Papers

Governments and development partners often seek Sustainable Development Goal (SDG) "accelerators" whose progress can propagate gains across human well-being, institutions, resources, and environmental priorities. Such claims require evidence on direction, timing, robustness, and trade-offs, not only network connectivity. We map directed SDG interdependence using a balanced panel of 114 countries observed annually from 2000 to 2024. Because the goal series are persistent, trending, and cross-sectionally dependent, we combine Dumitrescu-Hurlin panel Granger non-causality tests on first-differenced series with false-discovery control across 272 directed goal pairs, and panel local projections with Driscoll-Kraay standard errors for 31 theory-derived indicator linkages. We find 84 directed linkages after correction: 40 synergies and 44 trade-offs. This dense structure does not support a universal accelerator. Driver-receiver rankings are fragile across lag orders, centrality metrics, bootstrap resampling, and alternative dependence controls; only peace and strong institutions as a net receiver and poverty reduction as an effect-size-weighted driver are distinguishable in the bootstrap screen. Two local-projection pathways are supported, both leading to lower child mortality, and the education-child-health association is corroborated in independent World Development Indicators data across 183 countries. The policy implication is not to abandon SDG integration, but to replace fixed global accelerator rankings with adaptive portfolios built around supported, time-lagged linkages and monitored constituent indicators.

We study model-agnostic post-hoc calibration methods intended to improve probabilistic predictions in supervised binary classification on real i.i.d. tabular data, with particular emphasis on conformal and Venn-based approaches that provide distribution-free validity guarantees under exchangeability. We benchmark 21 widely used classifiers, including linear models, SVMs, tree ensembles (CatBoost, XGBoost, LightGBM), and modern tabular neural and foundation models, on binary tasks from the TabArena-v0.1 suite using randomized, stratified five-fold cross-validation with a held-out test fold. Five calibrators; Isotonic regression, Platt scaling, Beta calibration, Venn-Abers predictors, and Pearsonify are trained on a separate calibration split and applied to test predictions. Calibration is evaluated using proper scoring rules (log-loss and Brier score) and diagnostic measures (Spiegelhalter's Z, ECE, and ECI), alongside discrimination (AUC-ROC) and standard classification metrics. Across tasks and architectures, Venn-Abers predictors achieve the largest average reductions in log-loss, followed closely by Beta calibration, while Platt scaling exhibits weaker and less consistent effects. Beta calibration improves log-loss most frequently across tasks, whereas Venn-Abers displays fewer instances of extreme degradation and slightly more instances of extreme improvement. Importantly, we find that commonly used calibration procedures, most notably Platt scaling and isotonic regression, can systematically degrade proper scoring performance for strong modern tabular models. Overall classification performance is often preserved, but calibration effects vary substantially across datasets and architectures, and no method dominates uniformly. In expectation, all methods except Pearsonify slightly increase accuracy, but the effect is marginal, with the largest expected gain about 0.008%.

Cost-effectiveness analyses (CEAs) compare the costs and health outcomes of treatment regimes to inform medical decisions. With observational claims data, CEAs must address nonrandom treatment assignment, administrative censoring, and irregularly spaced medical visits that reflect the continuous timing of care and treatment initiation. In high-risk, early-stage endometrial cancer (HR-EC), adjuvant radiation is initiated at patient-specific times following hysterectomy, causing confounding between treatment and outcomes that can evolve with post-surgical recovery and clinical course. Most existing CEA methods use point-treatment or discrete-time models. However, point-treatment approaches break down with time-varying confounding, while discrete-time models bin continuous time, expand the data into a person-period format, and can induce zero-inflation by creating many intervals with no cost-accruing events. We propose a Bayesian framework for CEAs with sequential decision-making that jointly models costs and event times in continuous time, accounts for administrative censoring, and supports dynamic treatment regimes with minimal parametric assumptions. We use Bayesian g-computation to estimate causally interpretable cost-effectiveness measures, including net monetary benefit, and to compare regimes through posterior contrasts. We evaluate the finite-sample performance of the proposed method in simulations across censoring levels and compare it against discrete-time and fully parametric alternatives. We then use SEER-Medicare data to assess the cost-effectiveness of initiating adjuvant radiation therapy within six months following hysterectomy among HR-EC patients.

In this article, we study nonparametric inference problems in the context of multivariate or functional time series, including testing for goodness-of-fit, the presence of a change point in the marginal distribution, and the independence of two time series, among others. Most methodologies available in the existing literature address these problems by employing a bandwidth-dependent bootstrap or subsampling approach, which can be computationally expensive and/or sensitive to the choice of bandwidth. To address these limitations, we propose a novel class of kernel-based tests by embedding the data into a reproducing kernel Hilbert space, and construct test statistics using sample splitting, projection, and self-normalization (SN) techniques. Through a new conditioning technique, we demonstrate that our test statistics have pivotal limiting null distributions under strong mixing and mild moment assumptions. We also analyze the limiting power of our tests under local alternatives. Finally, we showcase the superior size accuracy and computational efficiency of our methods as compared to some existing ones.

The increasing reliance on human preference feedback to judge AI-generated pseudo labels has created a pressing need for principled, budget-conscious data acquisition strategies. We address the crucial question of how to optimally allocate a fixed annotation budget between ground-truth labels and pairwise preferences in AI. Our solution, grounded in semi-parametric inference, casts the budget allocation problem as a monotone missing data framework. Building on this formulation, we introduce Preference-Calibrated Active Learning (PCAL), a novel method that learns the optimal data acquisition strategy and develops a statistically efficient estimator for functionals of the data distribution. Theoretically, we prove the asymptotic optimality of our PCAL estimator and establish a key robustness guarantee that ensures robust performance even with poorly estimated nuisance models. Our flexible framework applies to a general class of problems, by directly optimizing the estimator's variance instead of requiring a closed-form solution. This work provides a principled and statistically efficient approach for budget-constrained learning in modern AI. Simulations and real-data analysis demonstrate the practical benefits and superior performance of our proposed method.

In this paper, we extend distance correlation to categorical data with general encodings, such as one-hot encoding for nominal variables and semicircle encoding for ordinal variables. Unlike existing methods, our approach leverages the spacing information between categories, which enhances the performance of distance correlation. Two estimates including the maximum likelihood estimate and a bias-corrected estimate are given, together with their limiting distributions under the null and alternative hypotheses. Furthermore, we establish the sure screening property for high-dimensional categorical data under mild conditions. We conduct a simulation study to compare the performance of different encodings, and illustrate their practical utility using the 2018 General Social Survey data.

Differential item functioning (DIF) is a widely used statistical notion for identifying items that may disadvantage specific groups of test-takers. These groups are often defined by non-manipulable characteristics, e.g., gender, race/ethnicity, or English-language learner (ELL) status. While DIF can be framed as a causal fairness problem by treating group membership as the treatment variable, this invokes the long-standing controversy over the interpretation of causal effects for non-manipulable treatments. To better identify and interpret causal sources of DIF, this study leverages an interventionist approach using treatment decomposition proposed by Robins and Richardson (2010). Under this framework, we can decompose a non-manipulable treatment into intervening variables. For example, ELL status can be decomposed into English lexical proficiency and instructional English comprehension, each of which influences the outcome through different causal pathways. We formally define separable DIF effects associated with these decomposed components, depending on the absence or presence of item impact, and provide causal identification strategies for each effect. We then apply the framework to biased test items in the SAT and Regents exams. We also provide formal detection methods using causal machine learning methods, namely causal forests and Bayesian additive regression trees, and demonstrate their performance through a simulation study and a real-world application. Finally, we discuss the implications of adopting interventionist approaches in educational testing practices.

Despite their promise, fair machine learning methods often yield Pareto-inefficient models, in which the performance of certain groups can be improved without degrading that of others. This issue arises frequently in traditional in-processing approaches such as fairness-through-regularization. In contrast, existing Pareto-efficient approaches are biased towards a certain perspective on fairness and fail to adapt to the broad range of fairness metrics studied in the literature. In this paper, we present BADR, a simple framework to recover the optimal Pareto-efficient model for any fairness metric. Our framework recovers its models through a Bilevel Adaptive Rescalarisation procedure. The lower level is a weighted empirical risk minimization task where the weights are a convex combination of the groups, while the upper level optimizes the chosen fairness objective. We equip our framework with two novel large-scale, single-loop algorithms, BADR-GD and BADR-SGD, and establish their convergence guarantees. We release badr, an open-source Python toolbox implementing our framework for a variety of learning tasks and fairness metrics. Finally, we conduct extensive numerical experiments demonstrating the advantages of BADR over existing Pareto-efficient approaches to fairness.

Linearly parametrized models are widely used in control and signal processing, with the least-squares (LS) estimate being the archetypical solution. When the input is insufficiently exciting, the LS problem may be unsolvable or numerically unstable. This issue can be resolved through regularization, typically with ridge regression. Although regularized estimators reduce the variance error, it remains important to quantify their estimation uncertainty. A possible approach for linear regression is to construct confidence ellipsoids with the Sign-Perturbed Sums (SPS) ellipsoidal outer approximation (EOA) algorithm. The SPS EOA builds non-asymptotic confidence ellipsoids under the assumption that the noises are independent and symmetric about zero. This paper introduces an extension of the SPS EOA algorithm to ridge regression, and derives probably approximately correct (PAC) upper bounds for the resulting region sizes. Compared with previous analyses, our result explicitly show how the regularization parameter affects the region sizes, and provide tighter bounds under weaker excitation assumptions. Finally, the practical effect of regularization is also demonstrated via simulation experiments.

Cluster-randomized trials (CRTs) are widely used to evaluate group-level interventions and increasingly collect multiple outcomes capturing complementary dimensions of benefit and risk. Investigators often seek a single global summary of treatment effect, yet existing methods largely focus on single-outcome estimands or rely on model-based procedures with unclear causal interpretation or limited robustness. We develop a unified potential outcomes framework for generalized treatment effects with multiple outcomes in CRTs, accommodating both non-prioritized and prioritized outcome settings. The proposed cluster-pair and individual-pair causal estimands are defined through flexible pairwise contrast functions and explicitly account for potentially informative cluster sizes. We establish nonparametric estimation via weighted clustered U-statistics and derive efficient influence functions to construct covariate-adjusted estimators that integrate debiased machine learning with U-statistics. The resulting estimators are consistent and asymptotically normal, attain the semiparametric efficiency bounds under mild regularity conditions, and have analytically tractable variance estimators that are proven to be consistent under cross-fitting. Simulations and an application to a CRT for chronic pain management illustrate the practical utility of the proposed methods.

Interpreting RNA-sequencing data requires identifying coordinated gene expression patterns that correspond to biological pathways. Standard factor models provide useful dimension reduction but typically ignore existing pathway knowledge or incorporate it through restrictive assumptions, limiting interpretability, and reproducibility. Here, we develop Bayesian Analysis with gene-Sets Informed Latent space (BASIL), a scalable framework for analyzing transcriptomic data that integrates annotated gene sets into latent variable inference. BASIL places structured priors on factor loadings, shrinking them toward combinations of annotated gene sets, enhancing biological interpretability and stability, while simultaneously learning new unstructured components. BASIL provides accurate covariance estimates and uncertainty quantification, without resorting to computationally expensive Markov chain Monte Carlo sampling, by exploiting a pre-training approach that pre-estimates the latent factors. An automatic empirical Bayes procedure eliminates the need for manual hyperparameter tuning, promoting reproducibility and usability in practice. Applying BASIL to the global fever transcriptomic cohort uncovers interpretable host-response modules, with phosphoinositide signaling and interferon-driven inflammation emerging as key drivers of gene-expression variability.

Understanding associations between paired high-dimensional longitudinal datasets is a fundamental yet challenging problem arising across scientific domains, including longitudinal multi-omic studies. The difficulty stems from the complex, time-varying cross-covariance structure coupled with high dimensionality, which complicates both model formulation and statistical estimation for association discovery. To address these challenges, we propose a new framework called Functional-Aggregated Cross-covariance Decomposition (FACD), tailored to analyzing associations in paired high-dimensional longitudinal datasets through a statistically efficient procedure. Unlike existing methods that are limited to low-dimensional data or rely on parametric modeling of temporal dynamics, FACD is capable of learning temporal structure by aggregating high-dimensional signals and accommodating variable selection to identify the most temporally associated features across datasets. We establish statistical guarantees for FACD and demonstrate its advantages over existing approaches through extensive simulation studies. Finally, we apply FACD to a longitudinal multi-omic human study, revealing blood molecules with time-varying associations across omic layers during acute exercise.

This paper addresses a long-standing gap in natural hazard modeling by unifying physics-based fragility functions with real-time post-disaster observations. It introduces a Bayesian framework that continuously refines regional vulnerability estimates as new data emerges. The framework reformulates physics-informed fragility estimates into a Probit-Normal (PN) representation that captures aleatory variability and epistemic uncertainty in an analytically tractable form. Stage 1 performs local Bayesian updating by moment-matching PN marginals to Beta surrogates that preserve their probability shapes, enabling conjugate Beta-Bernoulli updates with soft, multi-fidelity observations. Fidelity weights encode source reliability, and the resulting Beta posteriors are re-projected into PN form, producing heteroscedastic fragility estimates whose variances reflect data quality and coverage. Stage 2 assimilates these heteroscedastic observations within a probit-warped Gaussian Process (GP), which propagates information from high-fidelity sites to low-fidelity and unobserved regions through a composite kernel that links space, archetypes, and correlated damage states. The framework is applied to the 2011 Joplin tornado, where wind-field priors and computer-vision damage assessments are fused under varying assumptions about tornado width, sampling strategy, and observation completeness. Results show that the method corrects biased priors, propagates information spatially, and produces uncertainty-aware exceedance probabilities that support real-time situational awareness.

This study explores how Bayesian networks (BNs) can improve forecast accuracy compared to logistic regression and recalibration and aggregation methods, using data from the Good Judgment Project. Regularized logistic regression models and a baseline recalibrated aggregate were compared to two types of BNs: structure-learned BNs with arcs between predictors, and naive BNs. Four predictor variables were examined: absolute difference from the aggregate, forecast value, days prior to question close, and mean standardized Brier score. Results indicated the recalibrated aggregate achieved the highest accuracy (AUC = 0.985), followed by both types of BNs, then the logistic regression models. Performance of the BNs was likely harmed by reduced information from the discretization process and violation of the assumption of linearity likely harmed the logistic regression models. Future research should explore hybrid approaches combining BNs with logistic regression, examine additional predictor variables, and account for hierarchical data dependencies.

Large-scale dynamic inverse problems are often ill-posed due to model complexity and the high dimensionality of the unknown parameters. Regularization is commonly employed to mitigate ill-posedness by incorporating prior information and structural constraints. However, classical regularization formulations are frequently infeasible in this setting due to prohibitive memory requirements, necessitating sequential methods that process data and state information online, eliminating the need to form the full space-time problem. In this work, we propose a memory-efficient framework for reconstructing dynamic sequences of undersampled images from computerized tomography data that requires minimal hyperparameter tuning. The approach is based on a prior-informed, dimension-reduced Kalman filter with smoothing. While well suited for dynamic image reconstruction, practical deployment is challenging when the state transition model and covariance parameters must be initialized without prior knowledge and estimated in a single pass. To address these limitations, we integrate regularized motion models with expectation-maximization strategies for the estimation of state transition dynamics and error covariances within the Kalman filtering framework. We demonstrate the effectiveness of the proposed method through numerical experiments on limited-angle and single-shot computerized tomography problems, highlighting improvements in reconstruction accuracy, memory efficiency, and computational cost.

We introduce a novel model for time-varying, asymmetric, tail-dependent copulas in high dimensions that incorporates both spectral dynamics and regularization. The dynamics of the dependence matrix' eigenvalues are modeled in a score-driven way, while biases in the unconditional eigenvalue spectrum are resolved by non-linear shrinkage. The dynamic parameterization of the copula dependence matrix ensures that it satisfies the appropriate restrictions at all times and for any dimension. The model is parsimonious, computationally efficient, easily scalable to high dimensions, and performs well for both simulated and empirical data. In an empirical application to financial market dynamics using 100 stocks from 10 different countries and 10 different industry sectors, we find that our copula model captures both geographic and industry related co-movements and outperforms recent computationally more intensive clustering-based factor copula alternatives. Both the spectral dynamics and the regularization contribute to the new model's performance. During periods of market stress, we find that the spectral dynamics reveal strong increases in international stock market dependence, which causes reductions in diversification potential and increases in systemic risk.

We develop a multilevel Monte Carlo (MLMC) framework for uncertainty quantification with Monte Carlo dropout. Treating dropout masks as a source of epistemic randomness, we define a fidelity hierarchy by the number of stochastic forward passes used to estimate predictive moments. We construct coupled coarse–fine estimators by reusing dropout masks across fidelities, yielding telescoping MLMC estimators for both predictive means and predictive variances that remain unbiased for the corresponding dropout-induced quantities while reducing sampling variance at fixed evaluation budget. We derive explicit bias, variance and effective cost expressions, together with sample-allocation rules across levels. Numerical experiments on forward and inverse PINNs–Uzawa benchmarks confirm the predicted variance rates and demonstrate efficiency gains over single-level MC-dropout at matched cost.

Notions of positive curvature have been shown to imply many remarkable properties for Markov processes, in terms, e.g., of regularization effects, functional inequalities, mixing time bounds and, more recently, the cutoff phenomenon. In this work, we are interested in a relaxed variant of Ollivier's coarse Ricci curvature, where a Markov kernel $P$ satisfies only a weaker Wasserstein bound $W_p(\mu P, \nu P) \leq K W_p(\mu,\nu)+M$ for constants $M\ge 0, K\in [0,1], p \ge 1$. Under appropriate additional assumptions on the one-step transition measures $\delta_x P$, we establish (i) a form of local concentration, given by a defective Talagrand inequality, and (ii) an entropy-transport regularization effect. We consider as illustrative examples the Langevin dynamics and the Proximal Sampler when the target measure is a log-Lipschitz perturbation of a log-concave measure. As an application of the above results, we derive criteria for the occurrence of the cutoff phenomenon in some negatively curved settings.

We consider non-linear regression models corrupted by generic noise when the regression functions form a non-linear subspace of L^2, relevant in non-linear PDE inverse problems and data assimilation. We show that when the score of the model is injective, the Fisher information operator is automatically invertible between well-identified Hilbert spaces, and we provide an operational characterization of these spaces. This allows us to construct in broad generality the efficient Gaussian involved in the classical minimax and convolution theorems to establish information lower bounds, that are typically achieved by Bayesian algorithms thus showing optimality of these methods. We illustrate our results on time-evolution PDE models for reaction-diffusion and Navier-Stokes equations.

In this paper, the solution to the empirical risk minimization problem with $f$-divergence regularization (ERM-$f$DR) is presented and conditions under which the solution also serves as the solution to the minimization of the expected empirical risk subject to an $f$-divergence constraint are established. The proposed approach extends applicability to a broader class of $f$-divergences than previously reported and yields theoretical results that recover previously known results. Additionally, the difference between the expected empirical risk of the ERM-$f$DR solution and that of its reference measure is characterized, providing insights into previously studied cases of $f$-divergences. A central contribution is the introduction of the normalization function, a mathematical object that is critical in both the dual formulation and practical computation of the ERM-$f$DR solution. This work presents an implicit characterization of the normalization function as a nonlinear ordinary differential equation (ODE), establishes its key properties, and subsequently leverages them to construct a numerical algorithm for approximating the normalization factor under mild assumptions. Further analysis demonstrates structural equivalences between ERM-$f$DR problems with different $f$-divergences via transformations of the empirical risk. Finally, the proposed algorithm is used to compute the training and test risks of ERM-$f$DR solutions under different $f$-divergence regularizers. This numerical example highlights the practical implications of choosing different functions $f$ in ERM-$f$DR problems.

Design-based inference, also known as randomization-based or finite-population inference, provides a principled framework for trustworthy statistical inference. It attributes randomness solely to the design mechanism, such as treatment assignment, survey sampling, or missingness, without imposing super-population distributional or modeling assumptions on the outcome data. From the seminal work of Fisher and Neyman to its recent resurgence, design-based inference has played a central role in causal inference, survey sampling, and missing data analysis. However, its use in many modern applications has been limited by a fundamental obstacle: existing design-based inference theory typically assumes that propensity scores (i.e., design probabilities) are known, whereas they are usually unknown in observational studies, real-world surveys, and missing data problems. We propose propensity score propagation, a general framework for valid design-based inference with unknown propensity scores. The framework uses a regeneration-and-union procedure to propagate uncertainty from propensity score estimation into downstream design-based inference, without introducing super-population assumptions about the outcomes. It accommodates both parametric and nonparametric propensity score settings, integrates seamlessly with existing design-based methods developed for known propensity scores, and applies broadly across design-based problems. Theoretical and simulation results show that the proposed framework achieves nominal coverage, even when existing approaches exhibit substantial under-coverage.

Full conformal prediction is a framework that implicitly formulates distribution-free confidence prediction regions for a wide range of estimators. However, a classical limitation of the full conformal framework is the computation of the confidence prediction regions, which is usually impossible since it requires training infinitely many estimators (for real-valued prediction for instance). The main purpose of the present work is to describe a generic strategy for designing a tight approximation to the full conformal prediction region that can be efficiently computed. Along with this approximate confidence region, a theoretical quantification of the tightness of this approximation is developed, depending on the smoothness assumptions on the loss and score functions. The new notion of thickness is introduced for quantifying the discrepancy between the approximate confidence region and the full conformal one.

Evolutionary accumulation models (EvAMs) are an emerging class of machine learning methods designed to infer the evolutionary pathways by which features are acquired. Applications include cancer evolution (accumulation of mutations), anti-microbial resistance (accumulation of drug resistances), genome evolution (organelle gene transfers), and more diverse themes in biology and beyond. Following these themes, many EvAMs assume that features are gained irreversibly – no loss of features can occur. Reversible approaches do exist but are often computationally (much) more demanding and statistically less stable. Our goal here is to explore whether useful information about evolutionary dynamics which are in reality reversible can be obtained from modelling approaches with an assumption of irreversibility. We identify, and use simulation studies to quantify, errors involved in neglecting reversible dynamics, and show the situations in which approximate results from tractable models can be informative and reliable. In particular, EvAM inferences about the relative orderings of acquisitions and the core dynamic structure of evolutionary pathways – which features are likely present when another is acquired – are robust to reversibility in many cases, while estimations of uncertainty and feature interactions are more error-prone.

We develop a data-driven algorithm for automatically selecting the regularisation parameter in Bayesian inversion under random tree Besov priors. One of the key challenges in Bayesian inversion is the construction of priors that are both expressive and computationally feasible. Random tree Besov priors, introduced in Kekkonen et al. (2023), provide a flexible framework for capturing local regularity properties and sparsity patterns in a wavelet basis. In this paper, we extend this approach by introducing a hierarchical model that enables data-driven selection of the wavelet density parameter, allowing the regularisation strength to adapt across scales while retaining computational efficiency. We focus on nonparametric regression and also present preliminary plug-and-play results for a deconvolution problem.

Online continual learning (OCL) methods adapt to changing environments without forgetting past knowledge. Similarly, online time series forecasting (OTSF) is a real-world problem where data evolve in time and success depends on both rapid adaptation and long-term memory. Indeed, time-varying and regime-switching forecasting models have been extensively studied, offering a strong justification for the use of OCL in these settings. Building on recent work that applies OCL to OTSF, this paper aims to strengthen the theoretical and practical connections between time series methods and OCL. First, we reframe neural network optimization as a parameter filtering problem, showing that natural gradient descent is a score-driven method and proving its information-theoretic optimality. Then, we show that using a Student's t likelihood in addition to natural gradient induces a bounded update, which improves robustness to outliers. Finally, we introduce Natural Score-driven Replay (NatSR), which combines our robust optimizer with a replay buffer and a dynamic scale heuristic that improves fast adaptation at regime drifts. Empirical results demonstrate that NatSR achieves stronger forecasting performance than more complex state-of-the-art methods.

Background: Stepped wedge cluster randomized trials (SW-CRTs) involve sequential measurements within clusters over time. Initially, all clusters start in the control condition before crossing over to the intervention on a staggered schedule. In cohort designs, secular trends, cluster-level changes, and individual-level changes (e.g., aging) must be considered. Methods: We performed a Monte Carlo simulation to analyze the influence of different time effects on the estimation of the intervention effect in cohort SW-CRTs. We compared four linear mixed models with different adjustment strategies, all including random intercepts for clustering and repeated measurements. We recorded the estimated fixed intervention effects and their corresponding model-based standard errors, derived from models both without and with cluster-robust variance estimators (CRVEs). Results: Models incorporating fixed categorical time effects, a fixed intervention effect, and two random intercepts provided unbiased estimates of the intervention effect in both closed and open cohort SW-CRTs. Fixed categorical time effects captured temporal cohort changes, while random individual effects accounted for baseline differences. However, these differences can cause large, non-normally distributed random individual effects. CRVEs provide reliable standard errors for the intervention effect, controlling the Type I error rate. Conclusions: Our simulation study is the first to assess individual-level changes over time in cohort SW-CRTs. Linear mixed models incorporating fixed categorical time effects and random cluster and individual effects yield unbiased intervention effect estimates. However, cluster-robust variance estimation is necessary when time-varying independent variables exhibit nonlinear effects. We recommend always using CRVEs.

In this study, we apply functional regression analysis to identify the specific within-season periods during which temperature and precipitation anomalies most affect crop yields. Using provincial data for Italy from 1952 to 2023, we analyze two major cereals, maize and soft wheat, and quantify how abnormal weather conditions influence yields across the growing cycle. Unlike traditional statistical yield models, which assume additive temperature effects over the season, our approach is capable of capturing the timing and functional shape of weather impacts. In particular, the results show that above-average temperatures reduce maize yields primarily between June and August, while exerting a mild positive effect in April and October. For soft wheat, unusually high temperatures negatively affect yields from late March to early April. Precipitation also exerts season-dependent effects, improving wheat yields early in the season but reducing them later on. These findings highlight the importance of accounting for intra-seasonal weather patterns to provide insights for climate change adaptation strategies, including the timely adjustment of key crop management inputs.

The Bayesian approach provides powerful methods for variable selection. The ability to incorporate sparsity through prior beliefs and account for parameter uncertainty allows Bayesian variable selection to consistently identify which of the variables are active and exhibit strong finite-sample performance. However, Bayesian methods require the correct specification of full likelihoods for the data, and there is increasing awareness of the problems that model misspecification causes for variable selection. Current approaches to mitigate misspecification either require complex models, detracting from the interpretability of the variable selection task, or move outside rigorous Bayesian uncertainty quantification and provide no recognised method for variable selection. This paper establishes the model quasi-posterior as a principled tool for variable selection. We prove that the model quasi-posterior shares desirable properties of Bayesian variable selection without requiring full likelihood specification. Instead, the quasi-posterior combines a prior with a quasi-likelihood and requires only specification of mean and variance functions, and is therefore robust to other aspects of the data. Marginalising the quasi-likelihood is analytically possible for linear regression, and Laplace approximations are used beyond this to ensure computational tractability. Extensive simulation studies illustrate improved variable selection accuracy across diverse data-generating scenarios when compared with likelihood-based Bayesian variable selection and lasso-penalized methods. We further demonstrate practical relevance through applications to real datasets from social science and genomics.

Estimating the unknown reward functions driving agents' behaviors is of central interest in inverse reinforcement learning and game theory. To tackle this problem, we develop a unified framework for reward function recovery in two-player zero-sum matrix games and Markov games with entropy regularization, where we aim to reconstruct the underlying reward functions given observed players' strategies and actions. This task is challenging due to the inherent ambiguity of inverse problems, the non-uniqueness of feasible rewards, and limited observational data coverage. To address these challenges, we establish the reward function's identifiability using the quantal response equilibrium (QRE) under linear assumptions. Building upon this theoretical foundation, we propose a novel algorithm to learn reward functions from observed actions. Our algorithm works in both static and dynamic settings and is adaptable to incorporate different methods, such as Maximum Likelihood Estimation (MLE). We provide strong theoretical guarantees for the reliability and sample efficiency of our algorithm. Further, we conduct extensive numerical studies to demonstrate the practical effectiveness of the proposed framework, offering new insights into decision-making in competitive environments.

Entropic optimal transport problems play an increasingly important role in machine learning and generative modelling. In contrast with optimal transport maps which often have limited applicability in high dimensions, Schrodinger bridges can be solved using the celebrated Sinkhorn's algorithm, a.k.a. the iterative proportional fitting procedure. The stability properties of Sinkhorn bridges when the number of iterations tends to infinity is a very active research area in applied probability and machine learning. Traditional proofs of convergence are mainly based on nonlinear versions of Perron-Frobenius theory and related Hilbert projective metric techniques, gradient descent, Bregman divergence techniques and Hamilton-Jacobi-Bellman equations, including propagation of convexity profiles based on coupling diffusions by reflection methods. The objective of this review article is to present, in a self-contained manner, recently developed Sinkhorn/Gibbs-type semigroup analysis based upon contraction coefficients and Lyapunov-type operator-theoretic techniques. These powerful, off-the-shelf semigroup methods are based upon transportation cost inequalities (e.g. log-Sobolev, Talagrand quadratic inequality, curvature estimates), $\phi$-divergences, Kantorovich-type criteria and Dobrushin contraction-type coefficients on weighted Banach spaces as well as Wasserstein distances. This novel semigroup analysis allows one to unify and simplify many arguments in the stability of Sinkhorn algorithm. It also yields new contraction estimates w.r.t. generalized $\phi$-entropies, as well as weighted total variation norms, Kantorovich criteria and Wasserstein distances.