Papers

Online media platforms track the share of impressions associated with content attributes, or prevalence, to evaluate trade-offs and set guardrails in A/B experiments. LLM-based labeling provides a high-fidelity reference measurement, but is cost-prohibitive to run per experiment, per arm, per segment, and per day on a platform with hundreds of concurrent experiments. We describe a surrogate-based prevalence measurement system deployed in Pinterest's experimentation platform. The contribution is system-level rather than estimator-level: the system maintains a single global calibration of ML score buckets, continuously refreshed from a recurring LLM-labeled stream, and reuses the resulting bucket-level prevalences across every experiment via a per-experiment SQL metric and a delta-focused dashboard. Because the calibration is derived from the platform's daily-batch prevalence samples, it remains representative of production traffic as distributions drift, and in Pinterest's deployment it incurs zero incremental labeling cost. Teams without such infrastructure can instantiate the same pattern with a recurring calibration-labeling workflow whose cost is amortized across all downstream experiments rather than paid per experiment, arm, segment, and day. The system serves ~100 experiments and ~250 arms per day across six calibrated content categories, including a holdout program. Relative to per-experiment LLM labeling, which in practice yields a one-shot read per arm on a small subset of experiments, the surrogate provides daily per-arm prevalence on over 20$\times$ as many concurrent arms under the same labeling budget. Across roughly 300 production audits, the surrogate's 95% confidence interval contains the LLM-based reference point estimate in 92% of evaluations, and day-level delta aggregation recovers 2–5% relative shifts that no single per-arm LLM measurement can detect.

Stochastic simulation is widely used to study complex systems composed of various interconnected subprocesses, such as input processes, routing and control logic, optimization routines, and data-driven decision modules. In practice, these subprocesses may be inherently unknown or too computationally intensive to directly embed in the simulation model. Replacing these elements with estimated or learned approximations introduces a form of epistemic uncertainty that we refer to as submodel uncertainty. This paper investigates how submodel uncertainty affects the estimation of system performance metrics. We develop a framework for quantifying submodel uncertainty in stochastic simulation models and extend the framework to digital-twin settings, where simulation experiments are repeatedly conducted with the model initialized from observed system states. Building on approaches from input uncertainty analysis, we leverage bootstrapping and Bayesian model averaging to construct quantile-based confidence or credible intervals for key performance indicators. We propose a tree-based method that decomposes total output variability and attributes uncertainty to individual submodels in the form of importance scores. The proposed framework is model-agnostic and accommodates both parametric and nonparametric submodels under frequentist and Bayesian modeling paradigms. A synthetic numerical experiment and a more realistic digital-twin simulation of a contact center illustrate the importance of understanding how and how much individual submodels contribute to overall uncertainty.

As datasets continue to grow in size and complexity, finding succinct yet accurate data summaries poses a key challenge. Centroid-based clustering, a widely adopted approach to address this challenge, finds informative summaries of datasets in terms of few prototypes, each representing a cluster in the data. Despite their wide adoption, the resulting data summaries often contain redundancies, limiting their effectiveness particularly in datasets characterized by a large number of underlying clusters. To overcome this limitation, we introduce the Khatri-Rao clustering paradigm that extends traditional centroid-based clustering to produce more succinct but equally accurate data summaries by postulating that centroids arise from the interaction of two or more succinct sets of protocentroids. We study two central approaches to centroid-based clustering, namely the well-established k-Means algorithm and the increasingly popular topic of deep clustering, under the lens of the Khatri-Rao paradigm. To this end, we introduce the Khatri-Rao k-Means algorithm and the Khatri-Rao deep clustering framework. Extensive experiments show that Khatri-Rao k-Means can strike a more favorable trade-off between succinctness and accuracy in data summarization than standard k-Means. Leveraging representation learning, the Khatri-Rao deep clustering framework offers even greater benefits, reducing even more the size of data summaries given by deep clustering while preserving their accuracy.

Currently, work injury compensation boards in Canada track injury information using a standard system of codes (under the National Work Injury Statistics Program (NWISP)). These codes capture the medical nature and original cause of the injury in some detail, hence they potentially contain information which may be used to predict the severity of an injury and the resulting time loss from work. Claim duration easurements and forecasts are central to the operation of a work injury compensation program. However, due to the complexity of the codes traditional statistical modelling techniques are of limited value. We will describe an artificial neural network implementation of Cox proportional hazards regression due to Ripley (1998 thesis) which is used as the basis for a model for the prediction of claim duration within a work injury compensation environment. The model accepts as input the injury codes, as well as basic demographic and workplace information. The output consists of a claim duration prediction in the form of a distribution. The input represents information available when a claim is first filed, and may therefore be used in a claims management setting. We will describe the model selection procedure, as well as a procedure for accepting inputs with missing covariates.

The use of profiling evidence in criminal trials is a longstanding controversy in legal epistemology and evidence law theory. Many scholars, even when they oppose its use at trial, still assume that profiling evidence can be probative of guilt. We reject that assumption. Profiling evidence may support a generic hypothesis, but is not evidence that the defendant is guilty of the specific crime of which they are accused. We contrast profiling evidence with case-specific evidence, which speaks more directly to the facts of the case. Our critique departs from others by grounding the argument in a probabilistic analysis of evidentiary value. We also explore the implications of our account for debates about stereotyping.

Computational reproducibility is central to scientific credibility, yet verifying published results at scale remains costly. We develop an AI-assisted workflow for automated full-paper replication – retrieving materials, reconstructing environments, executing code, and matching outputs to point estimates reported in regression tables. We define a universe of all empirical and quantitative papers from the three top political science journals (2010–2025) and measure stated data availability using automated extraction. For a stratified sample of 384 studies, we apply the workflow to conduct full-paper replication, totaling 3,523 empirical models. We find that journal verification requirements, combined with data archiving mandates, drive reproducibility: the share of fully or largely reproducible papers rises from 20.8% before DA-RT adoption to 82.5% after, and conditional on accessible replication packages, 92.1% of papers are fully or largely reproducible (234/254). As a secondary application, we apply standardized IV diagnostics to 84 studies (597 IV specifications among 1,910 replicated models), illustrating how automated execution enables systematic reanalysis across heterogeneous empirical settings.

As artificial intelligence (AI)-generated content proliferates, models are increasingly trained on their own outputs, risking progressive degradation or collapse. In this article, we provide the first positive, rigorous theoretical results, to the best of our knowledge, showing that under model-agnostic mild conditions, the model converges to the true data-generating distribution. The convergence rate is the minimum of the model's intrinsic rate and the fraction of real data at each training iteration, revealing a phase transition between data-limited and model-limited regimes. We further show that, for biased real data, correcting the bias prevents the persistence and amplification of early bias over training iteration. Extensive experiments across simulations, real images and texts validate our theoretical framework, establishing quantitative conditions for long-term AI stability in contaminated environments.

This paper introduces a novel, open-source MARL simulation framework for studying implicit cooperation in LEMs, modeled as a decentralized partially observable Markov decision process and implemented as a Gymnasium environment for MARL. Our framework features a modular market platform with plug-and-play clearing mechanisms, physically constrained agent models (including battery storage), a realistic grid network, and a comprehensive analytics suite to evaluate emergent coordination. The main contribution is a novel method to foster implicit cooperation, where agents' observations and rewards are enhanced with system-level key performance indicators to enable them to independently learn strategies that benefit the entire system and aim for collectively beneficial outcomes without explicit communication. Through representative case studies (available in a dedicated GitHub repository in https://github.com/salazarna/marlem, we show the framework's ability to analyze how different market configurations (such as varying storage deployment) impact system performance. This illustrates its potential to facilitate emergent coordination, improve market efficiency, and strengthen grid stability. The proposed simulation framework is a flexible, extensible, and reproducible tool for researchers and practitioners to design, test, and validate strategies for future intelligent, decentralized energy systems.

This paper proposes implicit cooperation, a framework enabling decentralized agents to approximate optimal coordination in local energy markets without explicit peer-to-peer communication. We formulate the problem as a decentralized partially observable Markov decision problem that is solved through a multi-agent reinforcement learning task in which agents use stigmergic signals (key performance indicators at the system level) to infer and react to global states. Through a 3x3 factorial design on an IEEE 34-node topology, we evaluated three training paradigms (CTCE, CTDE, DTDE) and three algorithms (PPO, APPO, SAC). Results identify APPO-DTDE as the optimal configuration, achieving a coordination score of 91.7% relative to the theoretical centralized benchmark (CTCE). However, a critical trade-off emerges between efficiency and stability: while the centralized benchmark maximizes allocative efficiency with a peer-to-peer trade ratio of 0.6, the fully decentralized approach (DTDE) demonstrates superior physical stability. Specifically, DTDE reduces the variance of grid balance by 31% compared to hybrid architectures, establishing a highly predictable, import-biased load profile that simplifies grid regulation. Furthermore, topological analysis reveals emergent spatial clustering, where decentralized agents self-organize into stable trading communities to minimize congestion penalties. While SAC excelled in hybrid settings, it failed in decentralized environments due to entropy-driven instability. This research proves that stigmergic signaling provides sufficient context for complex grid coordination, offering a robust, privacy-preserving alternative to expensive centralized communication infrastructure.

Across business and social science applications, outcomes are often missing in ways that depend on the unobserved outcomes themselves. In service systems, for example, whether a customer submits a rating depends on the rating they would have provided. Such missing-not-at-random (MNAR) mechanisms make population quantities difficult to identify without strong assumptions on the observation process. Meanwhile, rich unstructured data, such as customer interaction histories, are increasingly available and can be used to construct structured measurements using tools such as large language models (LLMs). In this work, we develop an assumption-lean partial identification framework that uses such measurements as weak shadow variables, defined as outcome-informative proxies that are conditionally independent of missingness given the true outcome and observed covariates. Importantly, they need not accurately predict missing outcomes or satisfy the completeness requirement in the classical shadow variable literature. For identification, we characterize sharp bounds on population quantities through a pair of linear programs. For estimation and inference, we propose a localized penalized estimator that remains feasible under sampling error, and a subsampling algorithm for constructing confidence intervals. In semi-synthetic experiments using real customer-service dialogues, weak-shadow-variable intervals are about 89% narrower than those without auxiliary information, while their midpoints have around 41% lower estimation error than classical MNAR methods.

Current methods for statistical inference in networks often encounter substantial computational bottlenecks when applied to the massive network datasets that are increasingly common across scientific domains. In this paper, we develop Predictive Subsampling (PredSub), a scalable framework for estimation and two-sample testing in networks. The central idea is to replace a full-sample estimation procedure by estimation on a random subsample, followed by out-of-sample prediction of the remaining vertices. This construction exploits the fact that the subsample provides an inferential anchor, which enables each remaining vertex to be incorporated in a predictive manner through a fast vector operation. Building on this estimator, we develop two scalable procedures for two-sample testing, namely PredSubTest and PureSubTest. We establish finite-sample error bounds as well as estimation and testing consistency of the proposed methods in both Frobenius and two-to-infinity norms. These results formally characterize the trade-offs between statistical accuracy and computational efficiency with respect to the subsample size, the choice of test statistic, and the choice of norm. We demonstrate the empirical performance of the proposed methods through detailed simulation studies and two real-world applications involving DBLP coauthorship networks and the Cannes 2013 social media networks.

We apply covariate adjustment to the Wincoxon two sample statistic and Wincoxon-Mann-Whitney test in comparing two treatments. The covariate adjustment through calibration not only improves efficiency in estimation/inference but also widens the application scope of the Wilcoxon two sample statistic and Wincoxon-Mann-Whitney test to situations where covariate-adaptive randomization is used. We motivate how to adjust covariates to reduce variance, establish the asymptotic distribution of adjusted Wincoxon two sample statistic, and provide explicitly the guaranteed efficiency gain. The asymptotic distribution of adjusted Wincoxon two sample statistic is invariant to all commonly used covariate-adaptive randomization schemes so that a unified formula can be used in inference regardless of which covariate-adaptive randomization is applied.

Cardiovascular outcome trials commonly face competing risks when non-CV death prevents observation of major adverse cardiovascular events (MACE). While Cox proportional hazards models treat competing events as independent censoring, Fine-Gray subdistribution hazard models explicitly handle competing risks, targeting different estimands. This simulation study using bivariate copula models systematically varies competing event rates (0.5%-5% annually), treatment effects on competing events (50% reduction to 50% increase), and correlation structures to compare these approaches. At competing event rates typical of CV outcome trials (~1% annually), Cox and Fine-Gray produce nearly identical hazard ratio estimates regardless of correlation strength or treatment effect direction. Substantial divergence occurs only with high competing rates and directionally discordant treatment effects, though neither estimator provides unbiased estimates of true marginal hazard ratios under these conditions. In typical CV trial settings with low competing event rates, Cox models remain appropriate for primary analysis due to superior interpretability. Pre-specified Cox models should not be abandoned for competing risk methods. Importantly, Fine-Gray models do not constitute proper sensitivity analyses to Cox models per ICH E9(R1), as they target different estimands rather than testing assumptions. As supplementary analysis, cumulative incidence using Aalen-Johansen estimator can provide transparency about competing risk impact. Under high competing-risk scenarios, alternative approaches such as inverse probability of censoring weighting, multiple imputation, or inclusion of all-cause mortality in primary endpoints warrant consideration.

We study a type of Multi-Armed Bandit (MAB) problems in which arms with a Gaussian reward feedback are clustered. Such an arm setting finds applications in many real-world problems, for example, mmWave communications and portfolio management with risky assets, as a result of the universality of the Gaussian distribution. Based on the Thompson Sampling algorithm with Gaussian prior (TSG) algorithm for the selection of the optimal arm, we propose our Thompson Sampling with Clustered arms under Gaussian prior (TSCG) specific to the 2-level hierarchical structure. We prove that by utilizing the 2-level structure, we can achieve a lower regret bound than we do with ordinary TSG. In addition, when the reward is Unimodal, we can reach an even lower bound on the regret by our Unimodal Thompson Sampling algorithm with Clustered Arms under Gaussian prior (UTSCG). Each of our proposed algorithms are accompanied by theoretical evaluation of the upper regret bound, and our numerical experiments confirm the advantage of our proposed algorithms.

A P300 ERP-based Brain-Computer Interface (BCI) speller is an assistive communication tool. It searches for the P300 event-related potential (ERP) elicited by target stimuli, distinguishing it from the neural responses to non-target stimuli embedded in electroencephalogram (EEG) signals. Conventional methods require a lengthy calibration procedure to construct the binary classifier, which reduced overall efficiency. Thus, we proposed a unified framework with minimum calibration effort such that, given a small amount of labeled calibration data, we employed an adaptive semi-supervised EM-GMM algorithm to update the binary classifier. We evaluated our method based on character-level prediction accuracy, information transfer rate (ITR), and BCI utility. We applied calibration on training data and reported results on testing data. Our results indicate that, out of 15 participants, 9 participants exceed the minimum character-level accuracy of 0.7 using either on our adaptive method or the benchmark, and 7 out of these 9 participants showed that our adaptive method performed better than the benchmark. The proposed semi-supervised learning framework provides a practical and efficient alternative to improve the overall spelling efficiency in the real-time BCI speller system, particularly in contexts with limited labeled data.

Stochastic-gradient MCMC methods enable scalable Bayesian posterior sampling but often suffer from sensitivity to minibatch size and gradient noise. To address this, we propose Stochastic Gradient Lattice Random Walk (SGLRW), an extension of the Lattice Random Walk discretization. Unlike conventional Stochastic Gradient Langevin Dynamics (SGLD), SGLRW introduces stochastic noise only through the off-diagonal elements of the update covariance; this yields greater robustness to minibatch size while retaining asymptotic correctness. Furthermore, as comparison we analyze a natural analogue of SGLD utilizing gradient clipping. Experimental validation on Bayesian regression and classification demonstrates that SGLRW remains stable in regimes where SGLD fails, including in the presence of heavy-tailed gradient noise, and matches or improves predictive performance.

This paper addresses graph learning in Gaussian Graphical Models (GGMs). In this context, data matrices often come with auxiliary metadata (e.g., textual descriptions associated with each node) that is usually ignored in traditional graph estimation processes. To fill this gap, we propose a graph learning approach based on Laplacian-constrained GGMs that jointly leverages the node signals and such metadata. The resulting formulation yields an optimization problem, for which we develop an efficient majorization-minimization (MM) algorithm with closed-form updates at each iteration. Experimental results on a real-world financial dataset demonstrate that the proposed method significantly improves graph clustering performance compared to state-of-the-art approaches that use either signals or metadata alone, thus illustrating the interest of fusing both sources of information.

Recent work in the privacy literature shows that sample-targeted membership inference attacks (MIAs) significantly outperform untargeted approaches by a wide margin. Motivated by this observation, we address the following question: can the privacy vulnerability of individual training points be assessed without training shadow models? We show that per-sample exposure to MIA is governed not only by a point's loss, but also by a data-dependent geometric measure. In the linear setting, we derive a closed-form decomposition of individual black-box MIA vulnerability into a population leverage score and a residual loss term, making explicit how sample-dependent geometry translates into privacy exposure. Since the final layer of most modern architectures is linear, we extend this framework to deep networks and propose a surrogate score operating on last-layer representations that requires only a single trained model and no shadow models. Empirical evaluations across diverse datasets and architectures show that our score outperforms loss and gradient-norm baselines at identifying the highest-risk points under state-of-the-art attacks, providing a computationally efficient and theoretically grounded tool for per-sample privacy risk assessment.

We propose nonparametric identification and semiparametric estimation of joint potential outcome distributions in the presence of confounding. First, in settings with observed confounding, we derive tighter, covariate-informed bounds on the joint distribution by leveraging conditional copulas. To overcome the non-differentiability of bounding min/max operators, we establish the asymptotic properties for both a direct estimator with polynomial margin condition and a smooth approximation with log-sum-exp operator, facilitating valid inference for individual-level effects under the canonical rank-preserving assumption. Second, we tackle the challenge of unmeasured confounding by introducing a causal representation learning framework. By utilizing instrumental variables, we prove the nonparametric identifiability of the latent confounding subspace under injectivity and completeness conditions. We develop a “triple machine learning" estimator that employs cross-fitting scheme to sequentially handle the learned representation, nuisance parameters, and target functional. We characterize the asymptotic distribution with variance inflation induced by representation learning error, and provide conditions for semiparametric efficiency. We also propose a practical VAE-based algorithm for confounding representation learning. Simulations and real-world analysis validate the effectiveness of proposed methods. By bridging classical semiparametric theory with modern representation learning, this work provides a robust statistical foundation for distributional and counterfactual inference in complex causal systems.

Online platforms require robust systems to enforce content safety policies at scale. A critical component of these systems is the ability to evaluate the quality of moderation decisions made by both human agents and Large Language Models (LLMs). However, this evaluation is challenging due to the inherent trade-offs between cost, scale, and trustworthiness, along with the complexity of evolving policies. To address this, we present a comprehensive Decision Quality Evaluation Framework developed and deployed at Pinterest. The framework is centered on a high-trust Golden Set (GDS) curated by subject matter experts (SMEs), which serves as a ground truth benchmark. We introduce an automated intelligent sampling pipeline that uses propensity scores to efficiently expand dataset coverage. We demonstrate the framework's practical application in several key areas: benchmarking the cost-performance trade-offs of various LLM agents, establishing a rigorous methodology for data-driven prompt optimization, managing complex policy evolution, and ensuring the integrity of policy content prevalence metrics via continuous validation. The framework enables a shift from subjective assessments to a data-driven and quantitative practice for managing content safety systems.

This paper introduces a novel kernel density estimator (KDE) based on the generalised exponential (GE) distribution, designed specifically for positive continuous data. The proposed GE KDE offers a mathematically tractable form that avoids the use of special functions, for instance, distinguishing it from the widely used gamma KDE, which relies on the gamma function. Despite its simpler form, the GE KDE maintains similar flexibility and shape characteristics, aligning with distributions such as the gamma, which are known for their effectiveness in modelling positive data. We derive the asymptotic bias and variance of the proposed kernel density estimator, and formally demonstrate the order of magnitude of the remaining terms in these expressions. We also propose a second GE KDE, for which we are able to show that it achieves the optimal mean integrated squared error, something that is difficult to establish for the former. Through numerical experiments involving simulated and real data sets, we show that GE KDEs can be an important alternative and competitive to existing KDEs.

In 2015 the Open Science Collaboration (OSC) (Nosek et al 2015) published a highly influential paper which claimed that a large fraction of published results in the psychological sciences were not reproducible. In this article we review this claim from several points of view. We first offer an extended analysis of the methods used in that study. We show that the OSC methodology induces a bias that is able by itself to explain the discrepancy between the OSC estimates of reproducibility and other more optimistic estimates made by similar studies. The article also offers a more general literature review and discussion of reproducibility in experimental science. We argue, for both scientific and ethical reasons, that a considered balance of false positive and false negative rates is preferable to a single-minded concentration on false positive rates alone.

Hypothesis tests under order restrictions arise in a wide range of scientific applications. By exploiting inequality constraints, such tests can achieve substantial gains in power and interpretability. However, these gains come at a cost: when the imposed constraints are misspecified, the resulting inferences may be misleading or even invalid, and Type III errors may occur, i.e., the null hypothesis may be rejected when neither the null nor the alternative is true. To address this problem, this paper introduces safe tests. Heuristically, a safe test is a testing procedure that is asymptotically free of Type III errors. The proposed test is accompanied by a certificate of validity, a pre–test that assesses whether the original hypotheses are consistent with the data, thereby ensuring that the null hypothesis is rejected only when warranted, enabling principled inference without risk of systematic error. Although the development in this paper focus on testing problems in order–restricted inference, the underlying ideas are more broadly applicable. The proposed methodology is evaluated through simulation studies and the analysis of well–known illustrative data examples, demonstrating strong protection against Type III errors while maintaining power comparable to standard procedures.

Probabilistic modeling is an effective tool for evaluating team performance and predicting outcomes in sports. However, an important question that hasn't been fully explored is whether these models can reliably reflect actual performance while assigning meaningful probabilities to rare results that differ greatly from expectations. In this study, we create an inference-based probabilistic framework built on expected goals (xG). This framework converts shot-level event data into season-level simulations of points, rankings, and outcome probabilities. Using the English Premier League 2015/16 season as a data, we demonstrate that the framework captures the overall structure of the league table. It correctly identifies the top-four contenders and relegation candidates while explaining a significant portion of the variance in final points and ranks. In a full-season evaluation, the model assigns a low probability to extreme outcomes, particularly Leicester City's historic title win, which stands out as a statistical anomaly. We then look at the ex ante inferential and early-diagnostic role of xG by only using mid-season information. With first-half data, we simulate the rest of the season and show that teams with stronger mid-season xG profiles tend to earn more points in the second half, even after considering their current league position. In this mid-season assessment, Leicester City ranks among the top teams by xG and is given a small but noteworthy chance of winning the league. This suggests that their ultimate success was unlikely but not entirely detached from their actual performance. Our analysis indicates that expected goals models work best as probabilistic baselines for analysis and early-warning diagnostics, rather than as certain predictors of rare season outcomes.

Certified machine unlearning can be achieved through noise injection, with differential privacy guarantees obtained by calibrating the noise to worst-case sensitivity. Yet, the influence of individual training points is highly heterogeneous, making such uniform calibration unnecessarily conservative for most deletion requests. We consider certified per-instance unlearning, a data-dependent notion of certified deletion in which the unlearning mechanism and its certificate can adapt to the point being removed. Our framework turns point-specific sensitivity information into formal unlearning guarantees, allowing the amount of noise to reflect the difficulty of the deletion request rather than the worst case. When training is deterministic, we derive explicit per-instance unlearning certificates. For noisy gradient descent, in the case of ridge regression, similar certificates are obtained through high-probability sensitivity bounds. Experiments on NYU-Depth with frozen DINOv2 features show substantial variation in deletion difficulty across points, and demonstrate that per-instance calibration can substantially improve utility over uniform worst-case calibration.

This article investigates the causal antecedents of conflictual language and the geometry of interaction in online threaded conversations related to climate change. We employ three annotation dimensions, inferred through LLM prompting and averaging, to capture complementary aspects of discursive conflict (such as stance: agreement vs disagreement; tone: attacking vs respectful; and emotional versus factual framing) and use data from a threaded online forum to examine how these dimensions respond to temporal, conversational, and arborescent structural features of discussions. We show that, as suggested by the literature, longer delays between successive posts in a thread are associated with replies that are, on average, more respectful, whereas longer delays relative to the parent post are associated with slightly less disagreement but more emotional (less factual) language. Second, we characterize alignment with the local conversational environment and find strong convergence both toward the average stance, tone and emotional framing of older sibling posts replying to the same parent and toward those of the parent post itself, with parent post effects generally stronger than sibling effects. We further show that early branch-level responses condition these alignment dynamics, such that parent-child stance alignment is amplified or attenuated depending on whether a branch is initiated in agreement or disagreement with the discussion's root message. These influences are largely additive for civility-related dimensions (attacking vs respectful, disagree vs agree), whereas for emotional versus factual framing there is a significant interaction: alignment with the parent's emotionality is amplified when older siblings are similarly aligned.

Sampling from discrete distributions is a ubiquitous task in machine learning, recently revisited by the emergence of discrete diffusion models. While Langevin algorithms constitute the state of the art for continuous spaces, discrete versions lack similar theoretical guarantees when the step-size becomes small. In this paper, we address this limitation by interpreting discrete sampling algorithms as discretizations of continuous-time dynamics on the hypercube. In particular, we describe several score functions for discrete algorithms which result in approximations of Glauber dynamics for the correct target distribution. We also compute upper bounds for the contraction of these algorithms, with or without Metropolis adjustment.

This paper provides statistical guarantees on the accuracy of dynamical models learned from dependent data sequences. Specifically, we develop uniform error bounds that apply to quantized models and imperfect optimization algorithms commonly used in practical contexts for system identification, and in particular hybrid system identification. Two families of bounds are obtained: slow-rate bounds via a block decomposition and fast-rate, variance-adaptive, bounds via a novel spaced-point strategy. The bounds scale with the number of bits required to encode the model and thus translate hardware constraints into interpretable statistical complexities.

We study the problem of detecting a planted star in the Erdős–Rényi random graph $G(n,m)$, formulated as a hypothesis test. We determine the scaling window for critical detection in $m$ in terms of the star size, and characterize the asymptotic total variation distance between the null and alternative hypotheses in this window. In the course of the proofs we show a condensation phase transition in the likelihood ratio that closely resembles that of the random energy model from spin glass theory.

What, if anything, should a frequentist say about a single realized confidence interval (CI) and its chance of having covered the parameter? Jerzy Neyman's original answer was to refuse any nondegenerate probability for coverage ex post and, instead, to "state that the interval covers". In this paper I argue that the usual frequentist machinery already supports a different reading. I treat the coverage event as a Bernoulli random variable, with the nominal level 1-alpha as its design-based success probability, and view "confidence" as a probability forecast for that Bernoulli outcome. Using strictly proper scoring rules, I show that 1-alpha is the unique optimal constant forecast for coverage, both before and after observing the data, and that it remains optimal post-trial in common unbounded, translation-invariant models with pivot-based CIs. When the design yields a theta-free statistic–such as the relative width of the interval in a finite-window uniform model–the conditional coverage given that statistic provides a nonconstant, design-based refinement of 1-alpha that strictly improves predictive performance. Two thought experiments, a Monty Hall-style shell game and the "lost submarine" example of Morey et al. (2016), illustrate how this perspective resolves familiar interpretational puzzles about CIs without appealing to priors or single-case subjective degrees of belief. I conclude with simple "what to do when you see an interval" guidance for applied work and some implications for teaching confidence intervals as tools for forecasting long-run coverage. Keywords: Confidence intervals, coverage probability, proper scoring rules, probabilistic forecasting, frequentist inference Disclaimer: The findings and conclusions in this report are those of the author and do not necessarily represent the official position of the Centers for Disease Control and Prevention