What is the uniform distribution?


Venue   Statistics and Data Science Seminar, Queen Mary University of London, 20 October 2021

Abstract   Everyone knows what the uniform probability distribution is on a real interval or on a finite set, but it is not so obvious what we should understand "uniform distribution" to mean on a completely arbitrary space. I will give a general definition, taking "space" to mean something slightly more general than compact metric space. The definition rests on a maximum entropy theorem for distributions on metric spaces, which in turn arose from questions about the measurement of biodiversity. This idea of seeking a systematic general notion of uniform distribution is similar in spirit to the quest for an objective prior, and indeed, is at least loosely related to it, as I will explain.

(Joint work with Emily Roff.)

Slides   In this pdf file.

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