# Questions tagged [fisher-information]

For question about fisher information that appears in mathematical statistics.

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### Statistics with Fisher formalism : loss or gain of information with data cross-correlations

I am currently working on Fisher's formalism which is part of a more general theory, that of information. My problem applies to estimating cosmological parameters from input data with the Fisher ...
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### Fisher Information in Statistical Mechanics

I am studying the canonical ensemble and it seems to me there is an analogy between derivatives of the partition function, which can extract energy momenta for the system and Fisher score /information....
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### Fisher Information of log-normal distribution

I have the pdf of a log-normal distribution $$f(y;\theta)= \frac {1}{y\sqrt{2\pi\theta}}\exp \left(-{\frac {(\log y)^2}{ 2\theta}}\right)$$ for $y>0$ and $\theta>0$ and $f(y; \theta) = 0$ ...
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### Sign of a Fisher Information changes depending on the formula I use

I am trying to compute the Fisher Information for θ in the following scenario: ...
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### Fisher information matrix for normal distribution

The below is captured from my lecture note, for the third column of first and second row and for the third row of the first and second column, is it because the summation of $x_i - \alpha - Bz_i$ ...
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### MLE of simultaneous exponential distributions

Given the $X_i\sim \text{exp}({\theta})$ and $Y_i\sim \text{exp}(\frac{1}{\theta})$, where $X_i$ and $Y_i$ are indpendent, with the same $\theta>0$. I have to find the MLE and its distribution. I ...
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### Matrix Derivative of Fisher Discriminant Analysis

Let $Z_c \in \mathbb{R}^{D\times N_c}$ is column matrix which includes mapped data of class C, and $\alpha_c = \frac{1}{N_c}$ where $D:$ dimension, $N_c:$ data number of class C. $\mathbf{i}:$ One ...
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### How is the replicator dynamic a gradient flow of the Fisher information metric?

I am trying to understand how the replicator dynamic can be derived as a gradient flow of the Fisher information metric (aka Shahshahani metric). I have a question about understanding a particular ...
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### Fisher information of normal distribution with unknown mean and variance?

I am asked to find the fisher information contained in $X_1 \sim N(\theta_1, \theta_2)$ (ie: two unknown parameters, only one observation). How would I find the Fisher information here? I know that ...
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### Why can the best Fisher's linear discriminant vector be solved by $w_{lda}=S_W^{-1}(m_2-m_1)$?

Why can the best Fisher's linear discriminant vector be solved by $w_{lda}=S_W^{-1}(m_2-m_1)$? Background: https://www.cs.ccu.edu.tw/~wylin/publications/ieee_smc.pdf pages 11-12.
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### How to derive the optimal bayesian solution to a model of two normal distributed populations

In the "Introduction" section of the paper Support-Vector Networks, it mentioned Fisher's solution to a model of two normal distributed populations: My questions are: How to derive equation (1)? I ...
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### Exponential map on the Fisher manifold for exponential family distribution

So, I don't really understand too well Diff. Geometry and Manifolds currently. Hence, I've started studying it and it is very interesting. However, atm I just need to understand how to compute the ...
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### What/when does one need $E$ in expected Fisher information for?

What/when does one need $E$ in expected Fisher information for? Since I read an example which merely calculated the second derivatives, put a minus on them and then wrote them in matrix form. It ...
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### Fidning the Cramer Rao inequality using Fisher Information

$$I(\theta) = E\left[\left(\sum^{n}_{i=1} \frac{\partial}{ \partial\theta}\ln\{f(X_i;\theta\} \right)^2\right]$$ Is the definition of the Fisher criteria and in the text it says that because $X_i$'...
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### Fisher information of sufficient statistic

Why is it true that if $X \sim f_{\theta}(x)$ (let's assume for simplicty that theta is one dimensional) is some random variable and $T(X)$ a sufficient statistic then $I_{X}(\theta)$ (Fisher ...
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### Fisher convergence as sample goes to infinity.

I was wondering how does the Fisher law behave when $n => \inf.$. $F_{q, n-p} = \frac{SSE_0-SSE/q}{SSE/(n-p)}$ I expect the test statistics goes lower as n goes up but does the pdf of the law ...
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### Updating weight based on fisher scoring algorithm [wikipedia]

My understanding on weight update for fisher is based on wikipedia description. The fisher information is said as the expectation of hessian. Can someone explain how is the expection for each entry of ...