Statistics
Statistics educators recommend teaching with real data with relevant contexts, but defining relevancy is challenging and varies by student. We investigated whether providing student choice of data context increases engagement through a…
We study the Collatz total stopping time $\tau(n)$ over $n\le 10^7$ from a probabilistic machine learning viewpoint. Empirically, $\tau(n)$ is a skewed and heavily overdispersed count with pronounced arithmetic heterogeneity. We develop two…
Discovering causal direction from temporal observational data is particularly challenging for symbolic sequences, where functional models and noise assumptions are often unavailable. We propose a novel \emph{Dictionary Based Pattern Entropy…
What, if anything, should a frequentist say about a single realized confidence interval (CI) and its chance of having covered the parameter? Jerzy Neyman's original answer was to refuse any nondegenerate probability for coverage ex post…
Understanding behavioural responses to disturbances is vital for wildlife conservation. For example, in the Arctic, the decrease in sea ice has opened new shipping routes, increasing the need for impact assessments that quantify the…
Mixture models are widely used in modeling heterogeneous data populations. A standard approach of mixture modeling assumes that the mixture component takes a parametric kernel form. In many applications, making parametric assumptions on the…
Access to multiple predictive models trained for the same task, whether in regression or classification, is increasingly common in many applications. Aggregating their predictive uncertainties to produce reliable and efficient uncertainty…
Backtesting risk measures is a central task in financial regulation. While standard backtests evaluate whether a forecasting model is statistically consistent with observed losses, regulatory practice often requires assessing the…
Small influential data subsets can dramatically impact model conclusions, with a few data points overturning key findings. While recent work identifies these most influential sets, there is no formal way to tell when maximum influence is…
Inverse problems are crucial for many applications in science, engineering and medicine that involve data assimilation, design, and imaging. Their solution infers the parameters or latent states of a complex system from noisy data and…
In this paper, we study the quantitative convergence of shallow neural networks trained via gradient descent to their associated Gaussian processes in the infinite-width limit. While previous work has established qualitative convergence…
Treatment effect heterogeneity refers to the systematic variation in treatment effects across subgroups. There is an increasing need for clinical trials that aim to investigate treatment effect heterogeneity and estimate subgroup-specific…
We propose a method for evaluating the robustness of widely used LLM ranking systems -- variants of a Bradley--Terry model -- to dropping a worst-case very small fraction of preference data. Our approach is computationally fast and easy to…
This paper provides a formulation of the log-homotopy particle flow from the perspective of variational inference. We show that the transient density used to derive the particle flow follows a time-scaled trajectory of the Fisher-Rao…
Many learning algorithms can be represented as Markov processes, and understanding their generalization error is a central topic in learning theory. For specific continuous-time noisy algorithms, a prominent analysis technique relies on…
For decades, National Football League (NFL) coaches' observed fourth down decisions have been largely inconsistent with prescriptions based on statistical models. In this paper, we develop a framework to explain this discrepancy using an…
To characterize the community structure in network data, researchers have developed various block-type models, including the stochastic block model, the degree-corrected stochastic block model, the mixed membership block model, the…
Understanding how social networks form, whether through reciprocity, shared attributes, or triadic closure, is central to computational social science. Exponential Random Graph Models (ERGMs) offer a principled framework for testing such…
The progression of chronic diseases often follows highly variable trajectories, and the underlying factors remain poorly understood. Standard mixed-effects models typically represent inter-patient differences as random deviations around a…
This paper develops a comprehensive Markov-based framework for modelling reservoir behaviour and assessing key performance measures such as reliability and resilience. We first formulate a stochastic model for a finite-capacity dam,…