Harry Crane is Associate Professor and Chancellor's Excellence Scholar in Statistics, Co-Director of the Graduate Program in Statistics, and Affiliated Faculty in the Graduate Program in Philosophy at Rutgers University. He is co-founder of Researchers.One, a decentralized research platform for peer review, scholarly publication, community building and research dissemination. Crane is currently Fellow at the London Mathematical Institute, and has previously held positions as a Visiting Scholar in Mathematics at UC Berkeley, Research Associate at the RAND Corporation, and Research Fellow at the Foreign Policy Research Institute. Harry received his PhD in Statistics from the University of Chicago and BA in Mathematics and Economics from the University of Pennsylvania.
I work on probability, statistics, logic, and their applications to complexity science and the foundations of complex data analysis.
Whereas recent trends focus on "Big Data", whose core challenge lies in scaling up existing methods to handle larger data sets, the central challenges in
complex data analysis are conceptual, concerning basic questions of how complex structures can be represented mathematically and analyzed computationally.
Networks are the most basic complex data structures, for which I have written a book on Probabilistic Foundations of Statistical Network Analysis.
Invariance principles are a common theme in this work, mostly in the concept of exchangeability and its variants (partial exchangeability, relative exchangeability, edge exchangeability, relational exchangeability), and their limitations for modeling complex data structures.
Toward a more general framework for complex data analysis, my recent work draws on a range of techniques from probability theory, logic, combinatorics, homotopy type theory, category theory, and the Univalent Foundations of mathematics.