Papers

Between the classical (frequentist) approach, which is based solely on the data, and a fully Bayesian set-up where one assumes a prior distribution for the model parameters, lies the Empirical Bayes (EB) approach which appears to be a good compromise between the aforementioned two approaches. Even though many researchers have suggested various variants of the EB method, the standard practice is to derive the Bayes estimator under a family of suitable priors indexed by its own parameter(s), called the hyperparameter(s), and then replace the unknown hyperparameter(s) by their estimate(s) obtained from the marginal distribution of the data. But the fundamental question that is being raised here is: does the EB method really work to produce an improved estimator - the so-called Empirical Bayes Estimator (EBE)? In this work we are going to revisit the widely cited simple problem of estimating a Binomial parameter using the regular two-parameter Beta family of priors under the quadratic loss function, and prove that the Type-II maximum likelihood (ML-II) step does not work. If we further restrict our attention to one-parameter symmetric Beta family of priors then still the resultant EBE does not show any remarkable performance compared to the MLE details of which have been provided with extensive computations. The Binomial study has been extended to the Poisson model as well.

Prognostic regression models often synthesize data from multiple sites, whether within a multi-site study, across federated settings, or in individual participant data meta-analysis. Here, a site is any data source, such as a hospital, registry, trial, or study, and need not be a physical center. Analysts must then decide whether one regression model represents all sites or whether site-specific models are needed. Established measures such as coefficient-level tau^2 quantify heterogeneity but do not distinguish its source. We focus on diagnosing whether coefficient heterogeneity reflects case-mix or site-specific context effects. Case-mix heterogeneity can arise when linear regression terms approximate multivariable non-linear relationships in populations with different covariate distributions. Contextual heterogeneity arises when comparable patients require different regression relationships across sites. We do this by fitting site-specific local regressions in a dimension-reduced space and partitioning the smoothed coefficient surfaces into a cross-site reference and site-specific deviations. An autoencoder and custom loss structure the latent space around local prognostic relationships. We then project this partition onto the outcome scale to derive observation- and site-level summaries. We demonstrate the approach on a COPD trial with two sites. In the three leading latent slope coordinates, coefficient-surface variation was predominantly contextual. The derived observation-level outcome-scale variance partition was case-mix-leading, whereas its between-site aggregation was concentrated in contextual differences rather than case-mix shifts. A permuted-site negative control assesses whether the contextual summary can arise when site labels carry no signal. This diagnostic distinction can inform whether joint or site-specific regression models should be evaluated.

We study estimation of the drift matrix in a continuously observed high-dimensional Ornstein-Uhlenbeck process when the drift is exactly or approximately low rank. In this setting, exact low rank induces non-stable directions and hence a non-ergodic regime, resulting in a poorly conditioned empirical covariance matrix. To address this difficulty, we introduce a Weighted Nuclear Elastic Net Estimator that combines ridge regularization with a nuclear-norm penalty expressed in the empirical likelihood geometry. Under a general diagonalizable spectral framework, we establish oracle inequalities relative to arbitrary low-rank comparison matrices. For near low-rank drifts, the approximation error is naturally measured through the singular-value decay of the drift after weighting by the regularized empirical covariance. The stochastic term is controlled by self-normalized martingale arguments under appropriate choice of the tuning parameter. For a symmetric positive-semidefinite exact low-rank model, we verify the empirical-curvature condition required to translate the weighted bound into a Frobenius-norm bound. With an appropriate choice of tuning parameters, the resulting estimator satisfies, up to a logarithmic factor, the standard rank-$r$ matrix-estimation scaling $r d/T$: specifically, its squared Frobenius error is of order $r d\log(T)/T$ with high probability, under an explicit dimension-horizon condition.

Distribution steering seeks feedback laws that drive the state law of a dynamical system between prescribed initial and terminal distributions. Optimal transport provides a natural geometric approach, but its implementation generally requires a transport map or coupling in the full state space. Sliced optimal transport avoids this full-dimensional construction through one-dimensional projections. Yet, the resulting projected maps specify only directional displacements and do not by themselves prescribe a realizable feedback law. To this end, we develop a finite-horizon control framework based on sliced optimal transport. At each sampling instant, a projected optimal transport map defines a directional terminal condition, whose minimum-energy realization yields a randomized single-direction controller. Averaging over projection directions gives a deterministic sliced feedback. For the single-integrator dynamics, the averaged feedback makes the sliced Wasserstein distance to the target non-increasing. For Gaussian endpoint laws, it is affine, preserves Gaussianity, and steers the mean and covariance to their prescribed terminal values. We further identify a law-dependent gain that yields linear decay of the sliced Wasserstein distance together with an explicit characterization of the control energy. We also prove that the randomized controller converges to the averaged sliced flow as the sampling period vanishes. Finally, we extend the construction to linear dynamical systems. Reachability-normalized coordinates allow instantaneous realization of the sliced velocity for uniformly fully actuated systems, while local controllability Gramians provide exact finite-step realization for general controllable systems. Numerical examples illustrate the resulting distributional flows.

We develop a stable convergence theorem for partial sum processes on sample-size dependent stochastic bases. The result allows multidimensional semimartingale limits that have conditionally independent increments and both a continuous and discontinuous martingale part. Motivated by infill asymptotics, it complements classical Gaussian stable limit theorems and supports applications to likelihood based statistical inference.

We develop a new uniform drift condition and local minorization that implies a stronger weighted form of uniform ergodicity for Markov chains we call hyper-V uniform ergodicity. The convergence guarantees geometric decay of the bias towards the invariant measure independently of the initialization for all functions controlled by a dominating function V. A key advantage of the approach is that it bypasses the need to establish a global minorization condition, which is often substantially more difficult to verify in practice, while yielding stronger convergence guarantees than global minorization. Optimal convergence bounds in a minimax sense of the framework are established. The utility of the framework is demonstrated through applications to the P'olya-Gamma and Kolmogorov-Gamma Gibbs samplers. We also show qualitative hyper-V uniform ergodicity convergence for two-variable Gibbs samplers can be inferred by the form of the invariant measure, bypassing convergence analysis entirely.

Multivariate count data often contain overdispersion, excess zeros, and complex dependence. Existing multivariate zero-inflated count models usually use a single dependence structure to jointly model structural zeros and count outcomes. This makes the two sources of dependence difficult to interpret separately and often leads to slow computation or intractable likelihoods. This paper proposes a general framework for multivariate zero-inflated mixed Poisson models that explicitly separates these two sources of dependence within a unified likelihood-based formulation. The proposed hierarchical model combines zero-inflated mixed Poisson marginals with separate dependence models for the structural-zero and latent-intensity components. Dependence among structural zeros is modeled by standard parametric copulas, while dependence among latent mixing variables is modeled by checkerboard copulas. Likelihood-based inference is carried out using an inference-functions-for-margins procedure, and the proposed likelihood also supports full maximum likelihood estimation when computationally feasible. Simulation studies show accurate parameter estimation and good finite-sample performance under different dependence structures and latent mixing distributions. Applications to benchmark datasets from existing statistical software and a healthcare utilization dataset demonstrate the flexibility, computational efficiency, and practical usefulness of the proposed framework.

We consider a mixture of at most $k$ unit-covariance Gaussians in $\mathbb{R}^d$ whose means belong to a fixed-radius ball, with no separation or minimum-weight condition. Doss, Wu, Yang and Zhou (2023) proved that the minimax Hellinger risk is of order $\sqrt{d/n}\wedge 1$ and constructed a proper polynomial-time estimator with the slower general bound $(d/n)^{1/4}$; obtaining the sharp rate in polynomial time for fixed $k\geq 3$ was left open. We resolve this question. The key device is a moment-fiber range finder. A second-moment subspace controls the energy missed by projection. We then estimate finitely many one-free-index Hermite contractions. These vector-valued contractions recover every tensor component containing exactly one missed direction at the sharp $\sqrt{d/n}$ scale. Every remaining term contains at least two missed factors and is therefore controlled by the residual second-moment energy. The resulting subspace has dimension depending only on $k$. Exhaustive moment fitting in this constant-dimensional space produces a proper mixture and, together with the dimension-free moment characterization of Gaussian mixtures, achieves the optimal Hellinger rate in polynomial arithmetic time for every fixed $k$.

Motivated by sequential space-filling designs for computer experiments, we study algebraic constructions of extensible point sets in the $d$-dimensional unit cube whose two-dimensional coordinate projections are all quasi-uniform. Our two constructions share a common parametrization in terms of finite configurations of distinct rational directions on the projective line $\mathbb{P}^1(\mathbb{Q})$. First, using a cubic number field, we construct explicit Kronecker sequences for which the mesh ratios of all two-dimensional coordinate projections remain uniformly bounded over every initial segment of length $N\ge 2$. Second, using a real quadratic field, a split prime, and a compatible $p$-adic embedding, we construct nested rank-1 lattice designs with the same uniform projection property at every nesting level. The proofs combine algebraic norm estimates with transference principles between simultaneous and dual Diophantine approximation, yielding lower bounds for the separation radii and upper bounds for the covering radii, both of optimal order in the number of points, uniformly over all coordinate pairs. We also investigate how the choice of rational projective coefficients affects the resulting mesh ratios. This leads to a minimax problem for finite configurations on $\mathbb{P}^1(\mathbb{Q})$, in which one seeks to minimize the maximum mesh ratio over all two-dimensional coordinate projections. These constructions provide extensible point sets with uniformly controlled bivariate geometry.

An “Attention Residual U-Net” method is described for probabilistic quantitative precipitation forecasting (PQPF) that predicts the hourly probability of no precipitation plus the distribution of positive precipitation from a weighted mixture of two Gamma distributions. The neural network is trained on patches of numerical weather prediction (NWP) hourly precipitation from The Weather Company's convection-permitting GRAF (Global high-Resolution Atmospheric Forecasting) model along with terrain information and column-average relative humidity from the National Oceanic and Atmospheric Administration's (NOAA's) Global Forecast System (GFS). The target data are NOAA's Multi-Radar, Multi-Sensor (MRMS) gauge-corrected, quality controlled radar data sampled to the same grid as the GRAF data. The network outputs distributional parameters for each model grid point. Training uses negative log-likelihood as a proper scoring rule, with climatological initialization for stable convergence. Inference is performed as a single forward pass over the contiguous United States (CONUS) domain, with edge-replication padding to satisfy the network's spatial-divisibility requirement. The subsequent forecasts are spatially detailed, highly reliable, and skillful with respect to climatology and a simpler reference forecast method. The method is particularly useful for estimating probabilities in regions with large terrain variation.

The two-stage approach and Bayesian joint modeling are commonly used to analyze longitudinal biomarker measurements together with time-to-event outcomes. Using data from an HIV clinical trial of 467 patients with repeated CD4 measurements and all-cause mortality as the survival outcome, we compared a baseline two-stage approach with a Bayesian joint model. The two-stage analysis fitted a linear mixed-effects model and included each patient's predicted baseline CD4 value as a fixed covariate in a Cox proportional hazards model. The joint model simultaneously modeled the longitudinal CD4 process and survival while linking mortality risk to the current underlying CD4 value. The estimated association between ddI and mortality was similar in direction and magnitude across the two approaches. The two-stage estimate was HR = 1.342 (95% CI: 1.006-1.789), whereas the joint-model estimate was HR = 1.383 (95% CrI: 0.952-2.010). The estimated protective association of CD4 was stronger under the joint model (HR = 0.776) than under the two-stage approach (HR = 0.826). Because the approaches used different summaries of the longitudinal CD4 process, the observed differences cannot be attributed solely to measurement error or informative dropout. The findings demonstrate that the treatment of longitudinal biomarker information can materially affect statistical inference.

Khaleghi and Lugosi asked whether the sum of the $\phi$-mixing (uniform-mixing) coefficients of a real-valued discrete-time stationary ergodic process can be consistently estimated from a single sample path. We construct a deterministic sequence of Borel statistics that, for every such process, converges almost surely to the extended sum $\sum_{m\geq1}\phi(m)$, including divergence to $+\infty$ when the sum is infinite. The estimator combines finite dyadic cylinders with a vanishing empirical cutoff on conditioning-event frequencies. When the target is finite, $\alpha(m)\leq\phi(m)$ supplies summable covariance control for the growing finite classes, and a stable-division estimate yields the upper bound. Fixed positive-probability witnesses and Birkhoff's theorem give the lower bound, including the infinite-target case. No mixing rate or known positive lower bound on conditioning-event probabilities is required.

Cramer's V is the effect size reported beside almost every chi-square test, read against Cohen's labels, yet a large fraction of such numbers describe sampling noise and the standard bias correction (Bergsma 2013) does not fix it. We assemble three results and claim only the consequence of each. First, the squared effect size phi^2 admits no unbiased estimator at any sample size: under fixed-N multinomial sampling the expectation of any estimator is a polynomial in the cell probabilities, while phi^2 is not. Second, unbiasedness transfers across a rescaling of the effect size only if the rescaling is affine, and among affine choices V^2 = phi^2/k is the one bounded in [0,1] with value 1 at perfect association. Third, we give an interval with conservative, asymptotically valid coverage, obtained by projecting a likelihood-ratio confidence set for the cell probabilities through the effect-size map; its lower endpoint is zero in closed form exactly when the test of independence fails to reject. Because nothing is unbiased, the only question is where the irreducible error is placed. Bergsma's correction puts zero error at the null but several percent under the alternative; a delete-one jackknife on the V^2 scale spreads it thin everywhere (absolute bias at most 0.008 over a 180-design grid). Pooling does not remove bias: across 3,000 simulated meta-analyses, pooling 200 studies drives the naive estimator's chance of landing within 0.01 of the truth to zero, while the jackknife's rises to 0.99. The projected interval covers 0.997-1.000 across the tested designs, while a noncentral inversion undercovers (0.936 at phi^2 = 0.18) at two to three times the width. The point estimate and the interval are different problems with different answers; conflating them is why the literature has neither. We give a routing rule and a browser tool that implements it.

For solving nonconvex equality-constrained optimization problems, a recent Gradient-Eigenstep Algorithm by Goyens et al.~is an iteration-efficient approach, based on minimizing Fletcher's augmented Lagrangian function, for finding an approximate second-order stationary point from an arbitrary starting point. In this paper, the analysis of this algorithm is extended, offering a two-fold contribution. First, it is shown that a local-linear rate of convergence can be obtained by this method if it is initiated sufficiently close to a strong second-order stationary point and employs a sufficiently small step-size parameter and sufficiently large penalty parameter. In this case, the algorithm reduces to a gradient descent algorithm applied to minimize Fletcher's augmented Lagrangian. Second, as a particularly useful application of the first result, it is shown that the Gradient-Eigenstep algorithm can be used as an iteration-efficient subproblem solver in the context of a progressive sampling strategy for solving equality-constrained optimization problems when the objective and constraint functions are defined by large sample averages, ultimately offering an algorithm with an improved worst-case sample complexity when compared to an approach that solves a full-sample problem directly.

Wildfire susceptibility mapping typically relies on physical variables assembled from multiple remote-sensing, climate, and geospatial products. AlphaEarth Foundations (AEF) provides analysis-ready geospatial embeddings that may reduce this dependence on heavy harmonisation and task-specific feature engineering, but their value for wildfire susceptibility mapping has not been systematically evaluated. Using Victoria, Australia (2017-2025), as a case study, we show that AEF embeddings can reconstruct commonly used variables in wildfire susceptibility analysis with high accuracy. In downstream susceptibility models trained on satellite-derived fire occurrence data, embedding-based susceptibility models achieve ROC-AUC values above 0.92 and consistently identify high wildfire susceptibility across eastern Victoria, particularly Gippsland and the north-eastern uplands, with additional localized hotspots in central and northwestern Victoria. A key feature of AEF embeddings is their strong near-region transferability within climatically similar regions. When embedding-based models trained in Victoria are applied to Canberra and Western Sydney-Blue Mountains, ROC-AUC improves by around 4% at Canberra and declines by around 2% at Western Sydney-Blue Mountains, compared with a mean decrease of approximately 25% for physical-variable models. These findings provide practical guidance for using AEF embeddings and lay a foundation for scalable wildfire susceptibility mapping workflows for downstream users such as government agencies and (re)insurers.

An e-detector for a pre-change class $\mathcal P$ is a nonnegative process $M$ such that $\mathbb E_P[M_\tau] \leq \mathbb E_P[\tau]$ for all stopping times $\tau$ and all $P \in \mathcal P$. Thresholding e-detectors controls the average run length (ARL): declaring a change at the first time $T_b$ when $M$ crosses $b$ ensures that $\inf_{P \in \mathcal P}\mathbb E_P[T] \geq b$. But e-detectors do substantially more than control the ARL; they also satisfy a optional-horizon inequality: \[ P(T_b\leq\sigma)\leq \mathbb E_P[\sigma]/b \] for every data-dependent stopping time (monitoring horizon) \(\sigma\) and $P\in \mathcal P$. In particular, every e-detector-based procedure obeys $P(T\leq t)\leq t/b$ at each fixed $t$, thus avoiding early false alarms. Remarkably, the converse also holds: every stopping time $T$ that satisfies the optional-horizon inequality must in fact arise from thresholding an e-detector. We also derive a universal representation of stopping times that satisfy (only) ARL control. These are represented by weak e-detectors, that only require $\mathbb E_P[M_\tau] \leq \mathbb E_P[\tau]$ to hold at all threshold stopping times $T_b$. Appendices present universal representations for other (less common) change detection metrics.

Probabilities of causation (PoCs) characterize individual causal responses that cannot be directly observed and therefore generally require partial identification. Tian and Pearl first derived theoretically sharp bounds for binary PoCs, including the probability of necessity (PN), the probability of sufficiency (PS), and the probability of necessity and sufficiency (PNS). Mueller et al. subsequently tightened the bounds for binary PNS by incorporating causal information encoded in covariates and mediators. More recently, Li and Pearl, as well as Shu et al., extended PoCs to multivalued settings and derived corresponding theoretical bounds. These developments naturally raise the question of whether additional causal knowledge can further tighten the bounds in multivalued settings. This paper addresses this question by deriving tighter bounds for multivalued PoCs through the incorporation of causal information encoded in covariates and mediators. We illustrate the theoretical results with toy examples, while simulation studies further demonstrate that the proposed bounds are tighter than existing nonbinary bounds.

A flat training curve does not reveal whether a neural network has reached a global optimum, is locally trapped, is representation-limited, or is mismatched to its trainer. We introduce Training Under Challenge, an executable-certificate framework in which predeclared, architecture-valid procedures construct complete alternatives in the same certified class and reevaluate the same objective. Any lower-valued candidate is a replayable witness that lower-bounds the checkpoint's empirical global-optimality gap. Passing a finite suite is only suite-relative; global-gap conclusions require a separately justified coverage mechanism. We define a resource-indexed challenge-power modulus that characterizes the largest gap compatible with passage. For squared loss, current block-decrease operators make coverage checkable and yield uniform and realized-residual bounds. We prove the converse frontier: without coverage, a first-order ReLU trainer can reach infinitely many exact conditional head optima while converging to a non-global point. On a channel-gated ResNet-18 distillation problem with known optimum, eight internal challenges cover all 240 audited output directions, and realized-residual bounds lie within factors of 1.74–3.02 of the true gap. Paired predictive certificates separate decoder under-use from representation insufficiency, while quantized-denoising studies demonstrate diagnosis, repair, and current-state recertification.

Simulating realistic time-to-event data is essential for planning and evaluating complex clinical trial designs. Conventional approaches often sample event times from parametric families, such as Weibull or log-normal distributions, which restrict hazard shapes and may poorly represent observed survival data. We propose an empirical copula-based framework for simulating multivariate data containing continuous, binary, count, and right-censored time-to-event variables. The method completes censored historical survival data using a two-zone procedure that combines conditional Kaplan-Meier imputation with a parametric tail. It matches a target survival distribution through a log-scale location-scale transformation and a power distortion of the empirical percentile function, while preserving historical dependence through a Gaussian copula fitted to rank correlations. In an oncology trial of previously treated non-small-cell lung cancer, the method reconstructs overall survival and progression-free survival curves for the experimental arm using control-arm data and a small set of target percentiles. Simulations preserve rank correlations among baseline covariates and the dependence between progression-free and overall survival, with censored Kendall's tau of 0.522 compared with 0.549 in the observed data. The method is implemented in the R package EmpiricalSim.

Causal discovery aims to uncover the underlying causal relationships given data generated from a system. The goal, however, is not merely to predict causal edges given data, but also to be able to interpret and explain either observed or hypothesized phenomena, such as a particularly large causal effect. We consider this task of conditional causal discovery and cast it as a Bayesian inference problem, in which we target the posterior over causal graphs and parameters conditional on an event such as a causal-effect constraint. Unfortunately, this poses a computational challenge: existing approaches to Bayesian causal discovery struggle when the event has small posterior mass. To address this, we adapt rare-event estimation techniques to perform inference the joint graph-parameter space. Our method gradually drives a particle population toward the constrained region while maintaining samples that approximate the conditional posterior. Empirical evaluation on synthetic graphs validates the accuracy of our approach at small and large scales, and we show in a case study on the Sachs protein dataset how our method can be used to aid scientific exploration by providing pathway-level summaries.

We introduce an intrinsic spectral sparsity model for nonparametric density estimation on compact connected Riemannian manifolds. Instead of penalizing coefficients in an arbitrarily chosen Laplace–Beltrami eigenbasis, we group each complete eigenspace and measure the Hilbert norm of its spectral component. The resulting block-variation space is basis independent and isometry invariant. We establish its structural, atomic, and nonlinear approximation properties and clarify its relation to Sobolev, Besov, and coefficientwise spectral $\ell^1$ classes. We then construct a coordinate-free block-shrinkage estimator and prove a nonasymptotic signal-dependent $L^2$-oracle inequality that adapts to the unknown set of detectable eigenspaces. Under polynomial spectral growth, the risk theory separates the number of spectral blocks from their multiplicities and exhibits two regimes: one driven by a single high-dimensional eigenspace and the other by cumulative spectral complexity. Under matching spectral-growth and nondegeneracy assumptions, corresponding minimax lower bounds show that this multiplicity dependence is intrinsic, with sharp consequences for spheres and the rotation group $SO(3)$. Finally, we develop a positive, normalized, block-penalized exponential spectral sieve for log-densities and derive likelihood oracle inequalities together with expected Kullback–Leibler, Hellinger, and $L^2$ risk bounds. The resulting framework provides a geometry-respecting theory of sparse density estimation that remains invariant under changes of eigenbasis.

Language model classifiers with explanations are used for moderation, routing, topic triage, and low-resource annotation. We study black-box auditing when the defender has only clean calibration data without trigger information but can ask the classifier for a label plus a short rationale or quoted evidence. We introduce Groundedness Drift, a lightweight score measuring whether the answer summary remains grounded in the input. Across two 7B backbones, five datasets, and four common non-adaptive OpenBackdoor-style attack families, Groundedness Drift achieves higher AUROC and lower residual target ASR than every compared detector in all cases at a nominal 5% clean-FPR budget. We then evaluate Unsupported Groundedness, a multi-probe escalation for explanation-camouflage stress cases. Unsupported Groundedness improves signals but does not close the adaptive gap.

Calibrating computational models to experimental data is a core task in applied statistics, especially in scientific domains, where physical experiments are costly and simulations play a central role in design and inference. Motivated by uncertainty quantification challenges in particle accelerator experiments, we develop and evaluate a Hierarchical Bayesian Calibration framework. In contrast to standard Bayesian calibration, certain inputs - such as beam injection amplitude - must be estimated separately for each experiment. We adopt the Kennedy-O'Hagan formulation and extend it with a hierarchical prior structure to model the distribution of experiment-specific calibration parameters, thus borrowing strength and improving generalisation across repeated experiments. A key methodological challenge arises from the need to evaluate a large number of forward simulations, which renders conventional Markov chain Monte Carlo approaches computationally prohibitive. To address this, we leverage the Bayesian Committee Machine as a scalable modelling strategy for Gaussian Process emulators. The BCM provides a principled divide-and-conquer approach, enabling parallel inference and reducing computational cost without requiring problem-specific tuning of the emulator approximation. Posterior sampling is performed using the No-U-Turn Sampler, supported by automatic differentiation in Julia, which removes the need for analytic gradient derivation and facilitates flexible model specification. We assess the proposed framework using established benchmark problems and simulated data from the Argonne Wakefield Accelerator. The results demonstrate substantial computational savings and robust calibration performance, highlighting the applicability of the method to large-scale scientific modelling problems.

Factor-MIDAS regressions forecast a low-frequency target by extracting common factors from a large panel of high-frequency predictors via principal component analysis (PCA). While PCA mitigates the curse of dimensionality, it relies on factor pervasiveness, an assumption often violated when factors are weak, as is common in macro-financial forecasting. We propose SsPCA-MIDAS, which integrates supervised scaled PCA (SsPCA) into the mixed-data sampling framework. We establish consistency and asymptotic normality under weak factors, permitting inference on the prediction target. Simulations show that SsPCA-MIDAS outperforms competing PCA-based and supervised methods, especially when weak factors are prevalent. Applying machine-learning techniques such as boosting to the cleaner factors it extracts yields further gains. An extensive application to U.S. macro-financial forecasting shows that SsPCA-MIDAS selects economically meaningful predictors and improves forecasts of GDP, inflation, unemployment, asset prices, and volatility.

We propose a hierarchical Bayesian model for estimating time-varying outage risk from county-level power outage data. The model combines cubic B-spline basis functions with a Beta-Binomial likelihood to capture smooth, nonlinear recovery trajectories while accommodating overdispersion in observed customer counts. A shared hyperprior on the Beta-Binomial concentration parameter enables hierarchical shrinkage across geographically indexed groups, allowing sparse or short-lived events to borrow statistical strength from the broader population. Posterior inference is conducted via the No-U-Turn Sampler (NUTS) in PyMC, yielding full posterior distributions over latent outage probabilities and derived resilience metrics including the area under the risk curve (AUC). We assess predictive performance using posterior predictive coverage, RMSE, and leave-one-out cross-validation, and demonstrate the model across a heterogeneous set of outage events in southern Wisconsin drawn from the EAGLE-I power outage monitoring platform. A direct comparison against naive trapezoidal AUC estimation confirms that the posterior mean recovers the same point estimates as deterministic integration while providing calibrated uncertainty quantification that deterministic approaches structurally cannot. The framework offers utilities and emergency planners a principled tool for benchmarking recovery dynamics and comparing outage events under uncertainty.

We present a hierarchical Bayesian framework for non-homogeneous pairwise interaction Gibbs point process models, where the global and local effect functions are modeled via basis function expansions. We further propose a testing procedure in order to assess complete spatial randomness. The proposed methodology is exemplified through two real benchmark data examples involving water striders and forest fires.

Detection and attribution of climate change relies on fingerprinting–a linear errors-in-variables regression framework in which both predictors and responses exhibit internal variability governed by a proportional covariance structure, subject to a variability inflation factor. Accurate estimation of the scaling factors (regression coefficients) depends on inferring the precision matrix of the regression errors from limited climate model control runs. In high-dimensional settings, existing approaches often overlook the variance inflation of the predictors and suffer from imprecise precision matrix estimates, yielding biased estimators, underestimated uncertainties, and confidence intervals with poor coverage. We propose a nonlinear, rotation-invariant shrinkage framework for estimating the precision matrix that restores the asymptotic optimality of the total least squares estimator in high-dimensional regimes. Our procedure jointly estimates the scaling factors and the variability inflation factor, thereby correcting estimation bias, and incorporates consistent variance estimators to enable valid uncertainty quantification. We also develop a residual consistency test to assess model adequacy. Numerical studies demonstrate precise estimation, improved confidence interval coverage, and higher efficiency. Applied to annual mean near-surface air temperature data from 1951–2020, our method produces narrower and more reliable confidence intervals, yielding refined attribution results.

Organizations decide whom to treat under a budget and want to know what a targeting rule would have earned before deploying it. Off-policy evaluation promises this from logged data, but the deployable rule is a deterministic top-k policy: it removes all averaging over actions, so weak overlap hits the estimate directly. We benchmark six estimators across five datasets and two known-effect sweeps, and validate the mechanisms against a non-simulated paired reference. First, weak overlap is governed by logger-target action alignment, not by logging sharpness alone: what governs support is the logger's probability of the target's actions. Sharpening a logger built from the target's own score barely moves overlap over the tested range; action-level disagreement collapses it. Effective sample size ranks this risk across logging environments, but is weak at ranking candidates within the single log a practitioner holds, and its cut point does not transfer. Second, the optimizer's curse is not fixed by cross-fitting the outcome nuisance. When the rule is fit on the data used to evaluate it, cross-fitting the nuisance alone leaves the reuse bias in place and makes it worse. Honest policy-level splitting avoids the reuse by targeting the learning procedure's value – a change of estimand, not a de-biasing of the full-sample policy. Third, propensity-estimation error is the largest degradation we measure: an out-of-fold estimate hurts IPS more than any other stress we apply, leaves doubly-robust estimation almost unchanged, and can invert the overlap diagnostic itself. Logging is synthesized and propensities floored at 0.02, so every failure occurs with bounded weights; the floor also reduces the two tuned hybrids to their untuned parents, leaving four practically distinct estimators, and all exact-value surfaces are synthetic or semi-synthetic. We release the benchmark; public data only.

Large astrophysical simulation campaigns often generate training data by sampling parameters across a Uniform prior box. Due to the proposal's sharp edge, neural posterior estimators struggle to learn accurate approximations near the boundaries. We propose Tailed-Uniform, a family of hybrid proposal distributions for sampling training simulations for robust simulation-based inference. By padding the original hard-truncated training box with decaying tails, Tailed-Uniform-trained networks yield more accurate posteriors near and beyond the edges. We demonstrate these improvements on a family of tail shapes, including a widened Uniform box as a control. Our results suggest that additional simulations near the prior boundary better constrain the networks as it approaches the edge of the training box, even for Uniform assumed priors. We show these advantages on a toy problem and cosmological parameter inference from the matter power spectrum. These benefits increase in high dimensions, where boundaries dominate parameter space volume.

Neural combinatorial optimization (NCO) relies on parallel solution sampling for training, yet existing methods fail to fully exploit the rich information latent in a co-sampled solution group. Preference-optimization methods anchor on the single best solution and discard fine-grained quality and structural signal from all other peers-a failure we term gradient signal polarization. Mean-based baselines instead weight peers uniformly, so structurally near-identical peers flood the baseline with redundant information and keep gradient variance high-a failure we term baseline redundancy. We propose SSPO (Structure-Aware Similarity-Weighted Preference Optimization), which scores all $B$ sampled solutions jointly through a dissimilarity-weighted leave-one-out baseline: structurally distinct peers receive higher weight, resolving both failures in a single mechanism. The baseline uses zero-parameter, problem-adaptive solution embeddings built from the encoder's existing node representations. Experiments on TSP, EFL, and JSP benchmarks show consistent gains over prior best-anchor and uniform-weight baselines. A direct comparison against uniform RLOO on TSP and EFL confirms that structure-aware weighting is the primary driver of improvement. The SSPO-trained EFL policy has been deployed in a production facility-location system at JD$\mathord{.}$com, confirming practical viability at scale.