Papers

Working agricultural landscapes are often treated as background to wildfire disasters, even though they are managed fuel mosaics, productive assets, and parts of regional infrastructure systems. We examine vineyard wildfire resilience during the electrically initiated 2019 Kincade Fire in Sonoma County, California, using an open, event-anchored geospatial framework spanning 4,581 vineyard fields (8,813.2 ha), wildland vegetation, surveyed structures, roads, overhead smoke, and post-fire greenness. Sentinel-2, OpenET, gridMET, soils, terrain, NOAA smoke polygons, an ignition-date OpenStreetMap network, and three-dimensional data inventories were analyzed at native decision scales. Vineyard pixels showed substantially lower descriptive dNBR than wildland pixels inside the perimeter (means 0.130 and 0.337). This contrast did not identify a universal vineyard firebreak effect: a segment-clustered boundary model gave a small negative contrast at 100 m (tau = -0.0166) but changed across bandwidths, failed slope continuity, disappeared in a 100 m donut, and produced a wrong-signed placebo. A 250 m spatial GAM reversed the unconditional pattern: after conditioning on location, terrain, and water use, vineyard fraction was positively associated with dNBR, while residual Moran's I remained 0.519. Beyond spectral impact, all mapped vineyards intersected overhead smoke on at least one day (mean 7.78 potential smoke-days per field), 34.2% of road-network nodes were dead ends, and inside-perimeter vineyards showed a larger greenness deficit through 2021 (recovery ratios 0.815 inside and 0.854 outside). Lower immediate spectral impact therefore did not imply complete resilience. The study provides a reproducible urban-rural informatics template separating descriptive contrasts, conditional associations, exposure indicators, and recovery evidence for decisions in working landscapes.

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

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

Some of the sharpest challenges in sampling from the energy functions of physical systems arise at phase transitions, where the density of states changes abruptly and many sampling algorithms stall. Nested sampling is a particle method that traverses the density of states under a hard energy constraint and is known to be robust to such transitions, but its application in high dimension is limited by the difficulty of sampling under that constraint. In this work we introduce Quenched Ensemble Sampling, which generalises the hard constraint to a family of repulsive potentials at the energy boundary. This preserves the quenched path of monotonically decreasing energy while making the constrained target amenable to scalable gradient-based kernels. We demonstrate on synthetic models of phase transitions that our method estimates the marginal likelihood and draws posterior samples across a first-order transition where popular alternatives such as tempering fail. We apply the procedure to marginal likelihood estimation in Bayesian neural networks, enabling model comparison between network architectures. Finally, in a high-dimensional continuous lattice field theory, we show that this method traverses a first-order transition and estimates the partition function.

Spectral features can remain optimal under strongly uneven task preferences when they retain the directions most useful to the tasks. In a local-task model, expected probing gain depends on the task prior only through its covariance $\Lambda$: with $B$ recording dependence between views, $k$ spectral features span the leading eigenspace of $BB^\top$, while task-optimal features span that of $B\Lambda B^\top$. We derive alignment-dependent regret bounds, matching worst-case lower bounds for a flat leading spectrum, and bounds using the leading $2k$ directions with a spectral-tail term; a spectral gap makes the bound quadratic in small anisotropy. We also bound the imbalance from random preference patterns and from averaging independent tasks with an isotropic population covariance. With known $\Lambda$, changing one term of the spectral contrastive loss selects task-optimal features; with a labelled task bank, we propose a diagnostic and test correction without retraining. Correction reduces synthetic held-out regret from $0.858$ to $0.003$ with $2000$ tasks when less task-relevant directions dominate, and on CIFAR-100 lowers empirical regret by $0.031$–$0.053$ on held-out fine-label tasks using the same images. With a small task bank, however, correction can hurt.

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

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

We study exact community recovery in the Degree-Corrected Poisson Stochastic Block Model (DC-SBM) through the maximum profile likelihood estimator. Our main contribution is identifying an explicit complexity constant $C(\pi,S)$, which closely captures the exact recovery threshold. This constant combines a weighted Chernoff–Hellinger separation between communities with a Kullback–Leibler correction induced by the degree-normalized block volumes. We rigorously prove that $C(\pi,S)>1$ ensures the strong consistency of the maximum profile likelihood estimator, yielding exact community recovery down to the logarithmic sparsity scale. We conjecture that $C(\pi,S)=1$ represents the sharp information-theoretic threshold, providing an upper bound on the exact-recovery transition, and we discuss analogies with the binary SBM and binary DC-SBM cases. Additionally, we establish weak consistency when the average degree diverges, offering a unified picture across sparse and dense regimes. The proofs require new control of the profile likelihood in the presence of heterogeneous degree parameters, whose node-specific weights fundamentally alter the geometry and concentration of the recovery problem.

We develop a Gaussian comparison theory for posterior inference in non-Gaussian high-dimensional models. The framework allows for model misspecification and does not require the posterior distribution itself to be approximately Gaussian. Working directly with likelihood processes on separable function spaces, we establish explicit nonasymptotic free energy bounds controlled by first two moment discrepancies and local third moments. A perturbation-and-convexity argument transfers these comparisons to sandwich bounds for posterior mean squared error and posterior variance, including one-sided conclusions at nondifferentiable phase transitions. In high-dimensional product models, these conditions reduce to local moment controls and a canonical feature-radius scaling. Under weak regularity requirements, the resulting universality theory applies to a broad class of likelihood models, ranging from exponential families to more general regular local log-likelihoods. The framework is illustrated on sparse Bernoulli hypergraph inference.

We study density ratio estimation and importance-weighted regression under target shift with continuous outputs. Under target shift, the conditional distribution of the inputs given the outputs remains invariant across the training and test distributions, while the output marginal distribution may change. Although this problem has been extensively studied for discrete outputs, the continuous setting is substantially less understood: the importance weights are determined by an unknown density ratio function, for which existing estimation methods lack explicit finite-sample convergence rates. We propose a spectral regularization method in a reproducing kernel Hilbert space (RKHS) for estimating the continuous density ratio from labeled training samples and unlabeled test inputs. Under a source condition with regularity parameter $\iota>0$, we establish high-probability finite-sample guarantees and show that the estimator achieves the capacity-independent minimax-optimal RKHS-norm rate $O(n_\eta^{-\iota/(2\iota+2)})$. We then incorporate the estimated density ratio into importance-weighted regression and characterize the propagation of density-ratio estimation error to the final predictor. When sufficiently many samples are available for density ratio estimation, the resulting regression estimator attains the minimax-optimal rates of standard kernel regression. These results establish a finite-sample theory for continuous density ratio estimation and importance-weighted learning under target shift.

Nested cubature rules, in which each refinement retains all previously used nodes and thus reuses earlier function evaluations, are natural in multilevel and adaptive integration. For every fixed $s>d/2$, we show that the equal-weight QMC integration rate on $\mathbb S^d$ is compatible with such nested point sets. In the subcritical range $d/2<s<d$, cumulative unions of geometrically growing QMC blocks yield nested QMC design sequences whose successive cardinality ratios converge to any prescribed $\rho>1$. At and above the critical index $s=d$, where the block-averaging estimate no longer yields the optimal rate, we prove an equal-weight completion theorem based on low-frequency discrepancy cancellation. A block-sensitive estimate sharpens the iteration and yields nested QMC designs for all $s\ge d$ with $N_{j+1}\lesssim(j+1)^{2s/d-1}N_j$. Every prescribed finite point set also admits an optimal-rate completion.

We develop notions of covariance and principal component analysis (PCA) for probability measures on Riemannian manifolds of bounded geometry and a discrete counterpart for distributions on the vertex sets of weighted simple graphs. Rather than anchoring variation at the Fréchet mean, whose uniqueness and usefulness can fail in this context, we consider variation about every point. This leads to a representation of each point on the manifold by a vector field derived from the heat kernel and thus to a map of the underlying manifold into a Hilbert space of vector fields, in which covariance and PCA carry over from the Euclidean setting. A distinguishing feature of this formulation is that one typically obtains infinitely many principal components, capable of capturing highly nonlinear geometric features and patterns of variation. We prove an embedding theorem for the mapping into the space of vector fields and develop two computational reductions of the theory: RiePCA, a finite-dimensional reduction based on vector fields supported on finitely many points, and GraphPCA, a discrete formulation for measures on weighted graphs in which vector fields assign orientations and magnitudes to edges. Numerical examples and experiments illustrate the behavior of the proposed methods on both synthetic and real data.

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

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

Keyed watermark detection tests dependence between observed tokens and pseudorandom variables reconstructed from a secret key. Building on the pivotal framework of Li et al. (2025), we construct predictive likelihood ratios that average over uncertain probability deficits and residual-tail distributions. The aim is robust detection power across alternative specifications without requiring a single signal-strength tuning. A mixture prior combines tail shape and effective width; hierarchical extensions allow within-document variation in deficit or width. The test maximizes prior-averaged power at a fixed size, but is not generally uniformly most powerful or minimax. Under the exact conditional pivot null, normalized predictive alternatives selected before each observation yield a Bayes factor that is also a test martingale: Type I error control is unaffected by alternative misspecification and remains valid under optional stopping. This guarantee does not cover violations of the conditional null, and the interpolated implementation has no certified anytime guarantee. Gumbel marginal likelihoods are evaluated by fixed quadrature. Across the evaluated tail-shape and tail-width alternatives and three horizons, the union-tail mixture has maximum observed Type II error regret .0080, compared with .0962 for the equal-tail mixture, relative to the best tested rule. On temperature-matched outputs from two open models, it improves AUC over the equal-tail baseline in all eight non-saturated model-temperature cells, although the leading reference score generally has higher AUC. Supplementary experiments show retained power under independent null-like replacement and smaller changes from hierarchical dependence modeling. The evidence supports robustness across the evaluated alternatives, not uniform power guarantees or resistance to arbitrary text edits.

We study high-dimensional nonparametric regression on the Boolean hypercube \(\{0,1\}^d\), from a sample of size \(n\), under a Fourier–Sobolev budget, i.e., a bound \(B\) on the total quadratic influence of the regression function. The central object is the resolvable Fourier degree \(D^*(d,n)\), defined as the largest interaction order \(D\) such that the dimension of the degree-\(D\) Fourier–Walsh space does not exceed \(n\). We prove that the minimax risk over Fourier–Sobolev ellipsoids is of order \(B/D^*(d,n)\): estimation is possible up to the statistically visible interaction order, and the budget controls the residual mass carried by higher-order interactions. We then study monotone regression under the same budget. For monotone functions supported on a known set of \(s\) coordinates, with \(s\) of order \(\log n\), we obtain a matching minimax rate of order \(B/s\). Finally, we consider an unknown-support model in which the function is monotone and depends on at most \(s\) coordinates; its minimax risk is governed by the intrinsic dimension \(s\) together with the logarithmic cost of selecting the active support.

We study regression with subsets as covariates. The response is an unknown function of the input subset, and observations consist of noisy evaluations at uniformly sampled subsets, each containing exactly \(k\) items from a ground set of size \(d\). This problem arises in combination screening, bundle preference modeling, and other settings in which outcomes depend on collections of prescribed size. The fixed-cardinality constraint couples the membership coordinates, so standard product-domain notions of interaction and smoothness cannot be imported unchanged. We use the harmonic decomposition of the Johnson graph to define an intrinsic Johnson–Sobolev scale and determine the exact dimensions of low-order interaction spaces. We derive finite-sample risk bounds for harmonic projection and establish a nonasymptotic minimax characterization when the Johnson–Sobolev energy budget is controlled relative to the noise variance. We also show that stable least squares removes the signal-dependent fluctuation of empirical projection when the empirical Gram matrix is sufficiently well conditioned. For arbitrary signal-to-noise ratios, a rank-deficiency analysis quantifies the components left unidentified by the random design. Together, the rank-deficiency analysis and a centered completion estimator yield minimax bounds that match up to constants whenever \(\min(k,d-k)\) and the smoothness order are fixed. Numerical experiments reported in the Supplementary Material illustrate estimation under different interaction profiles and distinguish the effects of observation noise, random-design fluctuation, and incomplete coverage.

We extend the Ibragimov-Khasminskii likelihood ratio analysis method, in the one-dimensional parameter case, to a framework based on the Skorokhod $M\_1$ topology. The proposed framework applies to a broad class of statistical models, including those for which the normalized likelihood ratio processes are continuous while the limiting likelihood ratio process is discontinuous, a setting outside the scope of classical approaches based on the uniform or Skorokhod $J\_1$ topologies. We derive sufficient conditions for the weak convergence of likelihood ratio processes in the space of càdlàg functions on $\RR$ vanishing at $\pm\infty$, endowed with the Skorokhod $M\_1$ topology, and show how this convergence yields the asymptotic behavior of the maximum likelihood estimator. We also introduce new techniques for controlling the $M\_1$ modulus of continuity. Although these techniques are particularly well suited to models in which all jumps and steep continuous transitions are in the same direction, they are of independent interest and may prove useful beyond this setting. As an application, we study a smooth change-point model for inhomogeneous Poisson processes in the fast regime, where the transition interval shrinks faster than $1/n$. We establish that in this case the maximum likelihood estimator has the same asymptotic behavior (consistency, rate of convergence, limiting distribution and convergence of moments) as in the corresponding ”pure” change-point model.

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

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

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

End-to-end Supervised Graph Prediction (SGP) requires a permutation-invariant loss to compare predicted and target graphs with arbitrary node orderings. Such losses typically involve a costly graph-matching problem. We first study three Optimal Transport relaxations of this problem and show, theoretically and empirically, that the Gromov-Wasserstein (GW) objective is the most suitable for SGP. Then, to avoid solving the resulting inner optimization for every training example, we propose to amortize the graph matching (node alignment) problem. For each training sample, the loss function leverages a transport plan provided by a parametric matcher based on the differentiable Sinkhorn algorithm applied on empirical node distributions. The graph prediction module and the matcher are jointly learned. We showcase the efficiency of this approach on toy and real world SGP problems of increasing complexity including a novel Mass-spectra to Scaffold task that we introduce.

We study the uniform approximation of smooth scalar-valued functionals on an infinite-dimensional separable Hilbert space by ReLU neural networks. A key feature in deep learning for functional data is the varying importance of different coordinates/dimensions. Representing the functional input in a basis expansion, we quantify the importance of each coordinate through both the magnitude of its corresponding basis score and the directional sensitivity of the target functional. Our analysis combines coordinate truncation, anisotropic partitioning, local Taylor approximation, and ReLU network realization, while allowing unrestricted interactions among the retained coordinates. We establish a general nonasymptotic upper bound for the uniform approximation error and a complementary pseudo-dimension-based lower bound for the worst-case approximation error. Under generalized exponential coordinate decay $w_ds_d\asymp\exp(-cd^\rho)$, with $\rho>0$, the upper and lower bounds match at the leading order, which is stretched-exponential in the logarithm of the network size budget, and thus yield the nearly optimal approximation rate. This is the first work to characterize neural network approximation error for infinite-dimensional functional inputs explicitly through the joint dimensional decay of coordinate magnitudes and directional sensitivities.

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

Facial-expression classifiers convert video into multivariate time series of scores with measurement error from classifiers, videos, and recording conditions. Empirical score series cannot establish whether the score channels reflect a smaller set of latent expressive processes or whether an analysis would recover those processes. We introduce the Latent Oscillator Measurement Model (LOMM), a data-generating model that separates latent dynamics, time-varying activity, and a factor-analytic observation model. The latent processes are damped, undamped, or amplifying linear oscillators. LOMM generates bounded scores or continuous indicators. Study 1 used four-fold cross-fitting with scores from 100 MAFW videos to calibrate LOMM and evaluate generated series on held-out videos. Median plausibility and coverage were 0.970 and 0.920 for LOMM, versus 0.510 and 0.370 for a calibrated static logistic-normal generator. Study 2 tested whether Dynamic Exploratory Graph Analysis (DynEGA), static EGA, GraphicalVAR, and GIMME recovered a known dimensional structure from continuous indicators generated by LOMM. At 100 observations per clip, with failed or timed-out fits counted as incorrect, correct-dimension recovery was 0.939 for DynEGA, 0.884 for static EGA, 0.777 for GraphicalVAR, and 0.176 for GIMME. Replacing the common fixed initialization with independent stationary starts for stable dimensions and bounded independent starts for amplifying dimensions reduced recovery for DynEGA, static EGA, and GraphicalVAR. LOMM provides a controlled test of whether an analysis recovers aspecified latent structure before score patterns are interpreted psychologically.

Conformal counterfactual prediction constructs prediction sets with finite-sample coverage guarantees for counterfactual outcomes and individual treatment effects under the no-interference assumption. In this work, we relax this assumption by allowing each unit's potential outcomes to depend on other units' treatments and covariates. In this setting, propensity-score reweighting does not restore weighted exchangeability, and existing methods may fail to achieve valid coverage. To address this issue, we develop interference-adjusted weighted conformal prediction that accounts for interference by constructing an observable upper bound on the ideal and unobserved conformal $p$-value under the target intervention. The resulting prediction sets provide finite-sample marginal coverage guarantees for counterfactual outcomes and individual treatment effects in both transductive and inductive settings. We also derive a sharper construction when intervention-induced changes in nonconformity scores are bounded. Numerical experiments show that our methods preserve nominal coverage, whereas existing methods may not.

A learner probes at most $k$ of $n$ arms each round, receives the maximum of their rewards in $[0,1]$, and competes with the best fixed arm. When does the probing advantage pay for learning? We determine two minimax laws. Under independent stochastic rewards with winner feedback (the maximum and a winning label), or on arbitrary fixed sequences given a single signed contrast between block maxima, the minimax regret has order $\Phi_{n,k}(T)=\min\{\frac{n-k}{n}T,\frac{n-k}{k}\}$, $2\le k<n$. Under winner feedback, both arbitrary joint i.i.d. rewards and fixed sequences have minimax regret of order $R_{n,k}(T)=\frac{n-k}{n}\min\{T,\frac{n+T}{k},\sqrt{\frac{nT}{k}}\}$. Both laws have universal constants and anytime upper bounds. The first reduces regret to a pure coverage cost: same-round contrasts absorb the stability cost, and independence permits exact resampling whose gains fund sample advancement. The second adds a learning cost that becomes comparable to coverage at horizon $n$; beyond $nk$, numerical maxima improve over labels alone. The lower bound allows every adaptive action size.

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

Generative AI writing assistants and the Large Language Models (LLMs) that power them are increasingly part of how voters gather information before elections. With growing evidence that they influence users' opinions, it is increasingly important to understand the views and positions of these tools. To better understand these views, we examine the stances supplied by six LLMs on a variety of Swedish-language writing tasks ahead of the 2026 Swedish parliamentary election. We cross 107 policy propositions with 77 writing templates and neutral, positive, and negative prompt framings, producing 24,717 prompts per model and 148,302 responses. To study these, we look at the models' default stance tendencies, compare how they respond to similar issues, and compare their responses with those of each of Sweden's eight parliamentary parties on the same issue. We find that Claude, DeepSeek, Gemini, and Mistral have similar profiles; ChatGPT more often supplies neutral or ambivalent text; and Grok differs most on topics such as migration, crime, and gender. When comparing the political parties, we find that the Social Democrats are closest to all six models. Still, after correcting for multiple comparisons, none of the within-model differences in party distances remains significant. Overall, we find that no model has a clear preference, nor a clear preference for a party, but that this depends on the specific issue or task the user asks about.

Fraction-based information measures have received considerable attention for describing complex systems, as they enable the investigation of signals with high sensitivity \citep{machado2014fractional}. In this paper, we introduce quantile versions of fractional cumulative past inaccuracy (FCPI) and dynamic fractional cumulative past inaccuracy (DFCPI) measures based on the inverse Mittag-Leffler function (MLF) or fractional logarithm function, which are the extensions of the fractional cumulative past and dynamic fractional cumulative past entropies, respectively. The various properties of quantile-based FCPI and its dynamic version are provided. We also propose a nonparametric estimator for the proposed measure, and simulation studies are carried out for validation. Finally, we bring out real data application of the newly introduced quantile-based FCPI.