Probability as Shape
Harry Crane is an Associate Professor and Co-Director of the Graduate Program in Statistics and Biostatistics at Rutgers University. Before Rutgers, Harry received his PhD in Statistics from the University of Chicago and BA in Mathematics and Economics from the University of Pennsylvania. He 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.
My research interests are in probability theory, stochastic processes, foundations of statistical inference and probability, and logic.
A common theme throughout this work has been the concept of exchangeability, its variants (partial exchangeability, relative exchangeability, edge exchangeability, relational exchangeability), and the role they play in statistical inference.
I have recently been focusing on the limitations and implications of exchangeability to modeling network data, in which common assumptions are ill-suited for addressing widespread empirical properties.
This has led to the introduction of new concepts (relative exchangeability with Henry Towsner, edge and relational exchangeability with Walter Dempsey).
My other interests include intuitionistic logic, homotopy type theory, and the philosophical foundations of probability. A specific interest in this direction is the subjectivist justification for representing degrees of belief as numbers, and in particular numbers that satisfy the probability axioms.