Statistics

Classifier-free guidance (CFG) is the de facto standard for conditional sampling in diffusion models, yet it often reduces sample diversity. Using tools from statistical physics, we analyze the emergence of generative distortions induced by…

We study fixed-policy evaluation for finite Markov chains that may be reducible and periodic. Classical evaluation methods with gain and bias decomposition are not always diagnostic: the gain records only invariant Ces\`aro averages, while…

We develop diffusion-based samplers for target distributions known up to a normalising constant. To this end, we rely on the well-known diffusion path that smoothly interpolates between a simple base distribution and the target, popularised…

We present a method of constructing statistical intervals that obtain a natural middle ground between Bayesian and frequentist statistical intervals, previously unexplored in literature: To a p% Bayesian credible interval we should assign a…

Learning models that can handle distribution shifts is a key challenge in domain generalization. Invariance learning, an approach that focuses on identifying features invariant across environments, improves model generalization by capturing…

Fitted $Q$-iteration (FQI) and soft FQI are widely used value-based methods for offline reinforcement learning, but their standard stability guarantees often depend on Bellman completeness, a strong closure condition that can fail under…

Fitted $Q$-evaluation (FQE) is a standard regression-based tool for off-policy evaluation, but existing stability guarantees often rely on Bellman completeness, a strong closure condition that can fail under function approximation. We study…

Reliable long-horizon value prediction is difficult in offline reinforcement learning because fitted value methods combine bootstrapping, function approximation, and distribution shift, while standard guarantees often require Bellman…

An important class of spatio-temporal models is constructed by leveraging the hierarchical structure of dynamical (or, state-space) models. This paper proposes a new statistical dynamical model for spatio-temporal processes motivated by…

Model uncertainty is a central challenge in statistical models for binary outcomes such as logistic regression, arising when it is unclear which predictors should be included in the model. Many methods have been proposed to address this…

Instrumental variables (eliminate the bias that afflicts least-squares identification of dynamical systems through noisy data, yet traditionally relies on external instruments that are seldom available for nonlinear time series data. We…

We provide an inferential framework to assess variable importance for heterogeneous treatment effects. This assessment is especially useful in high-risk domains such as medicine, where decision makers hesitate to rely on black-box treatment…

Functional Principal Components Analysis (FPCA) provides a parsimonious, semi-parametric model for multivariate, sparsely-observed functional data. Frequentist FPCA approaches estimate principal components (PCs) from the data, then…

We introduce two families of inequality measures, $G_p$ and $H_q$, that converge to the classical Gini coefficient as $p,q\to\infty$. The tuning parameters $p>1$ and $q>0$ regulate the influence of disparities between observations. For each…

Many signals evolve in time as a stochastic process, randomly switching between states over discretely sampled time points. Here we make an explicit link between the underlying stochastic process of a signal that can take on a bounded…

Confidence sequences are collections of confidence regions that simultaneously cover the true parameter for every sample size at a prescribed confidence level. Tightening these sequences is of practical interest and can be achieved by…

In minimum trace (MinT) forecast reconciliation, the covariance matrix of the base forecasts errors plays a crucial role. Typically, this matrix is estimated and then treated as known. This can lead to underestimation of the variance of the…

Prior-data fitted networks (PFNs) have emerged as promising foundation models for prediction from tabular datasets, achieving state-of-the-art performance on small to moderate data sizes without tuning. While PFNs are motivated by Bayesian…

Computerized adaptive tests (CATs) play a crucial role in educational assessment and diagnostic screening in behavioral health. Unlike traditional linear tests that administer a fixed set of pre-assembled items, CATs adaptively tailor the…

Marine Protected Areas (MPAs) have been established globally to conserve marine resources. Given their maintenance costs and impact on commercial fishing, it is critical to evaluate their effectiveness to support future conservation. In…