Keith Was (Almost) Right

• Activity Number: 323
• Type: Invited
• Date/Time: Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
• Sponsor: ENAR
• Author(s): Robert J. Adler and Armin Schwartzman*+
• Companies: Technion and Harvard School of Public Health
• Keywords: Topology ; Random fields ; Persistence ; Inference ; Euler characteristic ; fMRI

Abstract

Keith Worsley used to claim that fMRI brain imaging data is to modern Statistics what agricultural data was to Statistics in its formative years, insofar as it generates new statistical problems and new paradigms for their solution. In particular, the topological approach that he and others, such as Karl Friston, took to the analysis of fMRI data led to the development of the notion of TI, or "topological inference".

In a development that is turning out to be both related and complementary to TI, applied topologists were developing the notion of TDA, or "topological data analysis", based heavily on notions such as persistent homology, albeit with comparatively little input from traditional statistical thinking.

In this talk I will discuss both TI and TDA from the point of view of random processes on high dimensional parameter spaces, and try to convince you that Keith's claim that "TI is the future" should be expanded to "when topologists, statisticians and probabilistic can speak a common language, the future he was dreaming of will have arrived".