FisherMetrics

! Work in progress !

This is a Julia package that extends Manifolds.jl to statistical manifolds in information geometry. Essentially, a Euclidean manifold where the local metric is given by the Fisher information matrix.

Example ways to create a manifold

    M = FisherMetricManifold(2,p -> fim(Normal(p...)))
    M = FisherMetricManifold(Beta)

Once created, one can calculate the distance between two points, p and q, in addition to calculating the shortest geodesic connecting p and q (amoung several other functions provided by Manifolds.jl).

    using Manifolds
    using FisherMetrics
    using Distributions

    M = FisherMetricManifold(Normal)

    p = [1.0,2.0]
    q = [5.0,4.0]

    B = default_basis(M,p)

    dist = distance(M,p,q)
    geo = shortest_geodesic(M,p,q)

Todo:

1. Provide test functions.
2. Provide documentation.
3. Create a more robust boundary value problem solver to compute geodesics (unstable for points that are far away).