Peter McCullagh: Categorical notions in statistics

Talk at the Categorical Probability and Statistics workshop 2020: http://perimeterinstitute.ca/personal... Title: Categorical notions in statistics Speaker: Peter McCullagh Chair: Alex Simpson Date: June 5th, 2020 Abstract: I will talk about three areas in which categorical thinking has helped to clarify statistical ideas. The first is in the mundane area of sampling, and specifically the importance of inheritance in the definition of symmetric functions. Inheritance leads directly to k-statistics and the classical cumulants. The second is related to symmetric functions for spectral samples or eigenvalues. Inheritance leads to a family of polynomial symmetric functions, called spectral k-statistics that are closely related in the limit to free cumulants. The third area is related to factorial models and is closely connected with representation theory for injective maps.