Papers

Neural emulation need not require learning a substitute for known physics. We investigate PolyNets that couple a continuous-time neural representation of polynomial dynamics with a simple recurrent network for discrete-time integration. When the governing coefficients are known, the resulting tensor graph requires no training and preserves the prescribed numerical scheme while enabling efficient hardware execution and parallel simulation. Using the one-dimensional Korteweg-de Vries equation, we compare PolyNet with CPU and GPU finite-difference Runge-Kutta solvers and three trained neural models: a state-map emulator, a physics-informed predictor, and a learned-tendency integrator. Analytical soliton solutions provide a reference for amplitude and phase errors across grid resolutions, 10^6 dispersively scaled time steps, ensembles of up to 10^4 trajectories, and varying initial amplitudes. PolyNet achieves accuracy comparable to the numerical solvers, including at amplitudes outside the learned models' training conditions. It combines this fidelity with high GPU throughput, approximately constant over the tested resolution range, and favorable ensemble scaling.

AI weather prediction (AIWP) models have emerged as a key complement to physics-based numerical weather prediction (NWP) models, and now often outperform them on aggregate skill. Yet, several studies report that physics-based models still forecast extreme events better, in particular record-breaking extremes, based on the evaluation of deterministic forecasts. Here we evaluate heat extreme forecasts from probabilistic AIWP models over global land and show that they clearly outperform the ECMWF IFS ensemble, both raw and post-processed, including for record-breaking events, in all regions and at all lead times considered. AIWP models better forecast the occurrence and intensity of extremes, are better calibrated in the tail and miss fewer records. Station observations confirm these results. We argue that many reported AIWP limitations stem from unsuitable verification choices, specifically comparing deterministic forecasts that target different quantities. Instead, a fair evaluation of extremes necessitates probabilistic verification.

Technological progress can give rise to new loss exposures or reduce existing risks. In either case, it strongly affects insurance companies' existing lines of business. As the magnitude of such effects is often closely connected to the innovation's market penetration, reliably predicting its adoption process is vital in enabling insurers to adapt their business strategy accordingly. To tackle this challenge, we propose a novel combination of contributions from the domain of innovation diffusion. Our methodology generates adoption scenarios that holistically account for different sources of uncertainty, offers a structured way to incorporate expert judgment and insights from pre-existing technologies, and updates its predictions as new information on the technology's diffusion becomes available. Its modular nature ensures that components can be easily replaced by suitable alternatives. Using publicly accessible data on privately-owned battery electric vehicles in Germany, the application of our approach for predicting changes to insurance losses and for supporting insurers' sustainability strategies is visualized in a motor insurance case study.

Discrete directional data exhibiting p-fold rotational symmetry, where directions separated by integer multiples of 2{\pi}/p are equivalent, arise in various applications but are often modeled using continuous distributions. In this article, we develop two general methods for constructing distributions for such data: symmetrization and folding of discrete circular distributions, and wrapping of discrete linear distributions. Particular models arising from these constructions are studied, together with their properties and estimation methods. For axial sand-grain orientation data, the proposed models are compared with discretized continuous axial distributions, whose category probabilities require numerical integration. The proposed models attain smaller Akaike information criterion values among the models considered while allowing direct likelihood evaluation without numerical integration. The framework is also applied to binned Manhattan street-orientation data, demonstrating its applicability to higher-order rotational structures, specifically the 4-fold case.

This paper introduces a new cumulative residual Rényi entropy (CRRE), which addresses limitations of the existing cumulative residual Rényi entropy. The conventional measure suffers from two primary drawbacks: its failure to converge to the cumulative residual entropy (CRE) as the order parameter approaches unity, and its lack of guaranteed positivity. Our proposed CRRE resolves these issues, offering a theoretically consistent and always nonnegative measure of uncertainty in residual lifetimes. We explore its mathematical properties, including its relationship with existing information measures. Furthermore, the concept is extended to its dynamic version, and its time-dependent characteristics are investigated. A non-parametric estimator of the proposed CRRE is developed, its almost sure convergence is established, and is validated through Monte Carlo simulation. The effectiveness of CRRE as a tool for quantifying uncertainty is confirmed through its application in chaotic theory and financial data.

Functional brain aging is often characterized by differences between people of different ages, although aging unfolds within individuals. This distinction is especially important for functional connectivity, where the direction of covariance change may evolve across adulthood. We introduce a Bayesian longitudinal covariance-operator framework that models each visit covariance as a latent positive-definite state informed by repeated resting-state fMRI runs. The approach calibrates run-level information for temporal dependence and replicate variability, separates within-person aging from between-person age differences, and uses an adaptive tangent representation to learn the low-dimensional structure of longitudinal change without relying on pooled covariance variation. The longitudinal operator varies smoothly in magnitude and orientation with age, while exact Fréchet derivatives translate the fitted trajectory to the covariance scale. This framework allows us to examine how brain covariance organization changes within individuals, whether longitudinal aging follows the population age gradient, and which functional systems contribute to their divergence. In the Dallas Lifespan Brain Study, within-person covariance aging differs substantially from the cross-sectional age gradient through early and middle adulthood, with the discrepancy diminishing later in life. Covariance reorganization is strongest around midlife, and the longitudinal signal is concentrated in a few coordinated directions, with most off-diagonal change occurring between functional systems. These findings demonstrate that population-level signatures of brain aging do not necessarily reflect individual aging trajectories and highlight the importance of modeling longitudinal covariance change directly.

A group does not usually consult all its members before every decision. This paper develops a quantitative framework for measuring how widely members are consulted in decision making within a group. Two kinds of records are considered: the number of members consulted for each decision and the number of decisions in which each member is consulted. From these records, two participation indices are defined, and their equality is proved analytically. A third index measures the fraction of decisions for which at least a specified percentage of members are consulted. The distribution of consultation levels is described using a discrete maximum-entropy model from statistical physics. Tail probabilities are used to obtain bounds for the main participation index. This study examines aggregate survey data from two groups. Their observed characteristics are broadly consistent with the patterns found across the full survey. Using binomial and Poisson calculations, the future probability that all members will be consulted for a decision is examined. Inequality in consultation among members is examined through Lorenz curves, the Gini coefficient and a normalised Shannon participation measure. The member-decision structure is represented as a bipartite network. Controlled simulations show that the same overall level of consultation can have different distributions among the members. The framework measures both the overall breadth of consultation and how consultation is distributed among the members. It therefore provides a quantitative sociophysical description of one measurable aspect of democracy in decision making within a group.

Anaerobic digestion (AD) models can be challenging to calibrate against real data due to limited practical identifiability, data scarcity, and model complexity. Weighted least squares objective functions and gradient-based solvers using finite differences are often used in literature, but result in suboptimal parameter estimates and large uncertainty bands. This paper identifies the parameters of a reduced-order ADM1 by comparing the frameworks of maximum likelihood estimation (MLE) and Bayesian inference (BI), and quantifies uncertainties of parameters and outputs. Multirate experimental data are taken from a lab-scale AD reactor fed with agricultural substrates and operated at organic loading rates of 3$\,$g VS $\mathrm{m^{-3}d^{-1}}$. Global optima are found via global and gradient-based local search algorithms using forward sensitivities. Enhanced scatter search provides the best global search results. These are refined by the Gauss-Newton algorithm as the best local search, which delivers $R^2$ values of 0.95 for acetic acid and 0.77 for biogas production. BI yields substantially narrower uncertainty bands than MLE and avoids the need for a global search by incorporating prior knowledge about parameter distributions. The search space is captured efficiently by log10 scaling of parameters. Algorithmic details on its implications are provided. Despite a high-resolution lab-scale dataset, the ADM1-specific inhibition parameter $K_\mathrm{I,nh3}$ is practically not identifiable with MLE, and shows a low output sensitivity, whereas a parameter for the effective ion concentration shows superb practical identifiabilty at high confidence with both MLE and BI. The present work lays a scalable base for calibration of nonlinear AD models by providing reliable simulations. It thus advances model-based monitoring and control applications of multirate processes such as agricultural AD plants.

Mortgage credit risk may exhibit dependence across economically connected areas, even when they are geographically distant. However, current models typically represent cross-area dependence through fixed geographical neighbourhoods, potentially overlooking economic connections that extend beyond physical proximity and evolve over time. These models may fail to capture shared risks among geographically distant but economically similar areas, and cannot describe a changing dependence of risk; it therefore risks retaining economically obsolete connections while omitting newly emerging ones. This paper uses similarities of industrial composition as a measure of economic proximity and develops a discrete-time survival model with dynamic industrial graphs to capture evolving cross-area dependence in mortgage default risk. The resulting graphs are reconstructed annually, allowing both their topology and edge weights to change as regional industrial compositions evolve. Jointly combining a proper conditional autoregressive process with a first-order autoregressive process governs the temporal cross-area dependence and the temporal persistence in latent risk simultaneously. The model is estimated using Integrated Nested Laplace Approximation and evaluated on U.S. mortgage loan-level data against the static industrial graph specifications. The results show that the proposed dynamic model achieves better in-sample fit and out-of-sample discrimination, while its estimated parameters indicate substantial graph-induced cross-area dependence and temporal persistence. These findings demonstrate the value of allowing economically defined neighbourhoods to evolve when modelling mortgage default risk.

Impact-echo testing is a nondestructive testing method used to detect internal defects in concrete structures. However, boundary reflections, structured interference, and measurement noise can produce complex Fourier amplitude spectra, making defect classification difficult. We constructed a two-dimensional frequency–amplitude persistence image (FA-PI) from the Fourier amplitude spectrum. Using a fixed parameterization of exact multi-parameter persistent homology, each retained Fourier component is represented with frequency-bin location as one coordinate and amplitude as the other, and Gaussian kernels are then applied in this two-dimensional space. This construction has a direct analytical connection to the corresponding one-dimensional Gaussian-smoothed Fourier amplitude spectrum. FA-PI was evaluated on an experimental backfill-void dataset and a public bridge-deck impact-echo dataset, and compared with raw and Gaussian-smoothed Fourier amplitude spectra using a linear classifier with a Softmax output and identical signal-level data splits. The evaluation included original signals and signals corrupted by Gaussian noise, sinusoidal interference, or mixed noise, with matching noise types and signal-to-noise ratios during training, validation, and testing. Performance was assessed using accuracy and macro-averaged precision, recall, and F1-score. Across the two datasets, FA-PI consistently outperformed the raw and Gaussian-smoothed Fourier baselines in the noisy-condition summaries. These findings indicate that representing Fourier spectral components in a two-dimensional frequency–amplitude space can improve impact-echo defect classification beyond frequency-axis smoothing alone.

Every October, the Nobel Prizes in Physics, Chemistry, Physiology or Medicine and Economic Sciences are announced, with one to three prizes in each discipline. Of the 769 Laureates (since 1901) in these four disciplines only 4% are women (30 Laureates). In 2026, there are eight Laureates within these disciplines and they are all men. Based on historical data across four fields and a Bayesian hierarchical model, we update the 8 year old model on bias in Nobel Prizes and confirm the gender gap, with exceedingly large confidence.

Climate-intensified hurricanes disrupt urban mobility, yet whether recovery is equitable across the rural-urban gradient is unclear. Analyzing device-based mobility for Hurricanes Helene and Milton, we find local activity restarted within approximately 4.5 days in both storms, whereas reconnection to the outside world took 5 days in coastal-urban Florida but 11 in inland-rural Appalachia. The gap lies in external reconnection, not local restart, implying planners should target rural isolation.

Unsupervised clustering is widely used to discover underlying group structure, after which researchers often seek to validate these groups via post-hoc hypothesis testing on the population means. However, using the same data both to form clusters and to test for a difference in means inflates the Type I error rate. Recent work in selective inference has proposed solutions when the underlying data are drawn from a multivariate Gaussian distribution with a known covariance matrix or an unknown isotropic covariance matrix. We propose a new selective test for the difference in means between two clusters that provably controls the Type I error rate under an arbitrary unknown covariance matrix. Our test statistic does not require estimating the feature covariance matrix; instead, it leverages a Monte Carlo sampling procedure over the set of orthogonal matrices. We show that this new selective test can be computed efficiently, and we derive closed-form solutions when clusters are formed using k-means or hierarchical clustering. In simulations, we demonstrate that our proposed p-value controls the selective Type I error rate and achieves substantial power, and we illustrate its application on gene expression and drug review data sets.

Although the frequentist versus Bayesian debate has a long-standing history, and both are well-established approaches for inference, they are often considered separately in pharmacometric literature, with their theoretical and practical differences receiving limited direct comparison. We address this gap by providing a conceptual background and comparative evaluation of frequentist and Bayesian methods for parameter inference in pharmacometrics. First, we highlight the theoretical and algorithmic differences between approaches within a general and pharmacometric context. We then apply both to classical compartmental pharmacokinetic models using simulated and real data; initially through evaluating four inference methods (two frequentist, two Bayesian) across a range of simulated data conditions, followed by investigating each inference approach in the practical setting. The simulation studies facilitate evaluation of the sensitivity of the methods to sample size, number of observations, residual noise and inter-individual variability, comparing the performance with respect to relative error, confidence/credible interval coverage and bias in the estimated variability. The real-world data analysis further highlights how each approach quantifies and presents uncertainty estimates by examining this for both the parameter estimates and system dynamics. By providing a theoretical and practical comparison that highlights the similarities and differences between approaches, this work aims to lower the barrier to understanding and implementing Bayesian and frequentist inference in pharmacometrics.

The Kullback–Leibler (KL) divergence is the expectation value of the log-likelihood ratio between two specified models, evaluated with respect to one of the two models. It provides an average measure of the distinguishability of the models. We examine its connection to discovery potential and the accuracy of parameter estimates when one model represents a null hypothesis, and the alternative is a family of models characterized by one or more continuous parameters. For data drawn from a multivariate Gaussian distribution, we derive the log-likelihood-ratio distribution and its cumulants under two such hypotheses. We then search over the alternative model's parameter space and use peak prominence, the height of a likelihood-profile peak above its surrounding baseline, as an operational detection statistic. Repeating this search on simulated data drawn from the null model allows us to calibrate the prominence threshold for a specified false-positive rate. We study a toy Gaussian model as well as three cosmological examples involving cosmic topology, the tensor-to-scalar ratio, and dark energy. In all these cases, detectability of a particular model depends not only on KL divergence, but also on the size of the model parameter space, the likelihood-ratio distributions, and the distance of the model from any parameter space boundaries. The relationship between KL divergence, discovery potential, and parameter estimation must therefore be calibrated for each family of models and detection statistic under consideration.

Local partner markets differ not only in population size but in relative partner availability, the scale of opportunity, marriage timing, and population turnover. This paper develops a county-level framework for comparing these conditions across local partner markets. The empirical application focuses on unmarried women ages 25-34 and uses observed partner-age pairings to construct age-specific weights for the relevant unmarried male population. We model absolute opportunity separately, fitting a Michaelis-Menten diminishing-returns transformation to 192 scenarios that vary dating intensity, search horizon, fit, and first-date conversion. The resulting index also incorporates the share of women ages 35-39 who have never married and the inflow rate of adults ages 25-34. Among 320 counties with complete data, the District of Columbia ranks first and New York County second under the baseline specification, and rankings remain highly stable under alternative component weights. An endogenous mobility extension shows that favorable markets attract additional male participants, producing substantial adjustment while leaving the top composite rankings relatively stable over the parameter values considered. The framework is intended as a structural comparison of local partner-market conditions rather than a predictor of individual relationship outcomes.

Understanding the predictability of life outcomes is important for public policy and science, but existing studies focus on a limited number of outcomes and therefore struggle to describe the broad patterns of predictability. We developed a high-throughput approach that uses a single dataset to study the predictability of many future outcomes using past data. We deployed this approach with hundreds of outcomes and thousands of machine learning models per outcome in the Future of Families and Child Wellbeing Study. Three findings emerged. First, most outcomes were not very predictable, but some were much more predictable than others. Second, even for the most predictable outcomes, our complex prediction procedure typically exhibited little skill relative to a simple procedure. Third, we found modest patterns in how predictability varied across outcomes. We conclude by discussing scope conditions and how future research might address them.

Current performance criteria used in Applied Behavior Analysis (ABA) are often based on whether a learner meets a predetermined benchmark e.g., 8 out of 10 correct responses across several sessions. Although these criteria help practitioners make instructional decisions, they provide limited information about how likely it is that the learner has truly acquired the skill. In this paper, we introduce a Bayesian approach that combines practitioners' prior expectations with the learner's ongoing performance data to estimate the learner's future performance level. Rather than providing only a pass or fail decision based on the criteria, we add an element of precision around that criteria to make decisions more nuanced to the testing conditions used. We also developed an R Shiny application for Measurement of Individualized, Evidence-Based Learning (MIEBL) that allows practitioners to apply this method in practice, supporting more informed instructional decisions and providing insight into the strengths and limitations of commonly used mastery criteria.

Realised kurtosis measures intraday tail risk but compresses the shape of the return distribution into a single scalar, so trading days with similar kurtosis may differ in how probability mass is spread across the peak, the shoulders and the tails. We propose a geometric description of intraday return shape based on the modified Brownian motion model (MBMM), which deforms a Gaussian benchmark through a nonlinear feedback governed by a shape parameter and a distortion intensity. Our main contribution is a peak-shoulder-tail decomposition that measures where the fitted return density gains or loses probability mass relative to the Gaussian, complemented by two feedback landmarks that explain how the shape parameter generates these deformations. We estimate the model at the stock-day level using a bin-free simulation-based minimum-distance estimator that matches empirical and model-implied intraday quantiles, and we document its finite-sample reliability by Monte Carlo. Using regular session one-minute returns for ten liquid U.S. stocks from May 2021 to April 2026, we find that the MBMM provides a substantially better in-sample fit than geometric Brownian motion on every estimator-ready stock-day, and that days with closely matched realised kurtosis can display materially different peak-shoulder-tail geometries. Finally, we show that the estimated shape parameters behave as persistent daily state variables: they are strongly forecastable relative to a random-walk benchmark, though their predictability reflects persistence around a slowly moving level rather than rich autoregressive dynamics. The proposed decomposition offers a risk-shape measurement layer that complements realised kurtosis by describing not only how large intraday tail risk is, but how it is formed, giving investors and risk managers additional distributional information for risk monitoring and, potentially, prediction.

A goodness-of-fit test tells whether a logistic risk model fits, but the analyst also needs to know what is wrong: an overall risk that is too high is repaired by updating the intercept, risks that are too extreme by recalibration, a curved relation between score and risk by a flexible recalibration, and misfit within groups of patients only by revising the model. We split any misfit into these four parts, which are orthogonal and match the calibration hierarchy. Each part gets a group of score tests that sees that part only, and the failing parts are named by closed testing. In external validation, in large samples and for small departures, a part is wrongly named with probability at most the chosen level, and the highest part named points to the lightest update that removes the misfit. Checking a model on its development data never sees an error in the overall risk or the calibration slope, and with binary or skewed covariates it can mistake misfit within patient groups for a curved link. External validation sees all four parts, for any prediction model. In simulations it kept its error rate when the model was right and for small departures, and usually pointed to the right update. On intensive-care data its verdicts for one model differed in-sample, on similar patients and after transport.

Many release rules accept a lot when a statistic built from the sample mean and standard deviation stays within a limit, and the probability that a process passes such a rule can be computed exactly for a broad class of parent distributions. This paper asks how well that probability is itself known once the parent has been estimated. Under a stated reference posterior the answer is an interval, narrow where a lot clearly passes or fails and wide where it is contested. In ninety-eight published content-uniformity lots that position, not the sample size, sets the width: among the forty-eight lots assayed at the same ten units, and so equally informed about the spread, the $95\%$ interval runs from essentially zero width to $0.96$. With the operating point held fixed while test and estimation sample grow together, the interval narrows only slowly, the contraction of the posterior being offset by the steepening of the operating characteristic; a calibrated study at the sample sizes of $1207$ occupational exposure assessments shows the same under a half-plane rule. For a pure-spread rule under a Normal parent the interval has an exact chi-square form in the plug-in value and the two sample sizes, extending to the mean-spread wedge with a measured residual and containing Bergum's lower bound as one endpoint. With the parent's posterior formed from the same published summaries through the evaluator's own likelihood, the qualitative pattern survives but shape moves both endpoints and width: on the same lots a strong right skew lowers the pessimistic endpoint by up to a fifth and widens the interval by up to $0.22$. At the content-uniformity operating point studied, under a Normal parent, the symmetric error bar in standard use puts the lower endpoint $0.21$ too high and returns an upper endpoint above one, even with the full posterior covariance.

The log-rank/Cox hazard-ratio test remains the standard approach for the primary analysis of randomized trials with time-to-event endpoints and is fully efficient under proportional hazards (PH). Two model-free alternatives that have recently gained attention are the difference in restricted mean survival time (D-RMST), a contrast on the time scale, and the more recently proposed ratio of average hazards (RAH), a contrast on the rate scale. Simulation studies suggest that the RAH-based test can outperform both under delayed treatment effects, but its efficiency has not been characterized analytically, and no unified framework explains how censoring and accrual affect the efficiency ordering among these tests. We show that all three statistics share a weighted-log-rank representation and derive their asymptotic relative efficiencies under local alternatives, including the first analytic efficiency results for the RAH-based test. Geometrically, each test defines a direction in a function space and the anticipated treatment effect defines a signal direction. A test's efficiency relative to the oracle test equals the squared cosine of the angle between these directions, so the asymptotic relative efficiency of any two tests is a ratio of squared cosines. Because censoring and accrual enter through an information weight, the framework shows how design choices can alter, and even reverse, the efficiency ordering. We illustrate the framework using the CheckMate 057 immunotherapy trial and corroborate the theoretical results through simulations spanning proportional- and non-proportional-hazards settings.

Historically, phase I oncology trials were designed with the focus to find the highest tolerable dose. However, given the FDA's acknowledgment that the highest tolerable dose might not be the dose which is optimal biologically, there is an increased emphasis the development of designs that explore the dose-toxicity and dose-efficacy relationship. Backfill designs have emerged as a popular response to address this need by allocating participants to doses deemed safe while awaiting participants outcomes. Previous designs have explored how to assign participants to doses in backfill designs in a rigorous manner while providing simplicity and performance (a class of designs known as model-assisted) for single agents. Still, a research gap exists in the lack of model-assisted backfill designs for drug combinations. Frequently, the combinations two of cancer agents are explored in phase I trials, with the goal of identifying the highest tolerable combination. This paper incorporates and extends methodology based on previous model-assisted backfill designs to provide clinicians with a simple-to-use backfill design for phase I drug combination trials.

Language models are increasingly used to create synthetic survey samples, also called silicon samples. Decision models are a new class of language models that return a probability for each point of a rating scale instead of text. We ask whether these models, or the newest generative LLMs, can stand in for human respondents on a psychometric survey. We test fourteen decision models from eleven providers and 47 generative LLMs on an open Lithuanian organisational-psychology survey (n=263, 68 items), with 100 real respondent profiles, the Psychometric Similarity Score (PSS) and statistical baselines. The best generative model, MiniMax M3, reaches PSS 0.813. This is level with a Gaussian copula fit only on other respondents (0.824) and below a copula fit in sample (0.927). A second sample of 100 real people scores below the best models, so at this size PSS cannot rank them against real respondents. In 5 of 10 product lines the newest generative release scores below an earlier release of the same line beyond resampling noise, and none gains beyond it. With the default rounded readout, 13 of 14 decision models score below the generative reference gpt-5.4-mini. Of the 47 generative models, 33 reproduce the pattern of item correlations better than any decision model. Averaged over respondents, the probability vectors are much closer to the human item marginals than rounded answers. They also rank respondents about as well as a profile regression fit on 163 real people. As forecasts of each person's own answers, however, every decision model is worse than the answer frequencies of other respondents, mainly because its average vector differs from them. The profile regression improves on these frequencies by only 1.0%, so the profile fields say little about how a person answers. Synthetic respondents built on such profiles should therefore aim at sample-level fidelity.

Human reference labels used to evaluate medical AI can vary across readers and annotation workflows. We quantified agreement of a fixed pathology AI system with a future qualified reader without treating inferred consensus as error-free biological truth. Linked Evaluation and Unbiased NuCLS multirater data were analyzed using a fixed external HoVer-Net decision vector. The selected frame contained 1,144 anchors, 52 fields of view, five slides/patients, and five primary readers. The target was fixed-AI agreement with a future reader, with descriptive contrast $\Delta=\theta_E-\theta_U$. Analyses included raw agreement and iMRMC benchmarks, reader-only and shared-detectability Bayesian models, structural sensitivities, adversarial simulations, and predictive assessment. Among 5,188 reader-anchor pairs observed in both conditions, 19.62% changed AI-agreement state, while raw agreement was 0.5466 in Unbiased and 0.5473 in Evaluation. The reader-only model gave $\Delta=-0.0008$ (95% CrI, $-0.0033$ to $0.0008$), and the shared-detectability model gave $\Delta\approx0$ ($-0.0140$ to $0.0127$). Across structural perturbations, absolute agreement ranged from 0.420 to 0.646 in Unbiased and 0.409 to 0.640 in Evaluation. Frozen adversarial simulations met the comparative-stability criterion (median $R=0.295$; 14/16 model-scenario cells had $R<1$). Held-out-AI prediction supported shared predictive information, but varied by slide composition. The Evaluation-minus-Unbiased contrast was comparatively stable, whereas absolute agreement was structurally sensitive. These findings do not establish equivalence, causal assistance effects, biological accuracy, or new-patient transportability. Evaluations using variable human references should report reader population, selected frame, observation mechanism, and structural sensitivity.

The flux variability of Active Galactic Nuclei (AGNs) is commonly modeled using the damped random walk (DRW), but increasingly rich multiband time-domain surveys motivate more flexible stochastic models that characterize variability beyond a single timescale and exploit dependence across bands. Multivariate continuous-time autoregressive moving average (MCARMA) processes extend the multivariate DRW to higher-order stochastic dynamics and provide a matrix-valued power spectral density for characterizing marginal variability and cross-band dependence. In a carefully selected Sloan Digital Sky Survey (SDSS) Stripe~82 sample, higher-order models are selected for 109 of 134 AGNs (81.3%), with substantial rather than marginal support in most objects; convergence diagnostics indicate that this fraction is conservative. The fitted models also reveal strong cross-band dependence that generally decreases with wavelength separation. Motivated by this richer structure, we investigate its recoverability under Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) observing conditions. Model-order recovery depends strongly on the underlying stochastic behavior as well as source brightness and observing cadence. Recovery is high across many of the simulated settings, but deteriorates when the characteristic features of higher-order variability become difficult to distinguish from the multivariate DRW. Additional simulations show that this loss of distinguishability can persist over a range of underlying variability behaviors. These results show that stochastic structure beyond the multivariate DRW is prevalent in our selected SDSS sample, while its recoverability with LSST depends on both observational conditions and the form of the underlying stochastic variability. The methodology is implemented in the Python package mcarma.

Quasi-periodic oscillations are characterized by fitting Lorentzian functions to a nonparametric estimate of the power spectral density, a two-step procedure that separates estimation from modeling and does not accommodate measurement error. We develop a parametric alternative based on autoregressive moving-average (ARMA) processes observed with measurement error. We derive an exact decomposition of the ARMA spectral density into real-valued components, one for each class of autoregressive roots under complex conjugation, plus a polynomial term when the moving-average order is at least the autoregressive order. Each component is a Wrapped Cauchy kernel, and for complex roots it is accompanied by a conjugate-Poisson term that makes the peak asymmetric and displaces its maximum from the frequency given by the argument of the root. We obtain closed-form expressions for the location, height, width, and asymmetry of each peak, and a matching variance decomposition. Parameters are estimated by maximum likelihood through the Kalman filter, and all descriptors follow by plug-in. Simulations show that the closed-form peak location is recovered without appreciable bias. An X-ray binary light curve illustrates the methodology.

This paper analyses spatial trends in armed conflicts in North and West Africa. It shows that all types of violence saw a significant increase in 2025. However, these violent incidents are distributed very unevenly across the region: while conflict is at its lowest in North Africa, the vast majority of violent incidents and victims are concentrated in five West African countries: Nigeria, Cameroon, Mali, Burkina Faso, and Niger. Coastal countries are experiencing a very mixed picture: jihadism is not advancing as a front, from the Sahel toward the Gulf of Guinea, and most of the violence stems from local disputes, ethnic conflicts, and banditry. Second, the spatial indicator developed by the OECD/SWAC to track the evolution of this violence confirms that the conflict landscape is expanding at its margins and intensifying at its center. Even more concerning is that peripheral areas are increasingly being drawn directly into well-established conflict zones, rather than going through a gradual, low-intensity transition phase. The geography of expansion is shifting from a diffuse, low-intensity spread toward peripheral areas to a rapid outward expansion from dense, well-established conflict hotspots. The local indicator used in the report suggests that violence continues to spread to new locations at the margins of established conflict zones. At the heart of these zones, tensions are intensifying relative to their historical baseline levels, and a growing number of regions have experienced clashes for a decade or more. Projections indicate that the intensity of violence is expected to increase in 2026, reaching more than 15,000 incidents and more than 32,500 deaths. Much of the increase is explained by the growing number of conflicts in Nigeria. In the Sahel, fatalities should increase in Mali and decrease in Burkina Faso.

Rating procedures are crucial in psychological and medical diagnosis, educational assessment, peer review, and grant evaluation. A major methodological challenge is disentangling multiple sources of variability in ratings, such as subject ability, rater behavior, and item characteristics. Item Response Theory-based models, most notably many-facet Rasch models and hierarchical rater models, have been widely adopted for jointly estimating subject, rater, and item effects, while retaining high interpretability. We introduce the Dynamic Extended Generalized Many-Facet Rasch model, a general class of Bayesian semiparametric models that integrate and extend existing approaches. Its measurement model allows location and discrimination parameters to depend jointly on item and rater characteristics and incorporates subject-item and rater-subject variation. The dynamic extension introduces a rater-specific cross-lagged effect capturing dependence on the previously rated subject, and a Bayesian P-spline capturing systematic changes in discrimination over the rating sequence, accounting for learning, fatigue, or adaptation effects. Subject heterogeneity is addressed through Bayesian nonparametric mixtures, flexibly learning the latent ability distribution without strict parametric assumptions and enabling model-based subject clustering. We also derive a closed-form, model-based inter-rater consensus coefficient and study its characteristics. We discuss theoretical properties, develop posterior computation strategies, and evaluate the model in simulation studies and two real-data applications.

Thyroid nodules affect a large proportion of the general population. Although most are benign, a non-negligible fraction is malignant. Ultrasound imaging is the primary diagnostic modality, and accurate nodule segmentation is a prerequisite for CAD systems to classify malignancy and assess metastatic risk.\\ In this work, we propose a thyroid nodule segmentation framework that integrates a DeepLabV3+, channel-attention modules and post-hoc conformal prediction, providing both accurate mask and pixel-level uncertainty estimates. We address thyroid ultrasound nodule segmentation as the first stage of a pipeline that also includes malignancy classification and metastatic risk prediction. We adopt DeepLabV3+, whose Atrous Spatial Pyramid Pooling (ASPP) captures multi-scale context, with an EfficientNet-B5 backbone for its accuracy-efficiency trade-off. Additionally, we test three channel-attention modules: Squeeze-and-Excitation, CBAM and Grouped Channel Attention (GCA), paired with two loss formulations (Dice-BCE and Boundary).\\ Since binary masks do not indicate prediction confidence, we wrap the trained model with a split conformal prediction layer that produces pixel-level uncertainty maps with statistical coverage guarantees.\\ We evaluate all configurations on the TN3K public benchmark using a fixed split and directly compare them with state-of-the-art methods. The plain backbone already improves upon previously reported results, with CBAM + Dice-BCE emerging as the best overall configuration.