Papers

Reinforcement Learning (RL) has attracted increasing interest in financial applications, including optimal trading and execution. However, the use of RL for optimal trading strategies that exploit latent information in the market has been, to the best of our knowledge, subject to little attention. In this paper, we consider an optimal trading problem in which the trading signal follows an Ornstein-Uhlenbeck process with regime switching parameters. The problem is naturally formulated as a partially observable Markov decision problem, requiring a trader to infer latent information directly from the history of the observable process. We combine recurrent neural networks (RNN) with RL to address both the filtering and trading components of the problem. More specifically, we propose three distinct RL-based approaches, on top of which we incorporate RNN to filter the latent state of the environment where the agent is trading. The first, a one-step approach, directly encodes hidden states from the GRU into the RL trader. The second and third are two-step methods: one that uses posterior regime probability estimates for the mean reverting regimes, while the other relies on forecasts of the next signal value. Through extensive simulations with increasingly complex Markovian regime dynamics for the trading signal's parameters, as well as an empirical application to equity pairs trading, we find that feeding posterior probability estimates on the latent long-run mean reversion regime achieves superior cumulative rewards and exhibits more interpretable strategies, in contrast with the other two approaches. Overall, our results show that the quality and structure of the information supplied to the agent are important for trading performance and policy interpretability.

This article establishes a rigorous spectral framework for the mathematical analysis of SHAP values. We show that any predictive model defined on a discrete or multi-valued input space admits a generalized Fourier expansion with respect to an orthonormalisation tensor-product basis constructed under a product probability measure. Within this setting, each SHAP attribution can be represented as a linear functional of the model's Fourier coefficients. Two complementary regimes are studied. In the deterministic regime, we derive quantitative stability estimates for SHAP values under Fourier truncation, showing that the attribution map is Lipschitz continuous with respect to the distance between predictors. In the probabilistic regime, we consider neural networks in their infinite-width limit and prove convergence of SHAP values toward those induced by the corresponding Gaussian process prior, with explicit error bounds in expectation and with high probability based on concentration inequalities. We also provide a numerical experiment on a clinical unbalanced dataset to validate the theoretical findings.

We derive concentration inequalities for sums of independent and identically distributed random variables that yield non-asymptotic generalizations of several strong laws of large numbers including some of those due to Kolmogorov [1930], Marcinkiewicz and Zygmund [1937], Chung [1951], Baum and Katz [1965], Ruf, Larsson, Koolen, and Ramdas [2023], and Waudby-Smith, Larsson, and Ramdas [2024]. As applications, we derive non-asymptotic iterated logarithm inequalities in the spirit of Darling and Robbins [1967], as well as pathwise (sometimes described as "game-theoretic") analogues of strong laws and laws of the iterated logarithm.

Motivated by practical applications, I present a novel and comprehensive framework for operator-valued positive definite kernels. This framework is applied to both operator theory and stochastic processes. The first application focuses on various dilation constructions within operator theory, while the second pertains to broad classes of stochastic processes. In this context, the authors utilize the results derived from operator-valued kernels to develop new Hilbert space-valued Gaussian processes and to investigate the structures of their covariance configurations.

Data on livestock farm locations and demographics are essential for disease monitoring, risk assessment, and developing spatially explicit epidemiological models. Our semantic segmentation model achieved an F2 score of 92 % and a mean Intersection over Union of 76 %. An initial total of 194,474 swine barn candidates were identified in the Southeast (North Carolina = 111,135, South Carolina = 37,264 Virginia = 46,075) and 524,962 in the Midwest (Iowa = 168,866 Minnesota = 165,714 Ohio = 190,382). The post processing Random Forest classifier reduced false positives by 82 % in the Southeast and 88 % in the Midwest, resulting in 45,580 confirmed barn polygons. These were grouped into 16,976 predicted farms and classified into one of the four production types. Population sizes were then estimated using the Random Forest regression model, with prediction accuracy varying by production type. Across all farms, 87 % of predictions for operations with 1,000 2,000 pigs were within 500 pigs of the reference value, with nursery farms showing the highest agreement (R2= 0.82), followed by finisher farms (R2 = 0.77) and sow farms (R2 = 0.56). Our results revealed substantial gaps in the existing spatial and demographic data on U.S. swine production.

In football, attacking teams attempt to break through the opponent's defensive line to create scoring opportunities. This action, known as a Line Break, is a critical indicator of offensive effectiveness and tactical performance, yet previous studies have mainly focused on shots or goal opportunities rather than on how teams break the defensive line. In this study, we develop a machine learning model to predict Line Breaks using event and tracking data from the 2023 J1 League season. The model incorporates 189 features, including player positions, velocities, and spatial configurations, and employs an XGBoost classifier to estimate the probability of Line Breaks. The proposed model achieved high predictive accuracy, with an AUC of 0.982 and a Brier score of 0.015. Furthermore, SHAP analysis revealed that factors such as offensive player speed, gaps in the defensive line, and offensive players' spatial distributions significantly contribute to the occurrence of Line Breaks. Finally, we found a moderate positive correlation between the predicted probability of being Line-Broken and the number of shots and crosses conceded at the team level. These results suggest that Line Breaks are closely linked to the creation of scoring opportunities and provide a quantitative framework for understanding tactical dynamics in football.

Modern imaging techniques heavily rely on Bayesian statistical models to address difficult image reconstruction and restoration tasks. This paper addresses the objective evaluation of such models in settings where ground truth is unavailable, with a focus on model selection and misspecification diagnosis. Existing unsupervised model evaluation methods are often unsuitable for computational imaging due to their high computational cost and incompatibility with modern image priors defined implicitly via machine learning models. We herein propose a general methodology for unsupervised model selection and misspecification detection in Bayesian imaging sciences, based on a novel combination of Bayesian cross-validation and data fission, a randomized measurement splitting technique. The approach is compatible with any Bayesian imaging sampler, including diffusion and plug-and-play samplers. We demonstrate the methodology through experiments involving various scoring rules and types of model misspecification, where we achieve excellent selection and detection accuracy with a low computational cost.

This paper studies optimization on networks modeled as metric graphs. Motivated by applications where the objective function is expensive to evaluate or only available as a black box, we develop Bayesian optimization algorithms that sequentially update a Gaussian process surrogate model of the objective to guide the acquisition of query points. To ensure that the surrogates are tailored to the network's geometry, we adopt Whittle-Matérn Gaussian process prior models defined via stochastic partial differential equations on metric graphs. In addition to establishing regret bounds for optimizing sufficiently smooth objective functions, we analyze the practical case in which the smoothness of the objective is unknown and the Whittle-Matérn prior is represented using finite elements. Numerical results demonstrate the effectiveness of our algorithms for optimizing benchmark objective functions on a synthetic metric graph and for Bayesian inversion via maximum a posteriori estimation on a telecommunication network.

This paper proposes a new test for inequalities that are linear in possibly partially identified nuisance parameters. This type of hypothesis arises in a broad set of problems, including subvector inference for linear unconditional moment (in)equality models, specification testing of such models, and inference for parameters bounded by linear programs. The new test uses a two-step test statistic and a chi-squared critical value with data-dependent degrees of freedom that can be calculated by an elementary formula. Its simple structure and tuning-parameter-free implementation make it attractive for practical use. We establish uniform asymptotic validity of the test, demonstrate its finite-sample size and power in simulations, and illustrate its use in an empirical application that analyzes women's labor supply in response to a welfare policy reform.

Sufficient dimension reduction (SDR) methods aim to identify a dimension reduction subspace (DRS) that preserves all the information about the conditional distribution of a response given its predictor. Traditional SDR methods determine the DRS by solving a method-specific generalized eigenvalue problem and selecting the eigenvectors corresponding to the largest eigenvalues. In this article, we argue against the long-standing convention of using eigenvalues as the measure of subspace importance and propose alternative ordering criteria that directly assess the predictive relevance of each subspace. For a binary response, we introduce a subspace ordering criterion based on the absolute value of the independent Student's T-statistic. Theoretically, our criterion identifies subspaces that achieve the local minimum Bayes' error rate and yields consistent ordering of directions under mild regularity conditions. Additionally, we employ an F-statistic to provide a framework that unifies categorical and continuous responses under a single subspace criterion. We evaluate our proposed criteria within multiple SDR methods through extensive simulation studies and applications to real data. Our empirical results demonstrate the efficacy of reordering subspaces using our proposed criteria, which generally improves classification accuracy and subspace estimation compared to ordering by eigenvalues.

In this paper, we expand upon and refine a monitoring strategy proposed for surveillance of diseases in finite, closed populations. This monitoring strategy consists of augmenting an arbitrarily non-representative data stream (such as a voluntary flu testing program) with a random sample (referred to as an "anchor stream"). This design allows for the use of traditional capture-recapture (CRC) estimators, as well as recently proposed anchor stream estimators that more efficiently utilize the data. Here, we focus on a particularly common situation in which the first data stream only records positive test results, while the anchor stream documents both positives and negatives. Due to the non-representative nature of the first data stream, along with the fact that inference is being performed on a finite, closed population, there are standard and non-standard finite population effects at play. Here, we propose two methods of incorporating finite population corrections (FPCs) for inference, along with an FPC-adjusted Bayesian credible interval. We compare these approaches with existing methods through simulation and demonstrate that the FPC adjustments can lead to considerable gains in precision. Finally, we provide a real data example by applying these methods to estimating the breast cancer recurrence count among Metro Atlanta-area patients in the Georgia Cancer Registry-based Cancer Recurrence Information and Surveillance Program (CRISP) database.

Score-based diffusion models have achieved remarkable empirical success in generating high-quality samples from target data distributions. Among them, the Denoising Diffusion Probabilistic Model (DDPM) is one of the most widely used samplers, generating samples via estimated score functions. Despite its empirical success, a tight theoretical understanding of DDPM – especially its convergence properties – remains limited. In this paper, we provide a refined convergence analysis of the DDPM sampler and establish near-optimal convergence rates under general distributional assumptions. Specifically, we introduce a relaxed smoothness condition parameterized by a constant $L$, which is small for many practical distributions (e.g., Gaussian mixture models). We prove that the DDPM sampler with accurate score estimates achieves a convergence rate of $$\widetilde{O}\left(\frac{d\min\{d,L^2\}}{T^2}\right)~\text{in Kullback-Leibler divergence},$$ where $d$ is the data dimension, $T$ is the number of iterations, and $\widetilde{O}$ hides polylogarithmic factors in $T$. This result substantially improves upon the best-known $d^2/T^2$ rate when $L < \sqrt{d}$. By establishing a matching lower bound, we show that our convergence analysis is tight for a wide array of target distributions. Moreover, it reveals that DDPM and DDIM share the same dependence on $d$, raising an interesting question of why DDIM often appears empirically faster.

Understanding the sources that contribute to fine particulate matter (PM$_{2.5}$) is of crucial importance for designing and implementing targeted air pollution mitigation strategies. Determining what factors contribute to a pollutant's concentration goes under the name of source apportionment and it is a problem long studied by atmospheric scientists and statisticians alike. In this paper, we propose a Bayesian model for source apportionment, that advances the literature on source apportionment by allowing estimation of the number of sources and accounting for spatial and temporal dependence in the observed pollutants' concentrations. Taking as example observations of six species of fine particulate matter observed over the course of a year, we present a latent functional factor model that expresses the space-time varying observations of log concentrations of the six pollutant as a linear combination of space-time varying emissions produced by an unknown number of sources each multiplied by the corresponding source's relative contribution to the pollutant. Estimation of the number of sources is achieved by introducing source-specific shrinkage parameters. Application of the model to simulated data showcases its ability to retrieve the true number of sources and to reliably estimate the functional latent factors, whereas application to PM$_{2.5}$ speciation data in California identifies 3 major sources for the six PM$_{2.5}$ species.

Meta-analyses require an effect-size estimate and its corresponding sampling variance from primary studies. In some cases, estimators for the sampling variance of a given effect size statistic may not exist, necessitating the derivation of a new formula for sampling variance. Traditionally, sampling variance formulas are obtained via hand-derived Taylor expansions (the delta method), though this procedure can be challenging for non-statisticians. Building on the idea of single-fit parametric resampling, we introduce SAFE bootstrap: a Single-fit, Accurate, Fast, and Easy simulation recipe that replaces potentially complex algebra with four intuitive steps: fit, draw, transform, and summarise. In a unified framework, the SAFE bootstrap yields bias-corrected point estimates and standard errors for any effect size statistic, regardless of whether the outcome is continuous or discrete. SAFE bootstrapping works by drawing once from a simple sampling model (normal, binomial, etc.), converting each replicate into any effect size of interest and then calculating the bias and sampling variance from simulated data. We demonstrate how to implement the SAFE bootstrap for a simple example first, and then for common effect sizes, such as the standardised mean difference and log odds ratio, as well as for less common effect sizes. With some additional coding, SAFE can also handle zero values and small sample sizes. Our tutorial, with R code supplements, should not only enhance understanding of sampling variance for effect sizes, but also serve as an introduction to the power of simulation-based methods for deriving any effect size with bias correction and its associated sampling variance.

We study the problem of nonparametric two-sample testing using the sliced Wasserstein (SW) distance. While prior theoretical and empirical work indicates that the SW distance offers a promising balance between strong statistical guarantees and computational efficiency, its theoretical foundations for hypothesis testing remain limited. We address this gap by proposing a permutation-based SW test and analyzing its performance. The test inherits finite-sample Type I error control from the permutation principle. Moreover, we establish non-asymptotic power bounds and show that the procedure achieves the minimax separation rate $n^{-1/2}$ over multinomial and bounded-support alternatives, matching the optimal guarantees of kernel-based tests while building on the geometric foundations of Wasserstein distances. Our analysis further quantifies the trade-off between the number of projections and statistical power. Finally, numerical experiments demonstrate that the test combines finite-sample validity with competitive power and scalability, and – unlike kernel-based tests, which require careful kernel tuning – it performs consistently well across all scenarios we consider.

This paper addresses the challenge of identifying a minimal subset of discrete predictor variables that best explains a binary class. We propose a greedy heuristic for feature selection that sequentially constructs a differential set by iteratively adding the variable that yields the most significant reduction in conditional entropy. The method incorporates a confidence-guided acceptance criterion that accounts for finite-sample uncertainty, allowing the search to adaptively balance the risk of including spurious variables against the opportunity to capture meaningful predictors. Because the procedure yields a compact set of statistically validated predictors together with an explicit confidence level for each one, it is well suited to healthcare innovation and management applications such as biomarker and risk-factor identification, diagnostic panel design, and clinical decision support, where minimizing the number of tests or indicators collected is critical for cost, feasibility, and patient burden.

In data-sparse regions, satellite and reanalysis rainfall estimates (SREs) are vital but limited by inherent biases. This study evaluates bias correction (BC) methods, including traditional statistical (LOCI, QM) and machine learning (SVR, GPR), applied to seven SREs across 38 stations in Ghana and Zambia. We introduce a constrained LOCI method to prevent the unrealistically high rainfall values produced by the original approach. Results indicate that statistical methods generally outperformed machine learning, though QM tended to inflate rainfall. Corrected SREs showed high capability in detecting dry days (POD $\ge$ 0.80). The ENACTS product, which integrates numerous station records, was the most amenable to correction in Zambia; most BC methods reduced mean error at >70% of stations. However, ENACTS performed less reliably at an independent station (Moorings), highlighting the need for broader validation at locations not incorporated into the product. Crucially, even after correction, most SREs (except ENACTS) failed to improve the detection of heavy and violent rainfall (POD $\le$ 0.2). This limits their utility for flood risk assessment and highlights a vital research gap regarding extreme event estimation.

Despite their enormous predictive power, machine learning models are often unsuitable for applications in regulated industries such as finance, due to their limited capacity to provide explanations. While model-agnostic frameworks such as Shapley values have proved to be convenient and popular, they rarely align with the kinds of causal explanations that are typically sought after. Counterfactual case-based explanations, where an individual is informed of which circumstances would need to be different to cause a change in outcome, may be more intuitive and actionable. However, finding appropriate counterfactual cases is an open challenge, as is interpreting which features are most critical for the change in outcome. Here, we pose the question of counterfactual search and interpretation in terms of similarity learning, exploiting the representation learned by the random forest predictive model itself. Once a counterfactual is found, the feature importance of the explanation is computed as a function of which random forest partitions are crossed in order to reach it from the original instance. We demonstrate this method on both the MNIST hand-drawn digit dataset and the German credit dataset, finding that it generates explanations that are sparser and more useful than Shapley values.

Flow Matching (FM) method in generative modeling maps arbitrary probability distributions by constructing an interpolation between them and then learning the vector field that defines ODE for this interpolation. Recently, it was shown that FM can be modified to map distributions optimally in terms of the quadratic cost function for any initial interpolation. To achieve this, only specific optimal vector fields, which are typical for solutions of Optimal Transport (OT) problems, need to be considered during FM loss minimization. In this note, we show that considering only optimal vector fields can lead to OT in another approach: Action Matching (AM). Unlike FM, which learns a vector field for a manually chosen interpolation between given distributions, AM learns the vector field that defines ODE for an entire given sequence of distributions.

Count regression models are necessary for examining discrete dependent variables alongside covariates. Nonetheless, when data display outliers, overdispersion, and an abundance of zeros, traditional methods like the zero-inflated negative binomial (ZINB) model sometimes do not yield a satisfactory fit, especially in the tail regions. This research presents a versatile, heavy-tailed discrete model as a resilient substitute for the ZINB model. The suggested framework is built by extending the generalized Pareto distribution and its zero-inflated version to the discrete domain. This formulation efficiently addresses both overdispersion and zero inflation, providing increased flexibility for heavy-tailed count data. Through intensive simulation studies and real-world implementations, the proposed models are thoroughly tested to see how well they work. The results show that our models always do better than classic negative binomial and zero-inflated negative binomial regressions when it comes to goodness-of-fit. This is especially true for datasets with a lot of zeros and outliers. These results highlight the proposed framework's potential as a strong and flexible option for modeling complicated count data.

Adding entropic regularization to Optimal Transport (OT) problems has become a standard approach for designing efficient and scalable solvers. However, regularization introduces a bias from the true solution. To mitigate this bias while still benefiting from the acceleration provided by regularization, a natural solver would adaptively decrease the regularization as it approaches the solution. Although some algorithms heuristically implement this idea, their theoretical guarantees and the extent of their acceleration compared to using a fixed regularization remain largely open. In the setting of semi-discrete OT, where the source measure is continuous and the target is discrete, we prove that decreasing the regularization can indeed accelerate convergence. To this end, we introduce DRAG: Decreasing (entropic) Regularization Averaged Gradient, a stochastic gradient descent algorithm where the regularization decreases with the number of optimization steps. We provide a theoretical analysis showing that DRAG benefits from decreasing regularization compared to a fixed scheme, achieving an unbiased $\mathcal{O}(1/t)$ sample and iteration complexity for both the OT cost and the potential estimation, and a $\mathcal{O}(1/\sqrt{t})$ rate for the OT map. Our theoretical findings are supported by numerical experiments that validate the effectiveness of DRAG and highlight its practical advantages.

We consider a bandit problem where the buget is smaller than the number of arms, which may be infinite. In this regime, the usual objective in the literature is to minimize simple regret. To analyze broad classes of distributions with potentially unbounded support, where simple regret may not be well-defined, we take a slightly different approach and seek to maximize the expected simple reward of the recommended arm, providing anytime guarantees. To that end, we introduce a distribution-free algorithm, OSE, that adapts to the distribution of arm means and achieves near-optimal rates for several distribution classes. We characterize the sample complexity through the rank-corrected inverse squared gap function. In particular, we recover known upper bounds and transition regimes for $\alpha$ less or greater than $1/2$ when the quantile function is $\lambda_\eta = 1-\eta^{\alpha}$. We additionally identify new transition regimes depending on the noise level relative to $\alpha$, which we conjecture to be nearly optimal. Additionally, we introduce an enhanced practical version, PROSE, that achieves state-of-the-art empirical performance for the main distribution classes considered in the literature.

Equivariant representation learning aims to capture variations induced by input transformations in the representation space, whereas invariant representation learning encodes semantic information by disregarding such transformations. Recent studies have shown that jointly learning both types of representations is often beneficial for downstream tasks, typically by employing separate projection heads. However, this design overlooks information shared between invariant and equivariant learning, which leads to redundant feature learning and inefficient use of model capacity. To address this, we introduce Soft Task-Aware Routing (STAR), a routing strategy for projection heads that models them as experts. STAR induces the experts to specialize in capturing either shared or task-specific information, thereby reducing redundant feature learning. We validate this effect by observing lower canonical correlations between invariant and equivariant embeddings. Experimental results show consistent improvements across diverse transfer learning tasks. The code is available at https://github.com/YonseiML/star.

It is known that the minimum-mean-squared-error (MMSE) denoiser under Gaussian noise can be written as a proximal operator, which suffices for asymptotic convergence of plug-and-play (PnP) methods but does not reveal the structure of the induced regularizer or give convergence rates. We show that the MMSE denoiser corresponds to a regularizer that can be written explicitly as an upper Moreau envelope of the negative log-marginal density, which in turn implies that the regularizer is 1-weakly convex. Using this property, we derive (to the best of our knowledge) the first sublinear convergence guarantee for PnP proximal gradient descent with an MMSE denoiser. We validate the theory with a one-dimensional synthetic study that recovers the implicit regularizer. We also validate the theory with imaging experiments (deblurring and computed tomography), which exhibit the predicted sublinear behavior.

We analyze loss development in NAIC Schedule P loss triangles using functional data analysis methods. Adopting the functional viewpoint, our dataset comprises 3300+ curves of incremental loss ratios (ILR) of workers' compensation lines over 24 accident years. Relying on functional data depth, we first study similarities and differences in development patterns based on company-specific covariates, as well as identify anomalous ILR curves. The exploratory findings motivate the probabilistic forecasting framework developed in the second half of the paper. We propose a functional model to complete partially developed ILR curves based on partial least squares regression of PCA scores. Coupling the above with functional bootstrapping allows us to quantify future ILR uncertainty jointly across all future lags. We demonstrate that our method has much better probabilistic scores relative to Chain Ladder and in particular can provide accurate functional predictive intervals.

Finding lower and better-generalizing minima is crucial for deep learning. However, most existing optimizers stop searching the parameter space once they reach a local minimum. Given the complex geometric properties of the loss landscape, it is difficult to guarantee that such a point is the lowest or provides the best generalization. To address this, we propose an adaptor "E" for gradient-based optimizers. The adapted optimizer tends to continue exploring along landscape valleys (areas with low and nearly identical losses) in order to search for potentially better local minima even after reaching a local minimum. This approach increases the likelihood of finding a lower and flatter local minimum, which is often associated with better generalization. We also provide a proof of convergence for the adapted optimizers in both convex and non-convex scenarios for completeness. Finally, we demonstrate their effectiveness in an important but notoriously difficult training scenario, large-batch training, where Lamb is the benchmark optimizer. Our testing results show that the adapted Lamb, ALTO, increases the test accuracy (generalization) of the current state-of-the-art optimizer by an average of 2.5% across a variety of large-batch training tasks. This work potentially opens a new research direction in the design of optimization algorithms.

In this work, we introduce CPLASS (Continuous Piecewise-Linear Approximation via Stochastic Search), an algorithm for detecting changes in velocity within multidimensional data. The one-dimensional version of this problem is known as the change-in-slope problem (see Fearnhead & Grose, 2022; Baranowski et al., 2019). Unlike traditional changepoint detection methods that focus on changes in mean, detecting changes in velocity requires a specialized approach due to continuity constraints and parameter dependencies, which frustrate popular algorithms like binary segmentation and dynamic programming. To overcome these difficulties, we introduce a specialized penalty function to balance improvements in likelihood due to model complexity, and a Markov Chain Monte Carlo (MCMC)-based approach with tailored proposal mechanisms for efficient parameter exploration. Our method is particularly suited for analyzing intracellular transport data, where the multidimensional trajectories of microscale cargo are driven by teams of molecular motors that undergo complex biophysical transitions. To ensure biophysical realism in the results, we introduce a speed penalty that discourages overfitted of short noisy segments while maintaining consistency in the large-sample limit. Additionally, we introduce a summary statistic called the Cumulative Speed Allocation, which is robust with respect to idiosyncracies of changepoint detection while maintaining the ability to discriminate between biophysically distinct populations.

Bayesian statistics has gained popularity in psychological research due to its intuitive uncertainty quantification and convenient information-updating rules. In many applications, however, prior distributions are introduced merely as instruments to facilitate computation, rather than as representations of genuine subjective belief. Consequently, relying on standard Bayesian justifications for inferential procedures becomes conceptually ungrounded. In this paper, we recommend evaluating finite-sample performance over repeated sampling of data and parameters as an alternative justification for "pragmatic Bayes." We demonstrate a key vulnerability in the usual posterior-based inference: when analysts' chosen prior distribution mismatches the true parameter-generating process, Bayesian inference can be misleading. Given that this true process is rarely known in practice, we propose a safer alternative: calibrating Bayesian credible regions to achieve frequentist validity. This latter criterion is stronger and guarantees validity of Bayesian inference regardless of the underlying parameter-generating mechanism. To solve the calibration problem in practice, we propose a novel stochastic approximation algorithm. A Monte Carlo experiment is conducted and reported, in which we observe that uncalibrated Bayesian inference can be liberal under certain parameter-generating scenarios, whereas our calibrated solution consistently maintain validity. We also illustrate the proposed calibration procedure using a real-data example involving location-scale regression.

Weather extremes pose major societal risks, especially in a changing climate, but due to their rarity, they are difficult to study using limited observations or complex climate models. We introduce AI+RES, a framework coupling fast AI weather forecasts with a high-fidelity physics model using a rare-event algorithm to efficiently characterize extremes. This approach enables the study of the statistics and physics of very rare events, such as once per millennium heatwaves at two orders-of-magnitude lower computational cost. AI+RES can be applied broadly across climate science and other fields concerned with rare events.

The dynamic structural load identification capabilities of the gated recurrent unit, long short-term memory, and convolutional neural networks are examined herein. The examination is on realistic small dataset training conditions and on a comparative view to the physics-based residual Kalman filter (RKF). The dynamic load identification suffers from the uncertainty related to obtaining poor predictions when in civil engineering applications only a low number of tests are performed or are available, or when the structural model is unidentifiable. In considering the methods, first, a simulated structure is investigated under a shaker excitation at the top floor. Second, a building in California is investigated under seismic base excitation, which results in loading for all degrees of freedom. Finally, the International Association for Structural Control-American Society of Civil Engineers (IASC-ASCE) structural health monitoring benchmark problem is examined for impact and instant loading conditions. Importantly, the methods are shown to outperform each other on different loading scenarios, while the RKF is shown to outperform the networks in physically parametrized identifiable cases.