Entropy Pooling

The Entropy Pooling method solves the problem

\[q=\text{argmin}\left\{ x'\left(\ln x-\ln p\right)\right\},\]

subject to the constraints

\[\begin{split}Ax=b, \\Gx\leq h.\end{split}\]

The method was first introduced by Meucci [2008], while the code is implemented using notation from Vorobets [2021].

entropy_pooling(p, A, b, G=None, h=None)

Function for computing Entropy Pooling posterior probabilities.

Parameters
  • p (ndarray) – Prior probability vector with shape (S, 1).

  • A (ndarray) – Equality constraint matrix with shape (M, S).

  • b (ndarray) – Equality constraint vector with shape (M, 1).

  • G (Optional[ndarray]) – Inequality constraint matrix with shape (N, S).

  • h (Optional[ndarray]) – Inequality constraint vector with shape (N, 1).

Return type

ndarray

Returns

Posterior probability vector with shape (S, 1).