An agent updates her beliefs over a set of variables after observing some of them. We provide a representation of updated beliefs that captures limited propagation of her observation's implications through the directed acyclic graph that represents the relations between all variables. Failure of contingent thinking occurs when she performs fewer inference steps from unobserved variables than observed ones, leading to correlation neglect and violations of iterated expectations. Our framework offers a new perspective on existing experiments about contingent thinking and suggests new directions. We characterize the model's relationship with familiar Bayesian and non-Bayesian benchmarks, and illustrate it with applications to public-good provision and social learning games.

Sequential development of a new product or technology, or natural resource exploration, often progresses through ordered stages with uncertain rewards and requires costly (ex ante) planning to make future stages accessible. We model this process as an ordered Pandora's box problem where a decision-maker first chooses an initial scope, paying a cost that rises with the number of stages made accessible, and may later expand the scope at a marginal adjustment cost. Since the paid planning costs are sunk, the continuation values depend on the state variable ``paid scope''. We prove existence and uniqueness of scope-dependent reservation values, characterize the optimal search strategy as a threshold rule indexed by paid scope, and derive comparative statics. Interactions among three economic forces shape the optimal behavior -- a guarantee effect (a higher current best offer reduces the expected improvement from the next stage and induces earlier stopping), a paid-scope effect (a larger prepaid scope lowers the marginal cost of future access, raises the continuation value, and supports continuation at higher guarantees), and a remaining-horizon effect (fewer stages remaining shrink the option value of continuing). Two examples illustrate how these forces generate distinct planning and search patterns under normal and fat-tailed rewards.

We build a dynamic model of data-driven automation in which data (i) is heterogeneous and task-specific; (ii) accumulates endogenously as a byproduct of economic activity; and (iii) exhibits spillovers such that data generated by one task can augment the productivity of another. Along the transition path of automation, data plays a dual role in simultaneously augmenting the productivity of already-automated tasks and expanding the automation frontier. We derive tight conditions for the economy to be partially versus fully automated in the long-run. In the latter case, automation exhibits rich short-run dynamics that depend on the pattern of data spillovers but is always slow in the long-run: the share of tasks produced by labor decays asymptotically as a power law in time. We show that the economy is generically inefficient and analyze how a planner optimally tilts the direction of data accumulation. With endogenous capital accumulation, data-driven automation generates explosive growth but stagnant long-run wages.

The increasing proliferation of inverter-based resources (IBRs) in distribution networks is presenting a major challenge for phasor-based overcurrent protection. This challenge stems from IBRs' lack of short-circuit current sourcing capacity. As a result, traditional overcurrent protection functions (e.g., ANSI 51) are inadequate in such scenarios, and warrant alternative approaches. Time-domain protection, for example, shows promise in overcoming this challenge. In this paper we propose a pre-fault voltage discrimination (PVD) strategy whose role is to detect faults and discriminate normal switching and transformer inrush disturbances from actual faults. The use of PVD allows for the design of a simple, yet effective fault detection algorithm by using time-domain protection principles for distribution networks containing IBRs. The introduction of PVD provides for faster fault detection without reducing security and dependability. Offline simulation experiments and controller hardware-in-the-loop real-time simulation validate the effectiveness of the proposed algorithm against various fault and normal switching events.

Background and Objective: Continuous wearable electrocardiogram (ECG) monitoring is increasingly used for ambulatory arrhythmia surveillance, yet forecasting impending atrial fibrillation (AF) is challenged by inter-patient ECG variability. This study investigated whether personalizing a global model via fine-tuning on an individual's ECG signals improves short-term forecasting of impending AF. Methods: A global model trained on the ICENTIA11K dataset was compared against personalized models fine-tuned across three cohorts: ICENTIA11K, IRIDIA-AF, and MobiCARE. Following preprocessing, models processed 60-second ECG segments for a five-minute forecast horizon. We evaluated the impact of adaptation data volume and analyzed ECG features, such as heart rate and RMSSD. Results: Personalized models significantly outperformed the global model, achieving AUROCs of 0.711 vs. 0.614 in ICENTIA11K and 0.686 vs. 0.585 in MobiCARE. Personalization benefits increased with the amount of patient-specific fine-tuning data. While the global model's accuracy rose as AF onset approached, personalized models in the two external cohorts exhibited distinct temporal dynamics, which may indicate the capture of patient-specific characteristics less dependent on proximity to the AF event. Pre-AF episodes showed elevated heart rates and RMSSD. Feature attributions highlighted clinically relevant precursors, including frequent premature atrial complexes (PACs) and short supraventricular tachycardias (SVTs). Conclusions: Adapting deep learning models with patient-specific wearable ECG data significantly enhances short-term forecasting of impending AF. This personalized framework supports timely preventive interventions and improved AF management in ambulatory monitoring environments.

The Information Bottleneck (IB) is a well established framework that looks for a latent compact representation of a data source, by trading rate and data-size representation, for information accuracy with respect to another target data. The Gaussian IB (GIB) is its simple closed form solution, when the target is jointly Gaussian with the source. Actually, in many practical problems the latent representation has to be stored or represented by a finite number of bits, while the optimal (G)IB solution has not. First, this manuscript theoretically analyzes the effect of scalar and vector quantization of the GIB latent representation, and its impact on the (dis)informativeness with respect to the target data. Then, task-oriented quantization designs are proposed by (jointly) reformulating the GIB optimization problem under a finite-rate constraint on the latent representation. Simulation results on MMSE regression problems confirm the effectiveness of the proposed quantization designs, which show significant gains with respect to more heuristic, or separate, quantization designs of the standard GIB latent representation. Finally, the paper extends the task-oriented philosophy to non-Gaussian settings, by properly modifying the cost function used in variational auto-encoders (VAEs) of IB-inspired vector quantizers.

Recent research has explored integrating Large Language Models (LLMs) with speech encoders to create speech-augmented LLMs capable of contextualized speech recognition. The main challenge lies in aligning the semantic embeddings of LLMs with the acoustic representations of speech encoders. We propose a novel approach that teaches the LLM to first predict phonemes from the speech features before generating the final transcript. By integrating a phoneme prediction step directly into the LLM, the model develops a fine-grained knowledge of pronunciation, reducing acoustic confusion and improving transcription accuracy and explainability. Our method is cheap and simple, as phoneme targets can be automatically derived from existing transcripts. Through comprehensive experiments, we show that intermediate phoneme prediction can improve speech recognition, particularly in low-resource settings, and yields outputs that are acoustically more faithful to the speech.

Speech-aware large language models (LLMs) can incorporate speech through pre-trained acoustic encoders that project speech features into the LLM embedding space. While the choice of the speech encoder critically influences performance, different encoders often exhibit complementary strengths, motivating their combination. In this work, we investigate whether fusing multiple pre-trained speech encoders can enhance speech-aware LLMs for automatic speech recognition (ASR). We explore several fusion strategies beyond simple feature concatenation, including learned combinations and Transformer-based fusion architectures, and evaluate them across mono- and multilingual ASR settings as well as diarized speech recognition. Our results indicate that carefully fusing multiple parallel speech encoders improves downstream performance in all scenarios with limited computational overhead.

Speech recognition often fails on rare, domain-specific terms and context-related named entities. Existing contextualization techniques typically bias decoding with keywords or phrase lists, which does not scale well or exploit deeper knowledge. We propose a training method that teaches a speech-LLM to use broad descriptions (e.g. from videos) as weak semantic priors to perform contextual reasoning grounded in the audio. We build 400 hours of reasoning-augmented speech data by pairing erroneous hypotheses with video metadata and LLM-generated reasoning explanations that justify context-driven corrections. We finetune the speech-LLM to perform chain-of-thought reasoning: generate an initial transcript, then reason over the context, and finally return a corrected transcript. On held-out YouTube-derived test sets, our approach reduces errors, with specific improvements on rare words and named entities, and lays groundwork for deeper contextual reasoning in speech recognition.

The proliferation of text-to-speech (TTS) systems capable of generating realistic synthetic speech poses growing challenges for audio forensics. While binary deepfake detection has received considerable attention, source tracing (i.e., identifying which TTS system produced a given audio sample) remains underexplored, particularly in open-set scenarios where unknown systems may be encountered. We propose a metric learning framework based on the Proxy-Anchor loss function that operates on Wav2Vec2-BERT embeddings to learn a discriminative embedding space for TTS source attribution and out-of-distribution (OOD) detection of unseen systems. We evaluate it on the MLAAD v9 dataset spanning 140 TTS systems across 51 languages, and introduce an architecture merging strategy that groups TTS system versions into unified classes, reducing inter-class confusion. Our system achieves 99.76% accuracy on 110 in-distribution classes and a False Positive Rate (FPR@95) as low as 2.04% for OOD detection. Also, for a fair comparison against the current state of the art, we further evaluate it on the MLAAD v5 official dataset splits, improving the OOD accuracy by almost doubling it. These results demonstrate that Proxy-Anchor metric learning, combined with architecture-aware class design and post-hoc OOD scoring, provides an effective framework for forensic TTS source tracing in both closed-set and open-set settings.

To address the heavy-tailed, spike-prone nature of sea clutter and the scarcity of labeled target data, an unsupervised complex-valued variational autoencoder (VAE) for maritime radar target detection is proposed. In implementation, each complex baseband slow-time sequence is represented by its in-phase and quadrature components, and the model learns their joint reconstruction from clutter-only data. A Student-\(t\) negative log-likelihood is adopted to capture heavy-tailed reconstruction errors while reducing sensitivity to outliers during clutter learning. In addition, a time-domain amplitude error constraint is introduced to penalize slow-time magnitude mismatch in the reconstruction. At inference, reconstruction deviation is used as the detection statistic, and the decision threshold is set via an empirical quantile estimated from a clutter-only validation set to enforce a constant false-alarm rate (CFAR). Experiments on measured sea-clutter data show that detection performance is consistently improved over MF, AMF, and a real-valued \(β\)-VAE under CFAR constraints.

Transformer-based Speech Foundation Models excel in most Automatic Speech Recognition tasks but often suffer performance degradation when applied to domains with mismatched acoustic characteristics. While Parameter Efficient Fine-Tuning (PEFT) methods, such as Low-Rank Adaptation (LoRA), adjust global attention, they lack the local context modeling crucial for capturing domain-specific variations. We propose GC-LoRA, a novel adapter architecture that injects Conformer-style local convolutional processing into pretrained Transformer encoders. By integrating a lightweight adapter to encoder attention output projections, our method efficiently captures local acoustic dependencies without disrupting pretrained global representations. Experiments across diverse datasets (acoustically-degraded, bandlimited, dialectal, child) demonstrate the efficacy of our approach, achieving Word Error Rate (WER) reductions of up to 10.9% compared to baselines while adding minimal trainable parameters.

Purpose: To develop an automatic dipole inversion method for quantitative susceptibility mapping (QSM) that preserves fine anatomical structures without the need for manual regularization-parameter tuning. Theory: The original approximate message passing with parameter estimation (AMP-PE) framework models image gradients with a single Laplace prior, which does not fully capture the heavy-tailed gradient distribution of brain susceptibility maps. This prior mismatch can lead to over-regularization and blocky reconstructions. We address this limitation by modeling the gradients with a two-component Laplace mixture prior. Methods: We propose a Laplace-Mixture Dipole Inversion (LAMDI) method by incorporating a two-component Laplace mixture prior into the AMP-PE framework with automatic parameter estimation. LAMDI was evaluated on a public in vivo dataset. Its performance was compared with FANSI, MEDI, and AMP-PE with a single-Laplace prior (AMP-PE-L1) under both standard default and reference-tuned settings. Results: On a public multi-orientation QSM dataset, LAMDI achieved NRMSE and SSIM comparable to AMP-PE-L1 while substantially reducing HFEN, suggesting improved preservation of high-frequency anatomical detail. Under reference-based tuning, FANSI and MEDI achieved the best performance for some metrics, but LAMDI remained competitive without requiring reference maps or manual regularization tuning. Conclusion: LAMDI provides an effective and automatic parameter-estimation alternative for QSM dipole inversion by combining competitive reconstruction accuracy with improved preservation of fine anatomical detail.

Reconfigurable intelligent surfaces (RIS) enable programmable control of wireless propagation but remain vulnerable to persistent deep fades in static deployments. This paper introduces a Movable Antenna-enhanced RIS (MA-RIS) architecture where antenna elements physically reposition to sample independent spatial channels, enabling mobility-induced diversity. We model antenna motion using a Stochastic Differential Equation (SDE) framework capturing controlled drift and environmental diffusion. It^o calculus-based analysis characterizes steady-state antenna distributions, spatial decorrelation, and outage probability, revealing fundamental trade-offs between control strength and mobility randomness. To maximize long-term SNR while accounting for control overhead, we propose an overhead-aware Two-timescale framework separating slow antenna trajectory control from fast phase adaptation. The stochastic optimal control problem is solved via predictive approximation of the Hamilton-Jacobi-Bellman (HJB) formulation, enabling real-time implementation. Simulations validate theoretical predictions: the Two-timescale strategy achieves up to 36 dB steady-state SNR with remarkable stability, outperforming position-only control by up to 15 dB and uncontrolled baselines by over 30 dB. Despite experiencing a lower SNR than Active RIS, the proposed approach delivers up to 16 times higher energy efficiency (EE) across varying system scales, establishing a new paradigm of mobility-enabled channel adaptation for resilient wireless systems.

In this paper, the problem of using curved beams to improve wireless communication performance in the presence of a blockage is studied. In particular, a transmitter equipped with a continuous aperture array can generate curved beams to serve multiple receivers by allowing signals to propagate along both straight and curved paths. To optimize the weighted sum-rate, a curved beam model is developed for controlling the beam steering, beam focusing, and beam curving functions, along with a segmented channel model to characterize practical channels induced by the blockage. Based on the introduced curved beam model, an optimization problem is posed with the goal of maximizing the weighted sum-rate of all users under a transmit power budget and physical constraints of curved beams. To solve this problem, the continuous aperture is first converted into finite summations via a discrete sampling of the continuous coordinate. Then, the performance gap between the ideal continuous aperture design and its practical discrete aperture approximation is analyzed. Based on the above discrete approximation, an iterative algorithm is developed to optimize curved beam control parameters. In particular, the original problem is reformulated as a trackable form via fractional programming (FP). Then, the transformed problem is solved by designing an enhanced block coordinate ascent (BCA) method which determines a surrogate-construction point leveraging the local descent from previous iterations, thereby accelerating convergence. Then, a proximal regularization term is included into the surrogate function to control the update magnitude and suppress aggressive update, thereby improving updates stability. Finally, the beam amplitudes are computed based on the effective channel gains. Simulation results show that the proposed method can improve the weighted sum-rate compared to using only straight beam.

This paper investigates human pose estimation from Orthogonal Frequency-Division Multiplexing (OFDM) signals in an indoor multistatic wireless network operating in the 6 GHz band. We design and validate a processing pipeline that exploits both the amplitude and phase of the Channel State Information (CSI) from multiple radio links to estimate the human body pose. Four deep learning architectures from the literature, namely DT-Pose, MetaFi++, HPE-Li, and VST-Pose, are adapted to the OFDM CSI structure and extended to jointly exploit the amplitude and phase information. The models estimate the pose of a human walking within the network coverage area. Performance evaluation is conducted on an open-access dataset using standard pose-estimation metrics such as Procrustes-aligned Mean Per-Joint Position Error (PA-MPJPE) and Bone Length Loss (BLL). Results indicate that reliable human pose reconstruction can be achieved from 6 GHz OFDM CSI measurements, with DT-Pose providing the best overall accuracy. On average, amplitude-only CSI yields performance comparable to joint amplitude-phase processing, whereas phase information is more beneficial as a complementary feature rather than as a standalone input.

Post-treatment variables (PVs), such as treatment noncompliance, behavioral responses, intercurrent events, often modify the ultimate treatment effect on the primary outcome. However, existing methods provide limited tools for studying treatment effect heterogeneity with respect to PVs. Conventional heterogeneous treatment effect estimands condition on baseline covariates. However, similarly conditioning on the observed PV can induce endogenous selection bias for the treatment effect estimation. Principal stratification offers a rigorous framework for studying principal causal effects across principal strata, but principal strata are latent and their identification often requires stringent assumptions. This paper develops an assumption-lean empirical stratification framework for characterizing treatment effect heterogeneity with respect to PVs. We define empirical scores using the predicted potential PV responses based on baseline covariates, and use the empirical scores to construct empirically accessible subgroups. The resulting empirical-stratum treatment effects (ETEs) are identifiable under standard causal assumptions. We connect the proposed framework to principal stratification by showing that the average ETE recovers principal causal effects under the principal ignorability assumption, but remains informative under violations of this assumption. We further introduce projected ETE curves and develop efficient influence function-based estimators for the semiparametric inference. We illustrate the proposed framework with two real-world applications.

Images represent objects characterized by contours and textures. From a statistical perspective these features can be defined as observations of continuous random functions. However, most existing approaches rely on pixel-based discretizations which lead to high-dimensional representations and heavy computational costs. In this note, we introduce an alternative more frugal representation. This representation assumes that the object has a star-shaped domain interior. Under this condition, we explore the analysis of images from a functional data analysis perspective. The proposed framework is illustrated on a real data supervised image classification problem.

Joint Models for longitudinal and time-to-event data are frequently used to model endogenous longitudinal covariates alongside a time-to-event outcome. However, the model class borrows some limitations of the survival submodels, including the necessity for non-separation for each category of categorical covariates. We therefore incorporate Firth's correction into the frequentist estimation procedure of joint models in order to make the model class applicable in settings with separation cases. We derive the needed quantities for the correction term and implement it in the Expectation-Maximization Algorithm for the parameter estimation in joint models. Our simulation study shows, that in data situations with separation issues, the Firth-corrected estimation procedure yields less biased estimates and the respective coefficients approach the estimated values observed in the non-separation cases. The application on a data set on satisfaction with and dropouts from vocational training demonstrates the advantages of the Firth-corrected joint model in a real world data set with separation. The results add to the literature on dropout from vocational training in Germany by explicitly modeling direct effects of socioeconomic and training-specific factors on the risk of dropout as well as their indirect contribution via satisfaction with the training.

The under-representation of women as sources cited in news media is one prominent representation of gender bias. Understanding where gender bias concentrates and how it evolves is essential for targeted mitigation. Because gender representation varies across topics, time, and reported-on regions, creating complex dependencies that are difficult to capture parametrically, we employ a nonparametric model to uncover latent cluster structures and temporal dynamics. We combine time-dependent Bayesian mixture modeling techniques with a Beta mixture kernel tailored to female quote shares, bounded between 0 and 1. Fitted on Canadian news articles from 2019 to 2024, the model reveals structural under-representation of women across all clusters, with news topic driving differences in female quote shares more strongly than the reported-on region. More than 85% of topic-region time series show no improvement toward gender parity over the observation period. Dynamic density estimation confirms that the aggregate distribution of female quote shares remains stable between 2019 and 2024. Our application demonstrates that advanced probabilistic models not only reproduce findings in gender bias research but also reveal latent dependencies and structural patterns that simpler approaches miss, encouraging future adoption of model-based frameworks for studying media bias.

This paper proposes a two-sample homogeneity test based on entropic optimal transport (EOT) maps from a common reference distribution -- the uniform law on the unit ball. The test statistic is the squared $L^2$-distance between the two empirical EOT maps. For fixed entropic regularization parameter, we prove that the population map discrepancy is identifiable, derive a functional central limit theorem for the empirical map difference under the null, and establish the Gaussian quadratic-form null limit. We also prove consistency against fixed alternatives and characterize local asymptotic power under contiguous alternatives. A weighted multiplier bootstrap is proposed to calibrate the non-pivotal null distribution, and its validity is established. Extensive simulations demonstrate that the proposed EOT-map test has reliable finite-sample size control and exhibits competitive power compared with other existing methods. The method is particularly powerful for location alternatives and, beyond a single scalar discrepancy, it provides additional diagnostic information on how the two distributions differ. Finally, a real data application concludes the paper.

High-dimensional discrete data arise in many contemporary applications, including genomics, microbiome research, survey studies, and digital behavioral analysis. Clustering such data remains challenging because existing methods are often computationally demanding, sensitive to sparsity and discreteness, or designed for specific data types. We propose a deterministic dimension-reduction framework for clustering high-dimensional discrete observations. The method compresses each observation into a low-dimensional continuous representation through weighted sums defined by a scaled positional encoding, yielding a numerically stable transformation applicable to binary, categorical, and count-valued data. We establish several theoretical properties of the proposed compression. The mapping is injective, ensuring that distinct observations remain distinct after compression. Under mild regularity conditions, the compressed variables admit an approximate Gaussian representation, providing a theoretical basis for model-based clustering in the compressed space. We further show that separation between cluster centroids is preserved under compression, implying that location-driven cluster structure remains identifiable after dimension reduction. Extensive simulation studies demonstrate accurate cluster recovery across a wide range of realistic settings. The proposed approach is also computationally efficient, providing substantial speed improvements over commonly used dimension-reduction techniques often used in conjunction with clustering. Applications to Irish baby-name records and microbiome data further illustrate its practical utility. The proposed framework offers a scalable, computationally efficient, and broadly applicable approach to clustering high-dimensional discrete data.

Objective. Longitudinal datasets frequently contain missing weight and height measurements, and studies that combine data sources may index measurements against different growth reference standards (e.g., the WHO reference and CDC charts). We describe and evaluate a reproducible two-stage method that imputes missing anthropometry while making the choice of reference standard an explicit parameter. Methods. Stage 1 applies within-subject linear interpolation across visit dates (interior gaps only, no extrapolation). Stage 2 imputes remaining values from an age- and sex-specific growth reference using the LMS method by estimating each subject's centile, carrying it forward and backwards within the subject, defaulting to the 50th centile when a subject is never measured, and reading the expected value off the reference at the visit age. Different references can be supplied per data source so that the standard applied is recorded and auditable. We assessed recovery accuracy by masking and re-imputing a random 20% of observed values. All evaluations used computer-generated synthetic data. Results. On synthetic data (n = 60 subjects, 288 visits, 30% missing), the method resolved missingness to 100% completeness. Masked-value recovery gave a mean absolute error of 1.78 kg for weight (3.5% mean absolute percentage error) and 2.84 cm for height (2.0%), with negligible bias. Values recovered by within-subject interpolation were more accurate than those recovered from the growth reference, as expected, supporting the two-stage ordering. Conclusion. The method offers a simple, dependency-free, and auditable approach to anthropometric imputation, with explicit handling of differing reference standards and per-value provenance. Application to empirical data and propagation of imputation uncertainty into downstream models are the necessary next steps before use in substantive analyses.

In large-scale complex surveys such as the National Health and Nutrition Examination Survey (NHANES), some outcomes are measured only in selected years, leaving incomplete records across survey waves. We develop a weighted conformal prediction framework that enables valid population-level prediction of unobserved outcomes using information from earlier surveys. The method accommodates covariate shift, where both continuous and categorical covariate distributions evolve over time while survey design affects representativeness. It integrates subgroup-specific density ratio and subgroup-proportion estimation to approximate likelihood ratios between the historical and target covariate distributions, and we establish coverage guarantees for the resulting prediction sets. Simulation studies and an application predicting low-density lipoprotein cholesterol (LDL-C) for the current U.S. population show that the proposed approach achieves coverage close to the nominal level and improved efficiency over existing methods, particularly when covariate distributions are complex or unknown.

Predictive Bayesian model comparison often relies on leave-one-out (LOO) cross-validation criteria such as the expected log predictive density (ELPD). However, model rankings can be overly sensitive to outliers and tail mismatch because ELPD is based on the log score. We propose a score-matched generalized ELPD framework that replaces the log score by a Bregman scoring rule to update model parameters through a generalized posterior and to evaluate LOO predictive utility. Candidate posterior predictive distributions are ranked by out-of-sample utility under the chosen scoring rule, yielding a direct proper-score generalization of standard ELPD. We focus especially on the $β$-divergence family, where $β$ controls the sensitivity of predictive comparison to low-density observations. Under model misspecification, the procedure asymptotically selects the model whose predictive distribution is closest to the data-generating process under the chosen Bregman divergence. A simulation study and applications to microbial and forensic data show that the generalized ELPD can change the selected model through reduced sensitivity to low-density observations.

In many decentralized supply chains, upstream firms do not observe market demand directly and instead infer downstream conditions from the order stream. A retailer's replenishment policy therefore plays a dual role: it governs inventory replenishment and shapes the information available for upstream forecasting. This creates a fundamental trade-off. Smoother orders improve upstream predictability, but delaying the response to demand can increase downstream inventory costs. We study how a retailer should optimally smooth demand in a two-tier supply chain with one retailer and one manufacturer when the manufacturer forecasts future orders from the retailer's order history. We propose Binomial Smoothing, a class of replenishment policies that implements delayed demand response by spreading each unit of demand over a finite horizon using binomial weights. The class is interpretable, easy to calibrate, and analytically tractable. Under weakly stationary Gaussian demand satisfying mild regularity conditions, we show that, for any fixed smoothing horizon, the Binomial policy minimizes the manufacturer's forecast error among all policies with the same degree of smoothing. It remains invertible, so the manufacturer can recover demand history from observed orders. More generally, Binomial Smoothing achieves a constant-factor approximation guarantee relative to an optimal policy. Our results yield a broader insight: replenishment policies should be designed not merely to reduce order variance, as in the traditional bullwhip measure, but to reduce the unpredictable component of orders. Carefully designed smoothing can improve supply-chain performance and partially substitute for information sharing, providing a concrete mechanism for coordination without collaboration.

Obtaining precise erosion measurements requires costly fieldwork, making it infeasible to directly survey large domains such as a province or river basin. To extend fieldwork results across such extensive domains, we propose a novel spatial prediction method that treats local erosion distributions as objects in the Wasserstein space. These distributions are mapped into square-integrable trajectories and represented via basis expansion, forming a multivariate random field that captures spatial dependence. By applying local regression and Kriging in this representation, our approach flexibly models and predicts erosion distributions at arbitrary locations. This framework improves prediction for functionals of the distribution, such as the mean and exceedance probabilities. Simulation studies demonstrate that the proposed method outperforms a misspecified parametric alternative and existing Fréchet regression approaches. We illustrate the approach with a detailed erosion analysis in Shaanxi province, China, where local measurements from surveyed watersheds are extended to predict erosion distributions across the entire province using covariates such as land use and elevation.

Covariate measurement error is pervasive in epidemiological research and distorts estimated exposure-outcome associations, yet correction methods have been studied almost exclusively under linear modelling assumptions. Their behaviour when the underlying association is non-linear and is itself estimated with flexible regression, remains poorly characterised. We report a blinded, multi-stage neutral comparison simulation study, conducted within the STRATOS initiative, evaluating measurement error correction coupled with flexible modelling of functional form. Six families of correction methods (pointwise and coefficient-based Simulation Extrapolation [SIMEX], Bayesian inference on the logit and risk scales, Multiple Imputation [MI], and Regression Calibration [RC]) were each combined with B-splines (BS), penalised splines (PS), fractional polynomials (FP), and natural splines (NS), yielding 23 analytic methods. Methods were applied to case-control data generated under five functional forms (J-shape, linear, two threshold models, and saturation) across simulated datasets spanning varying sample sizes, replication substudy sizes, error magnitudes, and error distributions, with classical additive error and a replication substudy for error calibration. Performance was assessed by the log mean squared error of the estimated function over the central 95 % of the exposure distribution. Pointwise SIMEX was the most accurate and most robust approach overall, followed by Bayesian methods and RC when paired with PS, FP, or NS; MI performed less well, and Bayesian estimation with unpenalised BS performed worst. PS, FP, and NS were near-equivalent, whereas BS was consistently inferior. No single method dominated across all scenarios, underscoring the value of sensitivity analyses.

We study distributional data under sparse sampling where each unit is represented by a probability distribution on the real line observed only through a small i.i.d.~sample. A natural notion of central tendency for one-dimensional distributional data is the Wasserstein barycenter, whose quantile function is the pointwise average of the unit-level quantile functions. We focus on pointwise estimation of the Wasserstein barycenter quantile function: at a given quantile level, the target is the population mean of the corresponding unit-level quantiles. A naive plug-in estimator is the empirical Wasserstein barycenter, which treats observed unit-level empirical distributions as the true latent unit-level distributions. Under sparse sampling, however, this estimator can be severely biased. We propose an approach that avoids directly estimating either the unit-level distributions or the full population law of distributions. We start with the more ambitious goal of characterizing the distribution of latent unit-level quantiles at a given quantile level. We show that this distribution can be written in terms of the marginal distributions of the unit-level CDF values, which can be estimated using binomial mixture methods. This motivates our estimator, the marginal-constructed barycenter (MCB) estimator, obtained by taking the mean of the estimated distribution of latent unit-level quantiles. We establish conditions under which the MCB estimator is pointwise consistent and asymptotically normal, and show through simulations that it can substantially outperform the empirical Wasserstein barycenter under sparse sampling. We illustrate the method in an analysis of HIV-1 sequence data from the HVTN 502/503 vaccine efficacy trials, using the barycenter to summarize and compare within-participant distributions of viral sequence features when only a small number of sequences are available per participant.

Embedding a standardized whole-person health measure in electronic health records (EHR) could be instrumental to preventative care. The allostatic load index (ALI), calculated from ten component stressors across three body systems, offers a promising snapshot of holistic health. The ALI can be calculated from EHR data, but many components are missing, since not all patients undergo all tests. Using statistical modeling and machine learning, EHR data for $1000$ patients from a large academic health system were used to predict in-patient hospitalization (as a count or binary) from ALI, controlling for age and sex. Various methods were evaluated to fill in information gaps for patients' missing ALI components, including summary measures combining components or using them separately. Performance was measured using receiver operating characteristic (ROC) curves and corresponding areas under the ROC curve (AUC). Count modeling of hospitalization did not improve upon binary, and logistic regression beat random forest. Overall, summary measures performed similarly, with the complete-case proportion (i.e., the proportion of non-missing components that were "unhealthy") performing best (AUC $= 0.64$) but by $\leq 0.01$. When using components separately, the pattern submodel approach most accurately predicted hospitalization (AUC $= 0.73$) in sample, but did not cross-validate as well (AUC $= 0.63$). All summary measures performed similarly. However, when including the ALI components separately, tailoring models to subsets of patients with the same missing data pattern performed best. Next steps include EHR implementation to enable prediction and support clinician decision-making at scale.