All Questions
5
questions
1
vote
1
answer
661
views
Stereographic Projection of Uniform Distribution on Sphere
Consider a (punctured) unit sphere $S = \{ (x,y,z) \mid x^2+y^2+z^2 = 1, z\neq 1 \} $ and the plane $L = \{ (X,Y,0) \}$ (let us use the shorthand $(X,Y)$ for $(X,Y,0)$).
We can define the ...
- 16.7k
2
votes
0
answers
49
views
Probability distribution on a complicated geometry.
Suppose you have a manifold with a very distorted, very complicated geometry defined by some metric tensor. However, let's say that this geometry is perhaps too complicated to predict exactly, and so ...
- 133
7
votes
1
answer
272
views
Information geometry: geometry of exponential families
I've read in various locations that the geometry of exponential families are flat.
Is this true? I don't understand because, I have also read that the family of gaussians with unknown mean and ...
- 419
3
votes
1
answer
167
views
Statistical Manifold with Non-trivial Topology
Let $(\Omega, E)$ be a measure space. An $n$-dimensional statistical model is then a tuple $(\Theta, \mathcal{M}, \Phi)$ where $\Theta \subseteq \mathbb{R}^n$ open, $\mathcal{M} = \{p_\theta := p(\...
- 3,380
2
votes
1
answer
908
views
Uniformly distributed points on spherical surface
Let $x=(x_1,\ldots,x_n)$ be uniformly distributed on the $(n-1)$-dimensional spherical surface $S^{n-1}(n^\frac{1}{2})$ of radius $n^\frac{1}{2}$. I'm trying to show that as $n\to\infty$, $x_1$ ...
- 1,354