arXiv:2502.06096v5 Announce Type: replace-cross Abstract: This paper addresses a fundamental but largely unexplored challenge in sequential changepoint analysis: conducting inference following a detected change. We develop a very general framework to construct confidence sets for the unknown changepoint using only the data observed up to a data-dependent stopping time at which an arbitrary sequential detection algorithm declares a change. Our framework is nonparametric, making no assumption on the composite post-change class, the observation space, or the sequential detection procedure used, and is non-asymptotically valid. We also extend it to handle composite pre-change classes under a suitable assumption, and also derive confidence sets for the change magnitude in parametric settings. We provide theoretical guarantees on the width of our confidence intervals. Extensive simulations demonstrate that the produced sets have reasonable size, and slightly conservative coverage. In summary, we present the first general method for sequential changepoint localization, which is theoretically sound and broadly applicable in practice.

arXiv:2505.11211v3 Announce Type: replace-cross Abstract: We propose Bayesian Hierarchical Invariant Prediction (BHIP) reframing Invariant Causal Prediction (ICP) through the lens of Hierarchical Bayes. We leverage the hierarchical structure to explicitly test invariance of causal mechanisms under heterogeneous data, resulting in improved computational scalability for a larger number of predictors compared to ICP. Moreover, given its Bayesian nature BHIP enables the use of prior information. We evaluate BHIP on both synthetic and real-world datasets, demonstrating its potential as an alternative inference method to ICP and related methods.

arXiv:2512.11919v3 Announce Type: replace-cross Abstract: The notion of causal effect is fundamental across many scientific disciplines. Traditionally, quantitative researchers have studied causal effects at the level of variables; for example, how a certain drug dose (W) causally affects a patient's blood pressure (Y). However, in many modern data domains, the raw variables-such as pixels in an image or tokens in a language model-do not have the semantic structure needed to formulate meaningful causal questions. In this paper, we offer a more fine-grained perspective by studying causal effects at the level of events, drawing inspiration from probability theory, where core notions such as independence are first given for events and sigma-algebras, before random variables enter the picture. Within the measure-theoretic framework of causal spaces, a recently introduced axiomatisation of causality, we first introduce several binary definitions that determine whether a causal effect is present, as well as proving some properties of them linking causal effect to (in)dependence under an intervention measure. Further, we provide quantifying measures that capture the strength and nature of causal effects on events, and show that we can recover the common measures of treatment effect as special cases.