All Questions
6
questions
0
votes
0
answers
28
views
Reference Hellinger distance as a geodesic distance
I consider a statistical manifold equipped with the Fisher Information Metric.
I want to show that for the exponential family (with no additional constraint), the Hellinger distance coincides with the ...
- 11
0
votes
1
answer
44
views
Links between sufficient statistics and Chentsov's characterization of Fisher metric
I've been self-studying "Information Geometry" by Ay et al. fascinated by the connection between Geometry, Probability and even Statistics. The proofs are clear to me, nonetheless, even in ...
- 59
1
vote
1
answer
64
views
Determining hyperbolic or euclidean geometry
Consider the Riemmanian product metric:
$$ ds^2= f(\theta)~d\theta^2 + f(r)~dr^2$$
for $\theta, r>0$ and $f(\theta)=2\sqrt{\theta}K_1(2\sqrt{\theta})$ where $K_1$ is a modified Bessel function.
I ...
- 756
1
vote
1
answer
164
views
Why are tangent vectors in statistical manifolds $\boldsymbol e_i\approx \partial_i \log p(x,\boldsymbol\xi)$?
In section 5.1 of Amari's book, when discussing statistical manifolds, the author states that, given a manifold whose points are probability distributions, one can identify tangent vectors $\...
- 7,095
3
votes
1
answer
293
views
What is the intuition behind the Fisher-Rao metric?
I've seen the Fisher-Rao metric introduced via the following argument (see Sidhu and Kok 2019):
There is a natural pairing between the simplex and its dual space of classical random variables: $\...
- 7,095
29
votes
3
answers
6k
views
Applications of information geometry to the natural sciences
I am contemplating undergraduate thesis topics, and am searching for a topic that combines my favorite areas of analysis, differential geometry, graph theory, and probability, and that also has (...
- 293