The significance of pi in a markov chain

[fahey32]

A question in regards to nomenclature. I am curious as to the significance of using the symbol π for a time-independent distribution. Does it have any relation to the number π or circular geometry? Or does it come maybe from the invariance of i in the P Matrix such that P_i,j → π_j? I don't like to think that the symbol was chosen arbitrarily with no regard for it's usual significance and I can't think of any examples of important greek letters being repurposed for other significant equations/notation. I hope I've posted this in the right section

 

[chiro]

Hey fahey32 and welcome to the forums.

Some symbols become standardized and others not so much.

In statistics, the lower case pi's are often used for probabilities in various scenarios (the Bernoulli and binomial being one common instance).

I wouldn't try and make too many connections regard to symbols: I'd make a guess to say that symbols were chosen, used a lot, and consequently stuck for all future generations to use them.

 

[statdad]

"In statistics, the lower case pi's are often used for probabilities"

True - part of the original motivation was to continue the writing of parameters (population descriptors) with Greek letters ($\mu , \pi, \sigma$, etc)