, a cheap conditional-variance model is more accurate and over one hundred times cheaper as a point estimator than the implemented block bootstrap, whose value lies in the sampling distribution it provides rather than in point tracking. In state-driven designs, only the structurally matched filter recovers the fast variation. Read directly, a trained network's forget gate does not track $\It$ — though a supervised linear probe on the full gate vector does, so $\It$ is linearly decodable but not available for free. These results yield a practical rule: identify the conditional-second-moment structure, match the estimator to it, and then choose the least costly adequate method.

We introduce a new density-based goodness of fit test for ergodic Markov processes. Our test compares the data against the class of models specified in the null hypothesis, and rejects if no model in the class yields a stationary density that matches with the data. No alternative needs to be specified in order to implement the test. Although our test compares densities, estimation of smoothing parameters is not required, and the test has nontrivial power against $1/\sqrt{n}$ local alternatives. The test provides new perspectives on some existing problems in econometric and financial modeling.

Weighted distributional tests for covariate balance are currently limited to two-group comparisons. We extend the Kolmogorov-Smirnov, Anderson-Darling, and Cramer-von Mises tests to an arbitrary number of weighted groups k >= 2, using existing k-sample generalizations and a shared permutation-inference procedure; each statistic reduces exactly to its two-group counterpart at k = 2. An accompanying post-hoc pairwise procedure with four multiple-comparison adjustments localizes which groups differ following an omnibus rejection. In a four-scenario simulation study at k = 3, Type I error remained close to nominal, and the comparative advantages established for two groups were preserved: Kolmogorov-Smirnov was most powerful against a centrally located discrepancy, Anderson-Darling against a tail-located discrepancy, and Anderson-Darling and Cramer-von Mises performed comparably against a diffuse discrepancy. Omnibus power was nonetheless uniformly lower than in the matching two-group setting - not because the underlying discrepancy is diluted, but because adding groups enlarges the null distribution itself, so the post-hoc procedure, whose pairwise statistics carry no such penalty, is often the more sensitive tool whenever a specific group's imbalance is suspected. The methods are implemented in the Stata commands kstest, adtest, and cvmtest.

Causal inference increasingly extends beyond classical causal effects defined by deterministic treatment assignments, such as the average treatment effect, to stochastic intervention effects that can weaken positivity requirements and offer greater policy relevance. Nonparametric Bayesian models are attractive for estimating these effects due to their flexibility and inherent uncertainty propagation, but this posterior uncertainty need not be well calibrated for the causal effect of interest. We develop a simple post-processing correction that can be applied to posterior samples without changing the prior or fitting algorithm. We prove that, for a broad class of stochastic interventions, the corrected posterior yields asymptotically efficient inference and credible intervals with asymptotically valid frequentist coverage; formally, it satisfies a semiparametric Bernstein-von Mises theorem. The theory covers interventions specified independently of the observed treatment process, as well as interventions that modify it, including incremental propensity score interventions and a new power-tilt intervention. A central contribution is new theory for SoftBART, including conditions under which this flexible tree-based Bayesian model supports calibrated Bayesian inference for stochastic intervention effects. In simulations, the correction reduces bias and improves coverage relative to the uncorrected Bayesian analysis while remaining competitive with frequentist alternatives. We illustrate the method by estimating how expected LDL cholesterol would change under hypothetical increases or decreases in the odds of receiving statin therapy.

The Transient Climate Response to cumulative CO2 Emissions (TCRE) is a key metric for linking greenhouse gas emissions to global temperature change and informing climate policy. However, extant estimates of the TCRE often depend on subjective model selection or assumed sensitivity ranges, with limited validation against observed data. We develop a fully statistical data-driven approach using a Bayesian Model Averaging (BMA) approach to estimate the TCRE. This uses 37 climate models from the Coupled Model Intercomparison Project phase 6 (CMIP6), weighted according to their consistency with observed temperature data. Compared to the Intergovernmental Panel on Climate Change (IPCC)'s Sixth Assessment Report (AR6) TCRE estimate, our BMA approach yields a very likely range (90% interval) that overlaps substantially with that from the AR6, but with a higher mean and a lower standard deviation. The resulting projections of global temperature change to 2100 show somewhat higher warming and less uncertainty than some current methods. The use of statistical modeling methods makes it easier to validate the approach and to partition the uncertainty according to its sources. Out-of-sample predictive validation shows the method to be well calibrated. Variance decomposition shows model parameter uncertainty to be a main source of projection variance.

Spectral clustering for community detection is analysed in multivariate time series models whose dependence structure is determined by an unobserved stochastic blockmodel. We establish that spectral clustering of the sample covariance matrix achieves exact recovery of the underlying communities. The recovery rates depend explicitly on the network size, sample length, block separation, and degree of data dependence. This demonstrates that exact community recovery under a stochastic blockmodel is possible even when the adjacency matrix is unobserved. Our theory provides extensions of both classical and fine-grained matrix perturbation theory to the setting of dependent data, which may be of independent interest.

In this note we describe a method for comparing inferred dynamics in evolutionary accumulation models (EvAMs). These models involve the acquisition of multiple, potentially codependent, binary features over time – for example, mutations in cancer development, or phenotypes in evolutionary biology. As the set of methods for inferring EvAM dynamics expands, approaches for comparing inference across algorithms, datasets, and covariates are required. In particular, a comparison method supporting reversible, stochastic dynamics, interactions between feature sets, and potentially non-independent samples (as well as simpler cases) has yet to be established. It is possible for EvAM with similar relative feature orderings to produce completely different sets of observed states due to “frameshift”-like differences; methods distinguishing state and transition similarity are therefore also desirable. Here we suggest a method focussed on ordering matrices, describing the probability that a feature is acquired under different conditions on other features, and is thus generally comparable across methods and datasets. We demonstrate how the approach captures both statistical robustness (given EvAM uncertainty) and scientifically meaningful differences in inferred dynamics. The method is applied to synthetic and real-world data on the evolution of chromosomal aberrations in different tumour types and of drug-resistant bacteria in different countries.

Multimodal supervised learning seeks to leverage multiple heterogeneous data sources to improve predictive performance. A central challenge is determining the fusion granularity across modalities: over-integration may amplify noise while under-integration fails to exploit cross-modal dependence. Existing approaches rely on pre-specified fusion architectures, from early to late fusion, that may not adapt to the underlying dependence structure among modalities. We propose DAIF, a data adaptive intermediate fusion framework that combines random matrix theory and non-parametric dependence measures to learn fusion structure directly from data. We operate under a Bayesian multimodal factor model where the prior on the latent factors determines the cross-modal dependence. Our method clusters modalities based on estimated intermodal dependence, then performs clusterwise empirical Bayes estimation of the priors. These estimated priors are used to construct denoisers within an approximate message passing (AMP) framework, yielding denoised low-dimensional features that borrow strength across related modalities while preserving modality-specific signal. The resulting embeddings are used for downstream supervised prediction. We evaluate the framework through simulations under varying dependence structures and signal regimes, comparing against several benchmark methods, and demonstrate its practical utility on two multimodal datasets, namely a trimodal TEA-seq dataset (Swanson et al., 2021) and TCGA-BRCA dataset (Goldman et al., 2020). In the first example, we predict the expression level of a T-cell differentiation marker protein and in the second case we analyze patient survival prediction based on multimodal information. Our method competes with or outperforms the state-of-the-art techniques in both prediction problems, demonstrating its versatility across diverse supervised learning tasks.

Conformal prediction inference yields intervals for out-of-sample random outcomes with designated coverage probabilities, given exchangeable or independent-and-identically distributed random variables. For regression analysis, valid coverage can be achieved given finite sample sizes, despite unavoidable misspecifications of the regression function. We propose a novel method of conformal inference, aimed to produce confidence intervals of the unknown expectations of the in-sample outcomes with the designated coverage probabilities conditional on the realised sample. These conformal confidence intervals fill a gap between classical regression and conformal inference. The proposed approach is applied to small area estimation problems.

Correlation matrices arise when marginal scales are removed from covariance matrices, yet a normalized likelihood must account for both quotient distance and quotient volume. We propose a Riemannian Gaussian model for full-rank correlation matrices under quotient-affine geometry. The distribution is proper and has finite radial moments. We derive exact score and profiled-scale equations and recover Fisher-transformed Gaussian inference for two-dimensional matrices. In higher dimension, a curvature calculation shows that the normalizing constant can vary with the center. Exact maximum likelihood and Fréchet estimation may therefore have different population targets. We develop chart-based methods for evaluating the normalizer, fitting the likelihood, and sampling. Numerical studies verify the analytic case and compare integration, estimation, and sampling procedures across dimensions and dispersion regimes. A rolling-finance application and a controlled prior study illustrate both the value and computational cost of the model. The method is most reliable in small to moderate dimensions, while proposal efficiency and numerical conditioning deteriorate near the boundary and at larger dispersion.

An overall treatment effect in a clinical trial may inadequately represent particular patient subgroups, creating uncertainty about whether a population-level efficacy conclusion can legitimately be transferred to them. Conventional interaction tests only investigate whether subgroup-specific treatment effects are exactly equal or not, but cannot detect whether the differences are small enough to be clinically negligible. We develop a formal framework for assessing subgroup treatment effect consistency for time-to-event outcomes within the Cox proportional hazards model. Consistency is formulated as an equivalence problem based on the (weighted) treatment-by-subgroup interaction coefficient. We consider detecting consistency between two complementary subgroups and consistency of subgroup-specific treatment effects with the overall treatment effect. For each setting, we develop a conventional two one-sided tests procedure (TOST) and a new test motivated by optimal equivalence testing for normally distributed parameters. We prove the asymptotic validity of all procedures and show empirically that the new tests are more powerful than their TOST counterparts. Finally, we apply the new methodology to a case study motivated by the CANTOS cardiovascular outcomes trial.

Boolean matrix factorization provides an interpretable framework for discovering latent binary patterns in high-dimensional data, yet existing methods typically analyze a single binary matrix or factorize multiple matrices independently, failing to exploit shared latent structure across related datasets. We propose Joint Bayesian Boolean Matrix Factorization (JBBMF), a model that simultaneously factorizes two related binary matrices through a shared latent Boolean pattern matrix and dataset-specific loading matrices. To capture dependence between paired datasets, we introduce a conditional prior linking the loading matrices, allowing latent factors to persist or change across conditions while preserving a common interpretable representation. The model combines Boolean matrix factorization with a Bernoulli observation model and conjugate priors, yielding closed-form full conditional distributions and an efficient Gibbs sampler for posterior inference,uncertainty quantification for latent factors, reconstructed matrices, and noise parameters. Simulation studies demonstrate that jointly modeling related binary datasets substantially improves recovery of shared latent factors compared with independently applying standard Boolean matrix factorization to each dataset, while maintaining high reconstruction accuracy. We apply JBBMF to paired chromosomal copy number alteration profiles from multiple myeloma patients collected at diagnosis and relapse. The analysis identifies recurrent chromosomal alteration signatures shared between disease stages and quantifies the uncertainty of these findings. JBBMF offers a flexible and interpretable Bayesian model for the joint analysis of related binary datasets in genomics and other application domains.

In applied research, the decision to utilize multilevel modeling (MLM) is commonly guided by comparing a point estimate of the unconditional intraclass correlation coefficient (ICC) against some recommended threshold (e.g., 0.05). This naive approach, however, fails to account for sampling uncertainty and provides no formal inferential justification for a decision. The current work introduces negligible effect significance testing (NEST; or equivalence testing) for the ICC, proposing a framework that performs this test using a pivotal quantity of the ICC based on the F statistic. Furthermore, we offer guidance to help researchers define "negligible" that utilizes the design effect to characterize a tolerable level of variance inflation. R code illustrating the proposed procedure is provided.

With AI systems gaining more access to individuals' information, it is important to protect privacy when reporting statistical answers. Equally important is to privatize the reporting of uncertainty in such answers. To this end, we adopt a Bayesian likelihood-free framework and make simulation from the posterior private. In particular, we propose a new private instantiation of the Bayesian bootstrap using a blocking strategy. Rather than assigning idiosyncratic random weights to each individual, we randomly group individuals and assign a single weight to each group. By concealing individuals' contributions within a group, we fortify differential privacy gates. We harness amortized inference that decouples private learning from posterior sampling. A push-forward map from observation weights to posterior samples is learned privately by adding calibrated noise during training. Subsequent posterior draws require no additional privacy and computation budget. We call the resulting method the Private Generative Bayesian Bootstrap (PGBB). We establish a differential privacy guarantee, analyze convergence to the non-private blocked-bootstrap target, and quantify the discrepancy between the ordinary and blocked Bayesian-bootstrap posteriors. In addition, we derive data-free tuning of the block Dirichlet concentration parameter that restores posterior dispersion asymptotically. We also show a single fit of PGBB can support a family of loss-based decision rules simultaneously without additional privacy cost. In simulations and in applications to U.S. Census returns to schooling and U.S. natality birthweight quantiles, PGBB gives competitive private uncertainty quantification and improves over private Bayesian alternatives that require a specified data-generating model in common settings.

Creator economy platforms face a strategic dilemma: allocating traffic to established stars for immediate ad revenue versus nurturing emerging creators to build a follower base for future monetization. We develop a continuous-time dynamic optimization model to characterize the optimal traffic allocation policy for a platform managing heterogeneous creators with dual revenue streams (advertising and direct follower contributions). We characterize the optimal policy analytically, revealing a “most-valuable-creator-first" rule driven by a forward-looking activation set. Under Bass diffusion dynamics, this policy exhibits a sophisticated “conditional reversal" strategy, where the platform temporarily prioritizes lagging creators to capitalize on word-of-mouth effects. Regarding the ecosystem structure, we find the optimal policy acts as a selective gatekeeper. Unlike myopic policies that lead to a harsh “winner-take-all" market, or naive fairness-driven heuristics that foster inefficient “indiscriminate growth," the optimal policy imposes a strict capability threshold that screens which creators receive platform traffic. Furthermore, it enforces disciplined growth for successful entrants, capping their follower bases at an optimal ceiling to prevent over-investment. Finally, we demonstrate that simple heuristics can lead to significant revenue losses (up to 25%) and propose a practical “follower-growth adjusted" heuristic that achieves near-optimal performance by leveraging observed growth momentum.

Distinguishing long memory behaviour from nonstationarity can be very difficult as in both cases the sample autocovariance function decays very slowly. Available stationarity tests either do not include long memory or fare poorly in terms of empirical size, especially near the boundary between long memory and nonstationarity. We propose a testing procedure based on evaluating periodograms at different epochs. Limiting distributions established here are easily tractable as sum of weighted independent $\chi^2$ random variables. Moreover, numerical studies are provided to show that the proposed approach seems to outperform existing methods.

Mediation analysis investigates whether part of the treatment effect is channelled through one or more mediators along the causal pathway between the treatment and the primary outcome. However, the presence of multiple, potentially dependent mediators raises substantial challenges, particularly when the outcome is binary, the mediators are measured on different scales, and interactions are present. We consider on causal mediation analysis with a binary treatment and a binary outcome, defining natural direct, indirect, and total effects on the relative-risk scale, thereby avoiding the interpretational difficulties associated with non-collapsible effect measures. Under a sequential ignorability assumption, we develop a unified regression-based framework that accommodates multiple continuous, binary, or mixed mediators. The proposed framework accounts for dependence among mediators and allows for both exposure-mediator and mediator-mediator interactions. We derive closed-form expressions for the causal effects across the different mediator settings and develop a likelihood-based inference procedure for estimating the causal effects and quantifying their uncertainty. The methodology is illustrated through two empirical applications.

When the target of inference is a group mean rather than an individual score, long assessments can be statistically inefficient. From the marginal score of the likelihood, we derive the asymptotic standard error of the marginal maximum likelihood estimator of a latent IRT mean under random item sampling, and obtain a closed-form approximation via a Gaussian-convolution treatment of the item information. The formula makes the test-length–sample-size trade-off explicit and includes an inflation factor for jointly estimating the population variance when the item pool is mistargeted. We validate it against exact benchmarks, Monte Carlo simulation under pool–population mismatch, and a NAEP mathematics resampling study; group means remain approximately unbiased even with single-item forms.

Non-parametric statistical testing is based on surrogate data generation that randomizes chosen features in the empirical data. In the graph setting, graph signal processing (GSP) brings forward versatile schemes; e.g., to preserve smoothness of graph signals as measured by the Dirichlet energy. However, how to deal with directed graphs remains an active area of research. We begin by revisiting the definition of directed graph wide-sense stationarity. The surrogate signals preserve covariance under the stationary assumption. We demonstrate the feasibility of the scheme to detect irregular node covariance and benchmark our method against conventional schemes using the symmetrized graph. We also investigate how the level of asymmetry affects the detection performance, thus assessing the advantages of the presented approach. Finally, we show results for a real-world graph extracted from the Freeman EIES social network dataset.

Detecting a change in a multivariate series answers only the first of two questions; the operational question is which coordinates changed. Existing answers are incomplete. Block-level procedures certify predefined groups of coordinates under an additive union bound, high-dimensional variable-selection methods return interpretable rankings without error guarantees, and the post-detection inference literature controls error along the time axis rather than across coordinates. We propose ARM (Attribution by Rank Maxima), a wrapper that accepts a changepoint located by an arbitrary detector and returns the set of coordinates certified to have changed, each carrying a location or scale type label. ARM scores each coordinate by a max-over-splits rank statistic. Because this statistic dominates the corresponding statistic at the estimated split, the resulting certificate is invariant to the manner, and to the accuracy, of the changepoint estimate. Three finite-sample guarantees follow from within-coordinate ranks alone: per-coordinate validity under any detector; exact family-wise error control through a Westfall–Young joint permutation that preserves cross-coordinate dependence, with a fully distribution-free Holm fallback; and false discovery rate control under arbitrary coordinate dependence in high dimensions through Benjamini–Yekutieli and e-BH. In simulations, naive per-coordinate testing at the estimated changepoint inflates its family-wise error beyond $0.66$ as the dimension grows, whereas ARM maintains the nominal level while retaining validity under heavy tails, power in high dimensions, and accurate type labels. On five financial series surrounding the 2008 collapse, ARM attributes a scale change to every asset class and excludes injected control coordinates.

In medical research, patients often have multiple interdependent outcomes, such as posttraumatic stress disorder (PTSD), depression, and pain among trauma survivors. Most existing research uses multinomial regression to analyze these interdependent outcomes separately, which ignores correlations between concurrent conditions. This omission may lead to loss of information and reduced predictive accuracy. Accounting for correlations between multiple categorical outcomes requires a high-dimensional parameter space, making model estimation challenging. In this paper, we propose a multivariate multinomial logit model that captures outcome correlations and uses the ANOVA decomposition of the parameter space to reduce the number of parameters. The ANOVA decomposition enables explicit conditional model formulations, which allow for a computationally much simpler composite likelihood for model estimation. We develop an efficient Minorization-Maximization (MM) algorithm to maximize the composite likelihood, which also incorporates variable selection via a bridge penalty. Simulation studies are conducted to evaluate our method, demonstrating its accuracy in parameter estimation and variable selection. We further illustrate our method using data from the AURORA study.

Target trial emulation structures observational causal analyses around the protocol of an ideal randomized trial. By aligning eligibility, treatment assignment, time zero, and follow-up, it can reduce avoidable biases, but implementation still requires coordinated decisions about data construction, inverse probability weighting, diagnostics, outcome models, standardization, competing risks, and uncertainty estimation. This article provides a self-contained methodological guide and practical tutorial for TTE, an R package for target trial emulations with longitudinal observational data. We describe target trial protocols, intention-to-treat and per-protocol estimands, identification assumptions, baseline and person-period data structures, temporal ordering for longitudinal weights, stabilized treatment and censoring weights, weight truncation, balance and effective-sample-size diagnostics, weighted pooled discrete-time survival models, model-based standardization, competing-risk analysis, weighted Kaplan-Meier and Aalen-Johansen estimation, and cluster bootstrap at the original-individual level. Two fully synthetic examples illustrate end-to-end workflows: sodium-glucose cotransporter 2 inhibitor versus dipeptidyl peptidase-4 inhibitor initiation with all-cause death, and sequentially nested angiotensin receptor blocker versus calcium channel blocker trials with heart-failure hospitalization and competing death. The examples show how to obtain and diagnose estimates in R and interpret relative hazards, absolute risks, cumulative incidence, and differences between intention-to-treat and per-protocol effects.