Showing stat.APShow all
3 papers · 1 filter
stat.AP2026
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…
stat.AP2026
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…
stat.AP2025
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…