The use of representative pre-crash scenarios is critical for assessing the safety impact of driving automation systems through simulation. However, a gap remains in the robust evaluation of the similarity between synthetic and real-world pre-crash scenarios and their crash characteristics. Without proper validation, it cannot be ensured that the synthetic test scenarios adequately represent real-world driving behaviors and crash characteristics. One reason for this validation gap is the lack of focus on methods to confirm that the synthetic test scenarios are practically equivalent to real-world ones, given the assessment scope. Traditional statistical methods, like significance testing, focus on detecting differences rather than establishing equivalence; since failure to detect a difference does not imply equivalence, they are of limited applicability for validating synthetic pre-crash scenarios and crash characteristics. This study addresses this gap by proposing an equivalence testing method based on the Bayesian Region of Practical Equivalence (ROPE) framework. This method is designed to assess the practical equivalence of scenario characteristics that are most relevant for the intended assessment, making it particularly appropriate for the domain of virtual safety assessments. We first review existing equivalence testing methods. Then we propose and demonstrate the Bayesian ROPE-based method by testing the equivalence of two rear-end pre-crash datasets. Our approach focuses on the most relevant scenario characteristics. Our analysis provides insights into the practicalities and effectiveness of equivalence testing in synthetic test scenario validation and demonstrates the importance of testing for improving the credibility of synthetic data for automated vehicle safety assessment, as well as the credibility of subsequent safety impact assessments.

This paper proposes an embedding method for co-occurrence data aimed at visual information exploration. We consider cases where co-occurrence probabilities are measured between pairs of elements from heterogeneous domains. The proposed method maps these heterogeneous elements into corresponding two-dimensional latent spaces, enabling visualization of asymmetric relationships between the domains. The key idea is to embed the elements in a way that maximizes their mutual information, thereby preserving the original dependency structure as much as possible. This approach can be naturally extended to cases involving three or more domains, using a generalization of mutual information known as total correlation. For inter-domain analysis, we also propose a visualization method that assigns colors to the latent spaces based on conditional probabilities, allowing users to explore asymmetric relationships interactively. We demonstrate the utility of the method through applications to an adjective-noun dataset, the NeurIPS dataset, and a subject-verb-object dataset, showcasing both intra- and inter-domain analysis.

This paper introduces Uncertainty Propagation Network (UPN), a novel family of neural differential equations that naturally incorporate uncertainty quantification into continuous-time modeling. Unlike existing neural ODEs that predict only state trajectories, UPN simultaneously model both state evolution and its associated uncertainty by parameterizing coupled differential equations for mean and covariance dynamics. The architecture efficiently propagates uncertainty through nonlinear dynamics without discretization artifacts by solving coupled ODEs for state and covariance evolution while enabling state-dependent, learnable process noise. The continuous-depth formulation adapts its evaluation strategy to each input's complexity, provides principled uncertainty quantification, and handles irregularly-sampled observations naturally. Experimental results demonstrate UPN's effectiveness across multiple domains: continuous normalizing flows (CNFs) with uncertainty quantification, time-series forecasting with well-calibrated confidence intervals, and robust trajectory prediction in both stable and chaotic dynamical systems.

This study compares probabilistic predictors based on information theory with Naive Discriminative Learning (NDL) predictors in modeling acoustic word duration, focusing on probabilistic reduction. We examine three models using the Buckeye corpus: one with NDL-derived predictors using information-theoretic formulas, one with traditional NDL predictors, and one with N-gram probabilistic predictors. Results show that the N-gram model outperforms both NDL models, challenging the assumption that NDL is more effective due to its cognitive motivation. However, incorporating information-theoretic formulas into NDL improves model performance over the traditional model. This research highlights a) the need to incorporate not only frequency and contextual predictability but also average contextual predictability, and b) the importance of combining information-theoretic metrics of predictability and information derived from discriminative learning in modeling acoustic reduction.

Data assimilation (DA) is the problem of sequentially estimating the state of a dynamical system from noisy observations. Recent advances in generative modeling have inspired new approaches to DA in high-dimensional nonlinear settings, especially the ensemble score filter (EnSF). However, these come at a significant computational burden due to slow sampling. In this paper, we introduce a new filtering framework based on flow matching (FM) -- called the ensemble flow filter (EnFF) -- to accelerate sampling and enable flexible design of probability paths. EnFF -- a training-free DA approach -- integrates MC estimators for the marginal FM vector field (VF) and a localized guidance to assimilate observations. EnFF has faster sampling and more flexibility in VF design compared to existing generative modeling for DA. Theoretically, we show that EnFF encompasses classical filtering methods such as the bootstrap particle filter and the ensemble Kalman filter as special cases. Experiments on high-dimensional filtering benchmarks demonstrate improved cost-accuracy tradeoffs and the ability to leverage larger ensembles than prior methods. Our results highlight the promise of FM as a scalable tool for filtering in high-dimensional applications that enable the use of large ensembles.

Multi-objective Bayesian optimization (MOBO) struggles with sparse (non-space-filling), scarce (limited observations) datasets affected by experimental uncertainty, where identical inputs can yield varying outputs. These challenges are common in physical and simulation experiments (e.g., randomized medical trials and, molecular dynamics simulations) and are therefore incompatible with conventional MOBO methods. As a result, experimental resources are inefficiently allocated, leading to subop-timal designs. To address this challenge, we introduce NOSTRA (Noisy and Sparse Data Trust Region-based Optimization Algorithm), a novel sampling framework that integrates prior knowledge of experimental uncertainty to construct more accurate surrogate models while employing trust regions to focus sampling on promising areas of the design space. By strategically leveraging prior information and refining search regions, NOSTRA accelerates convergence to the Pareto frontier, enhances data efficiency, and improves solution quality. Through two test functions with varying levels of experimental uncertainty, we demonstrate that NOSTRA outperforms existing methods in handling noisy, sparse, and scarce data. Specifically, we illustrate that, NOSTRA effectively prioritizes regions where samples enhance the accuracy of the identified Pareto frontier, offering a resource-efficient algorithm that is practical in scenarios with limited experimental budgets while ensuring efficient performance.

We present a novel Simultaneous Localization and Mapping (SLAM) method that employs Gaussian Process (GP) based landmark (object) representations. Instead of conventional grid maps or point cloud registration, we model the environment on a per object basis using GP based contour representations. These contours are updated online through a recursive scheme, enabling efficient memory usage. The SLAM problem is formulated within a fully Bayesian framework, allowing joint inference over the robot pose and object based map. This representation provides semantic information such as the number of objects and their areas, while also supporting probabilistic measurement to object associations. Furthermore, the GP based contours yield confidence bounds on object shapes, offering valuable information for downstream tasks like safe navigation and exploration. We validate our method on synthetic and real world experiments, and show that it delivers accurate localization and mapping performance across diverse structured environments.

A Bayesian player acting in an infinite multi-player game learns to predict the other players' strategies if his prior assigns positive probability to their play (or contains a grain of truth). Kalai and Lehrer's classic grain of truth problem is to find a reasonably large class of strategies that contains the Bayes-optimal policies with respect to this class, allowing mutually-consistent beliefs about strategy choice that obey the rules of Bayesian inference. Only small classes are known to have a grain of truth and the literature contains several related impossibility results. In this paper we present a formal and general solution to the full grain of truth problem: we construct a class of strategies wide enough to contain all computable strategies as well as Bayes-optimal strategies for every reasonable prior over the class. When the "environment" is a known repeated stage game, we show convergence in the sense of [KL93a] and [KL93b]. When the environment is unknown, agents using Thompson sampling converge to play $\varepsilon$-Nash equilibria in arbitrary unknown computable multi-agent environments. Finally, we include an application to self-predictive policies that avoid planning. While these results use computability theory only as a conceptual tool to solve a classic game theory problem, we show that our solution can naturally be computationally approximated arbitrarily closely.

Classical discriminant analysis assumes identically distributed training data, yet in many applications observations are collected over time and the class-conditional distributions drift. This population drift renders stationary classifiers unreliable. We propose a principled, model-based framework that embeds discriminant analysis within state-space models to obtain nonstationary linear discriminant analysis (NSLDA) and nonstationary quadratic discriminant analysis (NSQDA). For linear-Gaussian dynamics, we adapt Kalman smoothing to handle multiple samples per time step and develop two practical extensions: (i) an expectation-maximization (EM) approach that jointly estimates unknown system parameters, and (ii) a Gaussian mixture model (GMM)-Kalman method that simultaneously recovers unobserved time labels and parameters, a scenario common in practice. To address nonlinear or non-Gaussian drift, we employ particle smoothing to estimate time-varying class centroids, yielding fully nonstationary discriminant rules. Extensive simulations demonstrate consistent improvements over stationary linear discriminant analysis (LDA), quadratic discriminant analysis (QDA), and support vector machine (SVM) baselines, with robustness to noise, missing data, and class imbalance. This paper establishes a unified and data-efficient foundation for discriminant analysis under temporal distribution shift.

Using type Ia supernovae (SNae Ia) as cosmological probes requires empirical corrections, which correlate with their host environment. We present a unified Bayesian hierarchical model designed to infer, from purely photometric observations, the intrinsic dependence of SN Ia brightness on progenitor properties (metallicity & age), the delay-time distribution (DTD) that governs their rate as a function of age, and cosmology, as well as the redshifts of all hosts. The model incorporates physics-based prescriptions for star formation and chemical evolution from Prospector-beta, dust extinction of both galaxy and SN light, and observational selection effects. We show with simulations that intrinsic dependences on metallicity and age have distinct observational signatures, with metallicity mimicking the well-known step of SN Ia magnitudes across a host stellar mass of $\approx 10^{10} M_{\odot}$. We then demonstrate neural simulation-based inference of all model parameters from mock observations of ~16 000 SNae Ia and their hosts up to redshift 0.9. Our joint physics-based approach delivers robust and precise photometric redshifts (<0.01 median scatter) and improved cosmological constraints, unlocking the full power of photometric data and paving the way for an end-to-end simulation-based analysis pipeline in the LSST era.