报告简介  Abstract

Topological data analysis has become popular in recent years, though mainly outside the statistical literature.  In this talk we review some of the elements of topological data analysis and we show links to event history and survival analysis. We argue that exploiting topological data as event history can be useful in the analysis of data in the form of images. We propose a version of the well-known Nelson-Aalen cumulative hazard estimator for the comparison of topological features of random fields and for testing parametric assumptions. We suggest a Cox proportional hazards approach for the analysis of embedded metric trees. The Nelson-Aalen method is illustrated on globally distributed climate data and on neutral hydrogen distribution in the Milky Way.  The Cox method is used to compare vascular patterns in fundus images of the eyes of healthy and diabetic retinopathy patients.

嘉宾简介  About the Speaker

Robin Henderson is Professor of Statistics at Newcastle University, UK. Previously he was Professor of Biostatistics at Lancaster University, UK. He is a former Editor of Journal of the Royal Statistical Society Series and formerly the Assistant Editor of Biometrika. He is currently Series Editor for Chapman and Hall Monographs on Statistics and Applied Probability. He was Head of the School of Mathematics and Statistics at Newcastle from 2009 to 2017. Research interests include survival and event history analysis, longitudinal data, missing data, causal inference and dynamic treatment allocation.  His work is usually at the interface of theory and application, where he tries to develop appropriate new methods for real data-based problems.

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