3
votes
1answer
109 views

Two matrix Fisher distributions on SO(3)?

After the uniform distribution (normalized Haar measure), the matrix Fisher distribution seems to be the most popular probability distribution on the Lie group SO(3). The density is proportional to ...
1
vote
0answers
18 views

the 3th and 4th order statistics of Circularly Symmetric Complex Normal random vector?

Assume that ${\bf{z}} \in {\mathbb{C}}^{n \times 1}$ is a CSCG random vector denoted with $\mathcal{C} ~ (\bf{\mu} _0,\bf \Sigma _0)$ where $\mu _0$ and $\bf \Sigma _0$ are mean and contrivance ...
0
votes
0answers
45 views

Distinguishing two different matrix distributions in polynomial time

I have two distributions: $\{ (f^TA + e_1, f^T(As+e) \}$ and $\{ (f^TA, f^T(As+e) + s_i \}$ where $A$ is a randomly generated $m \times n$ binary matrix $A, A_{ij} \in \{0,1\}$, $f$ and $e$ are a ...
1
vote
1answer
74 views

Numerical optimisation for multivariate Gaussians

Hi, I want to calculate $ f_{\mathbf x}(x_1,\ldots,x_k)\, = \frac{1}{(2\pi)^{k/2}|\boldsymbol\Sigma|^{1/2}} \exp\left(-\frac{1}{2}({\mathbf x}-{\boldsymbol\mu})^T{\boldsymbol\Sigma}^{-1}({\mathbf ...
4
votes
1answer
866 views

Monotonicity of the hard EM algorithm.

Consider the problem where we want to find a maximum likelihood estimate of $\theta$, given $X$ and $$P_\theta(Y) = \sum_z P_\theta(Y,x)$$ where $x$ is a latent variable. I know that the soft EM ...
1
vote
0answers
233 views

Eigenvectors of convolution with a normal distribution over a restricted interval

Suppose I have a random variable $X_0$ with a p.d.f $f_0$ supported on the real interval $[a_0, b_0]$. $X_1$ is the restriction to $[a_1, b_1]$ of the sum $X_0 + g$, where $g$ is normally distributed ...
2
votes
0answers
269 views

Seeking the normalizing constant (or any references) for a distribution over a subset of positive definite martrices

I'm interested in a probability distribution over the set of positive definite matrices with unit diagonal elements. That is, and $X$ such that: $X \in S^{n+}, \forall_{i}X_{ii} = 1$ where $S^{n+}$ ...