I've been juggling with some concepts from statistics revolving around properties of estimators and sufficient statistics, and I can't help but notice that they have a strong categorical flavor, e.g. I'm pretty sure minimal sufficient statistics are terminal objects in an appropriate category.

I know someone must have worked these things out but haven't been able to find it - I'd be grateful if someone could give me a pointer to some illuminating discussion of applications of category theory to statistics.

  • $\begingroup$ I don't think that minimal sufficience is a universal property because no uniqueness of the function is required (and in fact does not hold). $\endgroup$
    – HeinrichD
    May 6, 2017 at 10:39
  • $\begingroup$ Minimal sufficient might be the coproduct of the information and equality up to isomorphism would hold? $\endgroup$ Oct 12, 2017 at 1:29
  • $\begingroup$ @HeinrichD : There is uniqueness up to a simple equivalence relation. $\endgroup$ Apr 3, 2018 at 18:20

2 Answers 2


The following paper of T. Fritz seems to be close to what you're after, arXiv:1908.01021. In particular the sections 14-15-16.


If you know russian, you can have a look at the book "Ченцов Н.Н. Статистические решающие правила и оптимальные выводы". It has some info about it.


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