Papers

Bayesian experimental design (BED) for complex physical systems is often limited by the nested inference required to estimate the expected information gain (EIG) or its gradients. Each outer sample induces a different posterior, creating a large and heterogeneous set of inference targets. Existing methods have to sacrifice either accuracy or efficiency: they either perform per-outer-sample posterior inference, which yields higher fidelity but at prohibitive computational cost, or amortize the inner inference across all outer samples for computational reuse, at the risk of degraded accuracy under posterior heterogeneity. To improve accuracy and maintain cost at the amortized level, we propose a grouped geometric pooled posterior framework that partitions outer samples into groups and constructs a pooled proposal for each group. While such grouping strategy would normally require generating separate proposal samples for different groups, our tailored ensemble Kalman inversion (EKI) formulation generates these samples without extra forward-model evaluation cost. We also introduce a conservative diagnostic to assess importance-sampling quality to guide grouping. This grouping strategy improves within-group proposal-target alignment, yielding more accurate and stable estimators while keeping the cost comparable to amortized approaches. We evaluate the performance of our method on both Gaussian-linear and high-dimensional network-based model discrepancy calibration problems.

Determining the number of factors in high-dimensional factor models remains a fundamental challenge, particularly when data are incomplete. This paper introduces the concept of identifiable factors, those that can be reliably recovered despite missing observations, and proposes the Missingness-Adaptive Thresholding Estimator (MATE). To our knowledge, MATE is the first missingness-adaptive framework for factor number determination that accommodates both homogeneous and heterogeneous missingness without imposing restrictive assumptions on factor strength. Notably, it operates without data imputation, circumventing the computational burden associated with most existing approaches. We establish a rigorous theoretical foundation for MATE, proving its consistency under a range of structural conditions. Extensive simulations and real-world applications demonstrate that MATE consistently outperforms state-of-the-art methods, exhibiting superior robustness in settings with high missingness rates and weak factor signals.

Empirical studies of trained models often report a transient regime in which signal is detectable in a finite gradient descent time window before overfitting dominates. We provide an analytically tractable random-matrix model that reproduces this phenomenon for gradient flow in a linear teacher–student setting. In this framework, learning occurs when an isolated eigenvalue separates from a noisy bulk, before eventually disappearing in the overfitting regime. The key ingredient is anisotropy in the input covariance, which induces fast and slow directions in the learning dynamics. In a two-block covariance model, we derive the full time-dependent bulk spectrum of the symmetrized weight matrix through a $2\times 2$ Dyson equation, and we obtain an explicit outlier condition for a rank-one teacher via a rank-two determinant formula. This yields a transient Baik-Ben Arous-Péché (BBP) transition: depending on signal strength and covariance anisotropy, the teacher spike may never emerge, emerge and persist, or emerge only during an intermediate time interval before being reabsorbed into the bulk. We map the corresponding phase diagrams and validate the theory against finite-size simulations. Our results provide a minimal solvable mechanism for early stopping as a transient spectral effect driven by anisotropy and noise.

We introduce a robust conformal prediction method based on the half-mass radius $\dP(x):=\inf\{r>0:P(B(x,r))>1/2\}$. Its empirical version is exactly the distance from a point to its $\mathbf{k}$-th nearest neighbour, with $\mathbf{k}=\lfloor n/2\rfloor+1$. The resulting conformal sets retain finite-sample marginal validity and asymptotically target the robust population central set $\Qba:=\{x\in\R^d:\dP(x)\le\beta_\alpha\}$. We prove consistency in symmetric-difference probability, derive non-asymptotic exponential bounds and obtain the rate $O((\log n/n)^{1/2})$ under a local mass condition. Under the same local regularity on the uncontaminated law, we also establish quantitative $O(\eta)$ stability, uniformly over arbitrary contaminations of sufficiently small mass $\eta$, prove Hausdorff convergence of the empirical central sets, and provide computable ball-based representations using only pairwise distances.

We propose an empirical Bayes framework for combining estimators obtained from multiple identification functionals associated with the same estimand. We adaptively pool a collection of asymptotically linear estimators, each of which may target a different parameter because of violations of their identification assumptions. Although all estimators are computed from the same sample and are therefore dependent, we show that a working independence construction preserves consistency of the posterior mean under centered heterogeneity. Inference is driven by a latent heterogeneity parameter governing the dispersion of the different identification images. When this parameter is zero, the functionals share a common estimand and we construct frequentist confidence intervals using either sandwich variance estimation or subsampling. When it is positive, the functionals are interpreted as exchangeable draws from a latent population of causal effects, and we construct asymptotically valid Bayesian prediction intervals for the latent target of a new identification functional. These inferential procedures answer different questions, rely on distinct assumptions, and are therefore complementary rather than competing. We illustrate the framework by augmenting evidence from randomized controlled trials with observational studies.

Smooth functions on graphs have wide applications in manifold and semi-supervised learning. In this paper, we study a bandit problem where the payoffs of arms are smooth on a graph. This framework is suitable for solving online learning problems that involve graphs, such as content-based recommendation. In this problem, each item we can recommend is a node and its expected rating is similar to its neighbors. The goal is to recommend items that have high expected ratings. We aim for the algorithms where the cumulative regret with respect to the optimal policy would not scale poorly with the number of nodes. In particular, we introduce the notion of an effective dimension, which is small in real-world graphs, and propose two algorithms for solving our problem that scale linearly and sublinearly in this dimension. Our experiments on real-world content recommendation problem show that a good estimator of user preferences for thousands of items can be learned from just tens of nodes evaluations.

LLMs utilizing chain-of-thought reasoning often waste substantial compute by producing long, incorrect responses. Abstention can mitigate this by withholding outputs unlikely to be correct. While most abstention methods decide to withhold outputs before or after generation, dynamic mid-generation abstention considers early termination of unpromising reasoning traces at each token position. Prior work has explored empirical variants of this idea, but principled guidance for the abstention rule remains lacking. We present a formal analysis of dynamic abstention for LLMs, modeling abstention as an explicit action within a regularized reinforcement learning framework. An abstention reward parameter controls the trade-off between compute and information. We show that abstaining when the value function falls below this reward strictly outperforms natural baselines under general conditions. We further derive a principled and efficient method to approximate the value function. Empirical results on mathematical reasoning and toxicity avoidance tasks support our theory and demonstrate improved selective accuracy over existing methods.

Selecting an appropriate kernel is a central challenge in kernel-based spectral methods. In Kernelized Diffusion Maps (KDM), the kernel determines the accuracy of the RKHS estimator of a diffusion-type operator and hence the quality and stability of the recovered eigenfunctions. We introduce two complementary approaches to adaptive kernel selection for KDM. First, we develop a variational outer loop that learns continuous kernel parameters, including bandwidths and mixture weights, by differentiating through the Cholesky-reduced KDM eigenproblem with an objective combining eigenvalue maximization, subspace orthonormality, and RKHS regularization. Second, we propose an unsupervised cross-validation pipeline that selects kernel families and bandwidths using an eigenvalue-sum criterion together with random Fourier features for scalability. Both methods share a common theoretical foundation: we prove Lipschitz dependence of KDM operators on kernel weights, continuity of spectral projectors under a gap condition, a residual-control theorem certifying proximity to the target eigenspace, and exponential consistency of the cross-validation selector over a finite kernel dictionary.

We discuss the regression-by-composition framework of Farewell, Daniel, Stensrud and Huitfeldt, highlighting a key consequence of its sequential construction: order dependence. Reordering the flows may change the implied conditional distribution, the interpretation of model parameters, and the associated estimation problem, with consequences for model specification, interpretation, and inference.

In an editorial in the Journal of Marketing, Steenkamp et al. (2026) make a valuable and timely intervention by urging marketing scholars to move beyond dichotomous significance testing and to report effect sizes that speak to substantive significance. Their editorial is especially strong in its insistence on exact p-values, richer statistical reporting, and closer alignment between rigor and relevance. Yet, their framework omits the local form of Cohen's f^2, that is f(B)^2 as an effect-size measure for the contribution of an individual predictor or predictor block B within a multivariable model. That omission matters because much of marketing research relies on regression-type models in which the central theoretical question is not merely whether a model fits globally, but whether a focal construct adds meaningful explanatory power beyond competing predictors and controls. This commentary argues that the R-squared foundation of local Cohen's f(B)^2 is a strength, especially in large-sample settings. Moreover, f-squared-type local effect sizes can be extended beyond ordinary least squares to multilevel models and, more tentatively, to neural networks and other machine-learning models.

Win statistics have become increasingly popular for analyzing hierarchical composite endpoints in clinical trials. The win ratio, win odds, net benefit, and desirability of outcome ranking (DOOR) share a pairwise-comparison framework and provide complementary summaries of treatment benefit. Despite recent progress in individually randomized trials, statistical inference for these measures in cluster-randomized trials (CRTs) remains underdeveloped. We provide a unified development and comparison of six testing procedures for all four win measures in parallel-arm CRTs: three Wald tests, two randomization-based tests, and a jackknife empirical likelihood ratio test. Through simulations with hierarchical semi-competing risks outcomes, we evaluate type I error rate and power across varying design parameters. With 20 clusters, the randomization-based procedures provided the most stable type I error rate control, while the clustered rank-sum Wald test with a t-distribution was the most reliable among the Wald tests, occasionally carrying a conservative test size. For the win ratio and win odds, the permutation test also yielded higher power than the clustered rank-sum Wald test. With 100 clusters, differences in type I error rate and power were small. These findings favor permutation inference in small CRTs, with the clustered rank-sum Wald test providing an analytic alternative, particularly for net benefit and DOOR. On the other hand, the analytic Wald procedures offer a computationally convenient choice for CRTs with a large number of clusters. We illustrate the methods by reanalyzing the STRIDE trial and implement all procedures in the WinsCRT R package.

Stepped-wedge cluster randomized trials (SW-CRTs) evaluate interventions rolled out across clusters over time. Standard analyses typically use immediate-treatment (IT) models, which assume effects begin at crossover and remain constant thereafter. When effects vary with exposure duration, IT models may misrepresent target effects. Exposure-time indicator (ETI) models address this by allowing treatment effects to differ by time since exposure and by targeting the time-averaged treatment effect (TATE) and long-term effect (LTE). Like IT models, ETI models require specification of a random-effects structure, which is often misspecified, and the performance of robust variance estimators (RVEs) in this setting is not well understood. We review RVEs for ETI models and evaluate them in simulation studies with continuous and binary outcomes under correctly specified (binary only) and misspecified random-effects structures. We compare the classic sandwich, Kauermann-Carroll (KC), Mancl-DeRouen (MD), and Morel-Bokossa-Neerchal (MBN) estimators for inference on the TATE and LTE. Our simulations show that under misspecified random-effects structures, model-based standard errors (SE) produced undercoverage, whereas RVEs improved performance. For continuous outcomes, MD with a t-distribution and degrees of freedom equal to the number of clusters minus two gave the most consistent coverage probabilities. For binary outcomes, MBN was the only consistently reliable option. MD, however, could be unstable in one-cluster-per-sequence designs because of data sparsity. Across scenarios, both model-based SE and RVE for LTE were unstable, indicating that greater caution is needed when targeting LTE under ETI models.

Selection bias arises when the probability that an observation enters a dataset depends on variables related to the quantities of interest, leading to systematic distortions in estimation and uncertainty quantification. For example, in epidemiological or survey settings, individuals with certain outcomes may be more likely to be included, resulting in biased prevalence estimates with potentially substantial downstream impact. Classical corrections, such as inverse-probability weighting or explicit likelihood-based models of the selection process, rely on tractable likelihoods, which limits their applicability in complex stochastic models with latent dynamics or high-dimensional structure. Simulation-based inference enables Bayesian analysis without tractable likelihoods but typically assumes missingness at random and thus fails when selection depends on unobserved outcomes or covariates. Here, we develop a bias-aware simulation-based inference framework that explicitly incorporates selection into neural posterior estimation. By embedding the selection mechanism directly into the generative simulator, the approach enables amortized Bayesian inference without requiring tractable likelihoods. This recasting of selection bias as part of the simulation process allows us to both obtain debiased estimates and explicitly test for the presence of bias. The framework integrates diagnostics to detect discrepancies between simulated and observed data and to assess posterior calibration. The method recovers well-calibrated posterior distributions across three statistical applications with diverse selection mechanisms, including settings in which likelihood-based approaches yield biased estimates. These results recast the correction of selection bias as a simulation problem and establish simulation-based inference as a practical and testable strategy for parameter estimation under selection bias.

Observational data are often used to answer causal questions, yet the legitimacy of doing so is often argued to hinge on strong, domain supported assumptions about underlying causal structure with limited guidance on how much domain knowledge support should exist to justify including a causal edge of interest in a directed acyclic graph. We introduce the criterion of embarrassingly causal scenarios, where the existence of an exposure outcome relationship is so uncontroversial that the assumptions needed to include the corresponding causal edge in a DAG can be reasonably made. Using the case of Magic The Gathering booster draft decisions and gameplay outcomes, we show how purely observational data from 17Lands are widely and effectively used to guide draft choices despite substantial confounding, selection effects, and post treatment conditioning. We argue that the embarrassingly causal quality is a sufficient condition for justifying the construction of causal estimands and the collection of observational data to estimate them. Correspondingly, we provide guidance on evaluating observational causal inference assumptions for authors, reviewers, and readers.

We address the problem of planning in an environment with deterministic dynamics and stochastic rewards with discounted returns. The optimal value function is not known, nor are the rewards bounded. We propose Platypoos, a simple scale-free planning algorithm that adapts to the unknown scale and smoothness of the reward function. We provide a sample complexity analysis for Platypoos that improves upon prior work and holds simultaneously over a broad range of discount factors and reward scales, without the algorithm knowing them. We also establish a matching lower bound showing our analysis is optimal up to constants.

Variational inference (VI) is a central tool in modern machine learning, used to approximate an intractable target density by optimising over a tractable family of distributions. As the variational family cannot typically represent the target exactly, guarantees on the quality of the resulting approximation are crucial for understanding which of its properties VI can faithfully capture. Recent work has identified instances in which symmetries of the target and the variational family enable the recovery of certain statistics, even under model misspecification. However, these guarantees are inherently problem-specific and offer little insight into the fundamental mechanism by which symmetry forces statistic recovery. In this paper, we overcome this limitation by developing a general theory of symmetry-induced statistic recovery in variational inference. First, we characterise when variational minimisers inherit the symmetries of the target and establish conditions under which these pin down identifiable statistics. Second, we unify existing results by showing that previously known statistic recovery guarantees in location-scale families arise as special cases of our theory. Third, we apply our framework to distributions on the sphere to obtain novel guarantees for directional statistics in von Mises-Fisher families. Together, these results provide a modular blueprint for deriving new recovery guarantees for VI in a broad range of symmetry settings.

Data equity is an emerging framework for responsible data science. However, its core concepts, including fairness, representativeness, and information bias, remain largely abstract and general, lacking the mathematical specificity needed for practical implementation. In this paper, we demonstrate how statisticians can operationalize data equity by translating its tenets into precise, testable formulations tailored to a given problem. Using the well-documented case of differential measurement error across racial groups in pulse oximetry, we first adopt an oracle approach, tracing how a single upstream violation of information bias compounds through the analytic pipeline into treatment disparities, fairness violations, and adverse health outcomes. We then demonstrate the inverse: starting from an observed outcome disparity, the data equity framework provides a principled structure for systematically identifying its statistical sources. Our exposition underscores how data equity, prediction equity, and decision equity are distinct requirements with distinct evaluation and policy needs–a nuance that highlights both the unique role of statisticians in the era of artificial intelligence as well as the necessity of interdisciplinary collaboration.

The first passage time problem is considered for stochastic logistic growth model with constant harvesting and multiplicative environmental noise. Explicit expressions for the moments and cumulants of both upcrossing and downcrossing FPTs in the presence of constant thresholds are obtained through a power-series expansion of the Laplace transform. Then a closed-form representation of the FPT density is recovered via an orthogonal Laguerre–Gamma expansion . This representation is used to numerically evaluate FPT densities, with the truncation order controlling the trade-off between accuracy and stability. Numerical experiments based on Monte Carlo simulations confirm the high accuracy of the method in regimes of moderate dispersion and highlight its limitations when higher-order moments grow rapidly. Application to fisheries management models shows that the method remains effective even for large-scale population. Finally, the approximated density is satisfactory used to estimate some parameters of the model.

In this paper, we present three neural network architectures designed for real-time classification of weather conditions (sunny, rain, snow, fog) from images. These models, inspired by recent advances in style transfer, aim to capture the stylistic elements present in images. One model, called "Multi-PatchGAN", is based on PatchGANs used in well-known architectures such as Pix2Pix and CycleGAN, but here adapted with multiple patch sizes for detection tasks. The second model, "Truncated ResNet50", is a simplified version of ResNet50 retaining only its first nine layers. This truncation, determined by an evolutionary algorithm, facilitates the extraction of high-frequency features essential for capturing subtle stylistic details. Finally, we propose "Truncated ResNet50 with Gram Matrix and Attention", which computes Gram matrices for each layer during training and automatically weights them via an attention mechanism, thus optimizing the extraction of the most relevant stylistic expressions for classification. These last two models outperform the state of the art and demonstrate remarkable generalization capability on several public databases. Although developed for weather detection, these architectures are also suitable for other appearance-based classification tasks, such as animal species recognition, texture classification, disease detection in medical imaging, or industrial defect identification.

\We introduce the horospherical depth, an intrinsic notion of statistical depth on Hadamard manifolds, and define the Busemann median as the set of its maximizers. The construction exploits the fact that the linear functionals appearing in Tukey's half-space depth are themselves limits of renormalized distance functions; on a Hadamard manifold the same limiting procedure produces Busemann functions, whose sublevel sets are horoballs, the intrinsic replacements for halfspaces. The resulting depth is parametrized by the visual boundary, is isometry-equivariant, and requires neither tangent-space linearization nor a chosen base point. For arbitrary Hadamard manifolds, we prove that the depth regions are nested and geodesically convex, that a centerpoint of depth at least $1/(d+1)$ exists, and hence that the Busemann median exists for every Borel probability measure. Under strictly negative sectional curvature and mild regularity assumptions, the depth is strictly quasi-concave and the median is unique. We also establish robustness: the depth is stable under total-variation perturbations, and under contamination escaping to infinity the limiting median depends on the escape direction but not on how far the contaminating mass has moved along the geodesic ray, in contrast with the Fréchet mean. Finally, we establish uniform consistency of the sample depth and convergence of sample depth regions and sample Busemann medians; on symmetric spaces of noncompact type, the argument proceeds through a VC analysis of upper horospherical halfspaces, while on general Hadamard manifolds it follows from a compactness argument under a mild non-atomicity assumption.

Smoothness has long been the dominant form of parsimony in functional data analysis, to the point of occasionally being conflated with the very notion of functional data. However, many core inferential tasks depend on the inverse covariance, where sparsity–rather than smoothness–emerges as the more natural structural constraint. In this paper, we explore Markovianity as an alternative to smoothness. Focusing on the Gaussian case as a central motivating setting, we exploit the fact that Markovianity induces a shape constraint on the covariance kernel. Building on this observation, we introduce a Markov transform of the empirical covariance together with a corresponding estimator that enforces the Markov structure. The estimator is adaptive and requires no regularity of the underlying covariance beyond continuity. In simulation experiments, it is seen to improve prediction performance even under model misspecification. Unlike smoothness-based assumptions, Markovianity is falsifiable. To assess its validity, we further propose a novel and computationally efficient test for the Markov property based on a new characterization of continuous graphical structure.

This paper introduces the separable covariance mixture model, which assumes a data-matrix $Y$ to be of the form $$ \sum\limits_{r=1}^R A_r X B_r $$ for one random $(d \times n)$-matrix $X$ with independent centered variance-one entries, and for two families of deterministic matrices $A_1,\dots,A_R \in \mathbb{C}^{d \times d}$ and $B_1,\dots,B_R \in \mathbb{C}^{n \times n}$. Under certain assumptions, it is shown that the resolvents $(\frac{1}{n} Y Y^* - z \operatorname{Id}_d)^{-1}$ and $(\frac{1}{n} Y^* Y - z \operatorname{Id}_n)^{-1}$ respectively approximate the deterministic matrices $$ -\frac{1}{z}\Big( \operatorname{Id}_d + \sum\limits_{r,s=1}^R \delta^{(B)}_{r,s}(z) A_{r} A_{s}^* \Big)^{-1} \ \ \text{ and } \ \ -\frac{1}{z}\Big( \operatorname{Id}_n + \sum\limits_{r,s=1}^R \delta^{(A)}_{r,s}(z) B_{s}^*B_{r} \Big)^{-1} \ , $$ where $\delta^{(A)}, \delta^{(B)} \in \mathbb{C}^{R \times R}$ are uniquely defined solutions to a certain dual system of equations. The results are non-asymptotic and do not require simultaneous diagonalizability of the families $(A_r)_{r \leq R}$ or $(B_r)_{r \leq R}$, as was required in previous works such as [Hazarika and Paul (2025)] or [Mei et al. (2023)]. An asymptotic application, which describes the limiting spectral distribution of the sample covariance matrix analogues $\frac{1}{n} Y Y^*$ or $\frac{1}{n} Y^* Y$, is included.

Deep learning (DL) has become a cornerstone of modern machine learning (ML) praxis. We introduce the R package mlr3torch, which is an extensible DL framework for the mlr3 ecosystem. It is built upon the torch package, and simplifies the definition, training, and evaluation of neural networks for both tabular data and generic tensors (e.g., images) for classification and regression. The package implements predefined architectures, and torch models can easily be converted to mlr3 learners. It also allows users to define neural networks as graphs. This representation is based on the graph language defined in mlr3pipelines and allows users to define the entire modeling workflow, including preprocessing, data augmentation, and network architecture, in a single graph. Through its integration into the mlr3 ecosystem, the package allows for convenient resampling, benchmarking, preprocessing, and more. We explain the package's design and features and show how to customize and extend it to new problems. Furthermore, we demonstrate the package's capabilities using three use cases, namely hyperparameter tuning, fine-tuning, and defining architectures for multimodal data. Finally, we present some runtime benchmarks.

This paper investigates the off-policy evaluation (OPE) problem from a distributional perspective. Rather than focusing solely on the expectation of the total return, as in most existing OPE methods, we aim to estimate the entire return distribution. To this end, we introduce a quantile-based approach for OPE using deep quantile process regression, presenting a novel algorithm called Deep Quantile Process regression-based Off-Policy Evaluation (DQPOPE). We provide new theoretical insights into the deep quantile process regression technique, extending existing approaches that estimate discrete quantiles to estimate a continuous quantile function. A key contribution of our work is the rigorous sample complexity analysis for distributional OPE with deep neural networks, bridging theoretical analysis with practical algorithmic implementations. We show that DQPOPE achieves statistical advantages by estimating the full return distribution using the same sample size required to estimate a single policy value using conventional methods. Empirical studies further show that DQPOPE provides significantly more precise and robust policy value estimates than standard methods, thereby enhancing the practical applicability and effectiveness of distributional reinforcement learning approaches.

Digital marketplaces processing billions of dollars annually represent critical infrastructure in sociotechnical ecosystems, yet their performance optimization lacks principled measurement frameworks that can inform algorithmic governance decisions regarding market efficiency and fairness from complex market data. By looking at orderbook data from double auction markets alone, because bids and asks do not represent true maximum willingnesses to buy and true minimum willingnesses to sell, there is little an economist can say about the market's actual performance in terms of allocative efficiency. We turn to experimental data to address this issue, `inverting' the standard induced value approach of double auction experiments. Our aim is to predict key market features relevant to market efficiency, particularly allocative efficiency, using orderbook data only – specifically bids, asks and price realizations, but not the induced reservation values – as early as possible. Since there is no established model of strategically optimal behavior in these markets, and because orderbook data is highly unstructured, non-stationary and non-linear, we propose quantile-based normalization techniques that help us build general predictive models. We develop and train several models, including linear regressions and gradient boosting trees, leveraging quantile-based input from the underlying supply-demand model. Our models can predict allocative efficiency with reasonable accuracy from the earliest bids and asks, and these predictions improve with additional realized price data. The performance of the prediction techniques varies by target and market type. Our framework holds significant potential for application to real-world market data, offering valuable insights into market efficiency and performance, even prior to any trade realizations.

Bayesian Deep Ensembles (BDEs) represent a powerful approach for uncertainty quantification in deep learning, combining the robustness of Deep Ensembles (DEs) with flexible multi-chain MCMC. While DEs are affordable in most deep learning settings, (long) sampling of Bayesian neural networks can be prohibitively costly. Yet, adding sampling after optimizing the DEs has been shown to yield significant improvements. This leaves a critical practical question: How long should the sequential sampling process continue to yield significant improvements over the initial optimized DE baseline? To tackle this question, we propose a stopping rule based on E-values. We formulate the ensemble construction as a sequential anytime-valid hypothesis test, providing a principled way to decide whether or not to reject the null hypothesis that MCMC offers no improvement over a strong baseline, to early stop the sampling. Empirically, we study this approach for diverse settings. Our results demonstrate the efficacy of our approach and reveal that only a fraction of the full-chain budget is often required.

Drowning is an omnipresent risk associated with any activity on or in the water, and rescuing a drowning person is particularly challenging because of the time pressure, making a short response time important. Further complicating water rescue are unsupervised and extensive swimming areas, precise localization of the target, and the transport of rescue personnel. Technical innovations can provide a remedy: We propose an Unmanned Aircraft System (UAS), also known as a drone-in-a-box system, consisting of a fleet of Unmanned Aerial Vehicles (UAVs) allocated to purpose-built hangars near swimming areas. In an emergency, the UAS can be deployed in addition to Standard Rescue Operation (SRO) equipment to locate the distressed person early by performing a fully automated Search and Rescue (S&R) operation and dropping a flotation device. In this paper, we address automatically locating distressed swimmers using the image-based object detection architecture You Only Look Once (YOLO). We present a dataset created for this application and outline the training process. We evaluate the performance of YOLO versions 3, 5, and 8 and architecture sizes (nano, extra-large) using Mean Average Precision (mAP) metrics mAP@.5 and mAP@.5:.95. Furthermore, we present two Discrete-Event Simulation (DES) approaches to simulate response times of SRO and UAS-based water rescue. This enables estimation of time savings relative to SRO when selecting the UAS configuration (type, number, and location of UAVs and hangars). Computational experiments for a test area in the Lusatian Lake District, Germany, show that UAS assistance shortens response time. Even a small UAS with two hangars, each containing one UAV, reduces response time by a factor of five compared to SRO.

Joint models for longitudinal and time-to-event data are increasingly used in health research to characterize the association between biomarker trajectories and the risk of clinical events. However, these models usually assume a linear relationship between the longitudinal marker and the log-hazard of the event. This assumption is rarely verified and often fails to capture complex biological mechanisms, such as U-shaped risk profiles or plateau effects. In this paper, we propose a fast and stable hierarchical framework for non-linear association structures in joint models using Integrated Nested Laplace Approximations (INLA), implemented in the INLAjoint R package. Our approach builds upon a unified framework where the scaling effect of the marker is decomposed into a parametric baseline (constant and linear components) and a data-driven smooth deviation modeled via an orthogonal basis derived from a second-order random walk. This natural hierarchy allows researchers to adapt model flexibility directly and verify the linearity assumption using standard information criteria. Through simulation studies, we demonstrate that the proposed method accurately recovers complex non-linear trajectories. We illustrate the practical utility of our framework by analyzing the joint association of the current value and current slope of body mass index (BMI) with all-cause mortality in the Health and Retirement Study. This analysis reveals a U-shaped mortality risk for the BMI value, and a non-linear effect for the rate of weight change, where a declining weight trajectory is associated with higher mortality risk.

High-resolution simulation models are essential for representing complex physical systems, yet their substantial computational cost severely limits the number of feasible high-fidelity (HF) evaluations. This problem is often addressed through multi-fidelity frameworks, which employ hierarchies of simulators with varying levels of fidelity and evaluation cost. A key difficulty in this setting is integrating information from such heterogeneous sources to accurately approximate HF simulators. This paper proposes a novel multi-fidelity emulation methodology based on ensemble learning. The base learners of the ensemble are hierarchical kriging emulators that systematically incorporate information from lower-fidelity models into HF predictions. Aggregation of these base learners via Bayesian model averaging yields the multi-fidelity emulator with principled uncertainty quantification. The between-model variance component of this uncertainty is then employed as the acquisition criterion in an adaptive design strategy to enrich the training set with informative samples. The predictive performance of the approach is assessed on a collection of well-established benchmark problems. Results show that our multi-fidelity emulator outperforms single-model alternatives in terms of accuracy and robustness. Furthermore, the adaptive design strategy effectively identifies informative samples and improves emulator performance under limited computational budgets.

Estimating conditional independence graphs from high-dimensional Gaussian data is challenging because methods must detect relevant edges while rigorously controlling statistical errors. We propose a Bayesian framework based on a prior accounts for degree heterogeneity edge sparsity, and graph topology the graph. The resulting posterior distribution is incorporated into a multiple testing procedure for graph inference with false discovery rate control. Computation is carried out through a combination of adaptive elastic nets and a variational expectation–maximization algorithm. In simulations, the method achieves reliable false discovery rate control while maintaining strong power, especially in heterogeneous networks such as graphs with hubs, and remains competitive under structural misspecification. Applications to breast cancer gene expression data and financial return networks show that the method yields sparse and interpretable conditional dependence graphs while retaining the most stable interactions detected by competing approaches.