7 papers
Brownian Motion with a Pulse: A Biostatistician's Guide to Diffusions, Bridges, Functional PCA, and First-Passage Models
Eliuvish Han Cui
Brownian motion is a compact mathematical language for continuous-time uncertainty in biostatistics. This tutorial develops the process from construction and path properties to too…
From Risk Sets to Martingales: A Counting-Process Framework for Event-History Learning
Eliuvish Han Cui
Counting-process notation separates predictable risk-set information from observed event jumps through decompositions of the form dN(t)=Y(t)alpha(t)dt+dM(t). This article develops…
Crossing the Kolmogorov-Smirnov Boundary: Exact Tails, Sharp Bounds, and Broken Pivots
Elvis Han Cui, Yihao Li, Zhuang Liu
The Kolmogorov-Smirnov statistic is usually introduced as a supremum, but its finite-sample behavior is governed by a more local question: where does the empirical process first cr…
Markov Renewal Proportional Hazards is All You Need
Elvis Han Cui
Transition probability estimation plays a critical role in multi-state modeling, especially in clinical research. This paper investigates the application of semi-Markov and Markov…
DSS-Prompt: Dynamic-Static Synergistic Prompting for Few-Shot Class-Incremental Learning
Linpu He, Yanan Li, Bingze Li +2
Learning from large-scale pre-trained models with strong generalization ability has shown remarkable success in a wide range of downstream tasks recently, but it is still underexpl…
A Metric-based Principal Curve Approach for Learning One-dimensional Manifold
Eliuvish Cuicizion
Principal curve is a well-known statistical method oriented in manifold learning using concepts from differential geometry. In this paper, we propose a novel metric-based principal…