arXiv subjects

J. E. Borgert

Publications and source records attributed to J. E. Borgert.

3 recordsLinked to original sources

arXiv2026

A Bernstein-von Mises Theorem for Generalized Fiducial Distributions

An established and growing literature on generalized fiducial inference and related fiducial ideas points to the adoption of fiducial inference as a mainstream perspective among modern statisticians. Like Bayesian posteriors, generalized fiducial distributions (GFDs) are known to satisfy Bernstein-von Mises (BvM)-type results under classical regularity conditions. Existing fiducial BvM results, however, rely on relatively restrictive smoothness assumptions and are limited in scope. In this paper, we establish a Bernstein-von Mises theorem for generalized fiducial inference under the general framework of local asymptotic normality, which accommodates non-i.i.d. data settings and reduces to the familiar differentiability in quadratic mean condition in the i.i.d. case. We apply our result to extend existing fiducial theory for free-knot spline models first developed in Sonderegger and Hannig (2014), and further illustrate its generality in models where classical regularity conditions fail or i.i.d. assumptions are not met.

math.ST↗

arXiv2025

Elastic Shape Analysis of Movement Data

Osteoarthritis (OA) is a highly prevalent degenerative joint disease, and the knee is the most commonly affected joint. Biomechanical factors, particularly forces exerted during walking, are often measured in modern studies of knee joint injury and OA, and understanding the relationship among biomechanics, clinical profiles, and OA has high clinical relevance. Biomechanical forces are typically represented as curves over time, but a standard practice in biomechanics research is to summarize these curves by a small number of discrete values (or landmarks). The objective of this work is to demonstrate the added value of analyzing full movement curves over conventional discrete summaries. We developed a shape-based representation of variation in full biomechanical curve data from the Intensive Diet and Exercise for Arthritis (IDEA) study (Messier et al., 2009, 2013), and demonstrated through nested model comparisons that our approach, compared to conventional discrete summaries, yields stronger associations with OA severity and OA-related clinical traits. Notably, our work is among the first to quantitatively evaluate the added value of analyzing full movement curves over conventional discrete summaries.

stat.AP↗

arXiv2021

Persistent topology of protein space

Protein fold classification is a classic problem in structural biology and bioinformatics. We approach this problem using persistent homology. In particular, we use alpha shape filtrations to compare a topological representation of the data with a different representation that makes use of knot-theoretic ideas. We use the statistical method of Angle-based Joint and Individual Variation Explained (AJIVE) to understand similarities and differences between these representations.

q-bio.BM↗