Which Distribution for Constrained Parameter vector Sum


#1

Hi.

I would like to have a vector of K parameters [B1… BK].
The main constraint I have is that their sum is 1.
No particular distribution is needed, except, I would like that the first parameter (B1) be larger than the rest. I can set it to some value.

How should I declare my B param vector?

Thanks in advance


#2

I think I am solving this for now with:
B = pm.Dirichlet(‘proportions’, np.ones(K))
Though, I don’t know yet how to pin the first parameter B[0] to be sufficiently large (~ 0.5)
any idea?


#3

You can control that by playing with the prior parameter of Dirichlet https://en.wikipedia.org/wiki/Dirichlet_distribution