Talk:Coupling (probability)

History

Does it deserve to be mentionned that the first occurence of coupling in probability theory seems to be the proof of convergence to the stationary distribution of a Markov chain by Wolfgang Doeblin ? I think so, for Wolfgang Doeblin is a rather romantic figure in Mathematics. I take this from T. Lindvall, Lectures on the coupling method. Wiley, New York, 1992, if my memory serves me well .... --Chassain (talk) 15:26, 6 February 2010 (UTC)

Example

What if A is in (4,x), B in (5,y), and A goes right? As far as I understood, B shall go left, so that A and B horizontal coordinates crosses. If initially A=(0,0) and B=(10,10), then it's ok, but if B has odd coordinates, then A and B never meet, right?... Levochik (talk) 13:38, 14 October 2011 (UTC)

Misleading introduction

It is extremely confusing to be told in the introduction that a "coupling is a proof technique".

It like virtually every imaginable definition in mathematics can be used to prove things. But a coupling is not a proof technique.

A coupling (of two or more probability distributions) is a joint distribution that has the given distributions as marginals.

To call it a "proof technique" just avoids saying what the word means.

By all means: Later in the article it is entirely appropriate to explain how couplings are used to prove things. But it is not a good idea at all to call something what it is not — especially in the introduction.

Also: The first examples provided in the article are good examples, but not as the first examples that someone sees.

It is a far better idea to start out by displaying two very simple probability distributions and one or more joint distributions having those as its marginals.

 — Preceding unsigned comment added by ~2026-38980-22 (talk) 16:49, 31 July 2026 (UTC)