Adaptively collected data has become ubiquitous within modern practice. However, even seemingly benign adaptive sampling schemes can introduce severe biases, rendering traditional statistical inference tools inapplicable. This can be mitigated by a property called stability, which states that if the rate at which an algorithm takes actions converges to a deterministic limit, one can expect that certain parameters are asymptotically normal. Building on a recent line of work for the multi-armed bandit setting, we show that the linear upper confidence bound (LinUCB) algorithm for linear bandits satisfies this property. In doing so, we painstakingly characterize the behavior of the eigenvalues and eigenvectors of the random design feature covariance matrix in the setting where the action set is the unit ball, showing that it decomposes into a rank-one direction that locks onto the true parameter and an almost-isotropic bulk that grows at a predictable $\sqrt{T}$ rate. This allows us to establish a central limit theorem for the LinUCB algorithm, establishing asymptotic normality for the limiting distribution of the estimation error where the convergence occurs at a $T^{-1/4}$ rate. The resulting Wald-type confidence sets and hypothesis tests do not depend on the feature covariance matrix and are asymptotically tighter than existing nonasymptotic confidence sets. Numerical simulations corroborate our findings.

Methods for probability updating, of which Bayesian conditionalization is the most well-known and widely used, are modeling tools that aim to represent the process of modifying an initial epistemic state, typically represented by a prior probability function P, which is adjusted in light of new information. Notably, updating methods and conditional sentences seem to intuitively share a deep connection, as is evident in the case of conditionalization. The present work contributes to this line of research and aims at shedding new light on the relationship between updating methods and conditional connectives. Departing from previous literature that often focused on a specific type of conditional or a particular updating method, our goal is to prove general results concerning the connection between conditionals and their probabilities. This will allow us to characterize the probabilities of certain conditional connectives and to understand what class of updating procedures can be represented using specific conditional connectives. Broadly, we adopt a general perspective that encompasses a large class of conditionals and a wide range of updating methods, enabling us to prove some general results concerning their interrelation.

We present an algorithm to identify sparse dependence structure in continuous and non-Gaussian probability distributions, given a corresponding set of data. The conditional independence structure of an arbitrary distribution can be represented as an undirected graph (or Markov random field), but most algorithms for learning this structure are restricted to the discrete or Gaussian cases. Our new approach allows for more realistic and accurate descriptions of the distribution in question, and in turn better estimates of its sparse Markov structure. Sparsity in the graph is of interest as it can accelerate inference, improve sampling methods, and reveal important dependencies between variables. The algorithm relies on exploiting the connection between the sparsity of the graph and the sparsity of transport maps, which deterministically couple one probability measure to another.

Many physical processes, however, generate data that are continuous but non-Gaussian.

Supervised anomaly detection methods perform well in identifying known anomalies that are well represented in the training set. However, they often struggle to generalise beyond the training distribution due to decision boundaries that lack a clear definition of normality. Existing approaches typically address this by regularising the representation space during training, leading to separate optimisation in latent and label spaces. The learned normality is therefore not directly utilised at inference, and their anomaly scores often fall within arbitrary ranges that require explicit mapping or calibration for probabilistic interpretation. To achieve unified learning of geometric normality and label discrimination, we propose Centre-Enhanced Discriminative Learning (CEDL), a novel supervised anomaly detection framework that embeds geometric normality directly into the discriminative objective. CEDL reparameterises the conventional sigmoid-derived prediction logit through a centre-based radial distance function, unifying geometric and discriminative learning in a single end-to-end formulation. This design enables interpretable, geometry-aware anomaly scoring without post-hoc thresholding or reference calibration. Extensive experiments on tabular, time-series, and image data demonstrate that CEDL achieves competitive and balanced performance across diverse real-world anomaly detection tasks, validating its effectiveness and broad applicability.

We address the challenge of forecasting counterfactual outcomes in a panel data with missing entries and temporally dependent latent factors -- a common scenario in causal inference, where estimating unobserved potential outcomes ahead of time is essential. We propose Forecasting Counterfactuals under Stochastic Dynamics (Focus), a method that extends traditional matrix completion methods by leveraging time series dynamics of the factors, thereby enhancing the prediction accuracy of future counterfactuals. Building upon a PCA estimator, our method accommodates both stochastic and deterministic components within the factors, and provides a flexible framework for various applications. In case of stationary autoregressive factors and under standard conditions, we derive error bounds and establish asymptotic normality of our estimator. Empirical evaluations demonstrate that our method outperforms existing benchmarks when the latent factors have an autoregressive component. We illustrate Focus results on HeartSteps, a mobile health study, illustrating its effectiveness in forecasting step counts for users receiving activity prompts, thereby leveraging temporal patterns in user behavior.

Background/Objectives: Efficient task allocation in hospital emergency departments (EDs) is critical for operational efficiency and patient care quality, yet the complexity of staff coordination poses significant challenges. This study proposes a simulation-based framework for modeling doctors and nurses as intelligent agents guided by computational trust mechanisms. The objective is to explore how trust-informed coordination can support decision making in ED management. Methods: The framework was implemented in Unity, a 3D graphics platform, where agents assess their competence before undertaking tasks and adaptively coordinate with colleagues. The simulation environment enables real-time observation of workflow dynamics, resource utilization, and patient outcomes. We examined three scenarios - Baseline, Replacement, and Training - reflecting alternative staff management strategies. Results: Trust-informed task allocation balanced patient safety and efficiency by adapting to nurse performance levels. In the Baseline scenario, prioritizing safety reduced errors but increased patient delays compared to a FIFO policy. The Replacement scenario improved throughput and reduced delays, though at additional staffing cost. The training scenario forstered long-term skill development among low-performing nurses, despite short-term delays and risks. These results highlight the trade-off between immediate efficiency gains and sustainable capacity building in ED staffing. Conclusions: The proposed framework demonstrates the potential of computational trust for evidence-based decision support in emergency medicine. By linking staff coordination with adaptive decision making, it provides hospital managers with a tool to evaluate alternative policies under controlled and repeatable conditions, while also laying a foundation for future AI-driven personalized decision support.