Questions tagged [fisher-information]
For question about fisher information that appears in mathematical statistics.
190
questions
0
votes
0
answers
8
views
Parametric and non parametric probability distributions
Non-parametric Statistical Models on Finite and Infinite Measure Spaces
Consider the following sets of probability densities:
In Amari it says Consider a family $S$ of probability distributions on $X$...
- 181
1
vote
0
answers
41
views
Fisher's information for a function that consist in many indicator functions
I have the following pdf:
$$
f(x) = \theta I_{(-\frac{1}{2},0]}+ I_{(0,\frac{1}{2}]}+(1-\theta) I_{(\frac{1}{2},1]}
$$
I've tried the following
\begin{align}
I(\theta) &=-E[\frac{d^2}{d\...
- 79
0
votes
0
answers
34
views
Trigamma-free Negative Binomial regression: doubts on Hessian and Fisher Information Matrix in the dispersion parameter
I have been looking at alternative versions of the Hessian and Fisher (expected) Information Matrix for the Negative Binomial regression specification, which are given by widely-cited academic sources ...
- 63
0
votes
0
answers
19
views
Calculation of the projection w from Linear Discriminant Analysis
In an assigment focused on Linear Discriminant Analysis(LDA) there is this theoritical exercise:
A dataset has been derived from two classes $ \omega_A$ and $\omega_B$, the distributions of which are ...
1
vote
1
answer
39
views
Question about the Fisher information metric
suppose we have the two one dimensional gaussian probability distribution functions $f(x)$ and $g(x)$ with parameters $P=(\mu_1,\sigma_1)$ and $Q=(\mu_2,\sigma_2)$ so we know that we can give the ...
- 181
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
1
vote
0
answers
45
views
What am I doing wrong when finding the Fisher information of a binomial distribution? [closed]
I am trying to find the Fisher information of a binomial distribution where $n=2$ and $n=\theta$. I have the log-likelihood function as $$n\ln2 + \sum^{n}_{x=1}x_i\ln \theta + (2n-\sum^{n}_{x=1}x_i)(...
0
votes
0
answers
22
views
Fisher Information and Parameter Space
I am reviewing Fisher information and saw that one of the requirements is that the distribution of the data, say $f(x|\theta)$, involves a parameter $\theta$ that is unknown but lies within a given ...
- 571
0
votes
2
answers
179
views
Deriving the Fisher information matrix for a reparameterised gamma distribution
Let $X \sim \mathrm{Gamma}(\alpha, \theta),$ where $$f(x) = \frac {x^{\alpha - 1} e^{-\frac x \theta}} {\theta^{\alpha}\Gamma(\alpha)}.$$ The log-likelihood function can be shown to be $$l(\alpha, \...
- 2,187
0
votes
0
answers
102
views
Intuition for vector calculus
In my statistics class, I was introduced to Fisher Information. As it comes from the Taylor Expansion in vector form, I wanted to know terms were ordered in a certain way - whether it was just to make ...
- 151
0
votes
0
answers
34
views
Differential inequality with KL-divergence and covariance
Let $p_t$ and $q_t$ be two families of probability densities on $\mathbb{R}^d$ indexed by time $t\geq 0$.
Does the following differential inequality imply that the KL-divergence is identically zero?
$$...
- 91
2
votes
0
answers
41
views
Fisher information with known moments
I have a sequence $X^n$ of length $n$, where each $X_i$ takes a value from a finite set with probability vector $\mathbf{p} = [p_1, \ldots, p_K]^T$, i.e., $X_i \in [K]$, where $p_{X_i}(k) = p_k, k = 1,...
- 355
0
votes
0
answers
12
views
Difference between Likelihood Estimation and CRLB Estimation for Cooperative Radar
I do not know if this question fits this stack but I do not know if there's other place where I can ask.
The question is about the difference between the cooperative/collaborative radar system when ...
1
vote
0
answers
44
views
About Calculate fisher information of normal distribution [closed]
Suppose $X_1, \ldots, X_n$ are iid $\mathrm{N}(0, \exp (2 \gamma))$; that is, the density of $X_i$ is
$$
(2 \pi)^{-1 / 2} e^{-\gamma} \exp \left(-x^2 e^{-2 \gamma} / 2\right) .
$$
I want to calculate ...
- 11
0
votes
0
answers
32
views
Derive Cramer-Rao lower bound for $Var(\hat{\theta})$ given that $\mathbb{E}[\hat{\theta}U]=1$
I am trying to derive the Cramer-Rao lower bound for $Var(\hat{\theta})$ given that we already know $\mathbb{E}[U]=0$, $Var(U)=I(\theta)$ and $\mathbb{E}[\hat{\theta}U]=1$. I am struggling with using ...
- 1