Fisher Definition and 22 Threads

Hi, I have been studying the Fisher matrix to apply in a project. I understand how to compute a fisher matrix when you have a simple model for example which is linear in the model parameters (in that case the derivatives of the model with respect to the parameters are independent of the...

I have 2 Fisher matrixes which represent information for the same variables (I mean columns/rows are the same in the 2 matrixes). Now I would like to make the cross synthesis of these 2 matrixes by applying for each parameter the well known formula (coming from Maximum Likelihood Estimator...

I'm getting interested in quantum-enhanced metrology and have come across the quantum Fisher information (QFI) as a measure of how much a quantum state ##|\Psi(\theta)\rangle## changes with respect to some variable, for example, the phase accumulated during an interferometer, ##\theta##. This is...

In the context of a forecast, 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 formalism and recipes to build a Fisher matrix. The context is...

Hello, I am working on Fisher's formalism in order to get constraints on cosmological parameters. I am trying to do cross-correlation between 2 types of galaxy populations (LRG/ELG) into a total set of 3 types of population (BGS,LRG,ELG). From the following article...

I am currently studying Fisher's formalism as part of parameter estimation. From this documentation : They that Fisher matrix is the inverse matrix of the covariance matrix. Initially, one builds a matrix "full" that takes into account all the parameters. 1) Projection : We can then do...

Homework Statement [/B] For reference: Book: Mathematical Statistics with Applications, 7th Ed., by Wackerly, Mendenhall, and Scheaffer. Problem: 10.81 From two normal populations with respective variances ##\sigma_1^2## and ##\sigma_2^2##, we observe independent sample variances ##S_1^2## and...

Hey there, Just wondering where I can get a nice treatment of this with derivations. I could swear I read about this in Jon Cardy's Scaling and renormalization in statistical physics but I can't find it again so maybe I was wrong.

I'm trying to construct a Fisher Forecast for the upcoming S4 CMB survey. I don't understand what the C_l is in this formula. It is H(z) and the Angular Distance? Or is it some covariance matrix and if it is a covariance matrix how do I calculate it considering the experiment hasn't been done...

I'm trying to recreate the results of this paper https://arxiv.org/pdf/1607.08016.pdf to obtain the constraints for the matter density and Hubble constant h. However every time I try to create there results my Fisher Matrix has elements of order of 10^14 which is far to high. I suspect this is...

I'm doing a Fisher Forecast to satisfy my experimental physics requirement. I never done anything like this before so I'm kind of in the dark of how to proceed. I have done some readings on Fisher Forecasting and would like to outline how I would do it and then ask if you can tell me if I'm...

Carrie Fisher, Child of Hollywood and ‘Star Wars’ Royalty, Dies at 60 http://www.nytimes.com/2016/12/27/movies/carrie-fisher-dead-star-wars-princess-leia.html?_r=0

More at http://www.rollingstone.com/movies/news/carrie-fisher-princess-leia-in-star-wars-dead-at-60-w457713 You will be missed, Carrie Fisher.

Homework Statement Let X1, X2,...Xn be a random sample from pdf, f(x|θ) = θx-2 where 0 < θ ≤ x < ∞ Find the MLE of θMy attempt: Likelihood fxn: L(θ|x) = ∏θx-2 = θn∏ θx-2 And to find MLE, I take Log of that function and partial derivative (w.r.t θ, of log L(θ|x) and set that = 0, and get...

Hello, I'm trying to calculate Fisher information (and eventually the Cramer-Rao lower bound) for this particular pdf with Mathematica: \text{pte}[t,\Theta ] = \frac{P_{\text{ec}}}{\tau _d-\tau _r}\left[e^{\frac{-(t-\Theta )}{\tau _d}}-e^{\frac{-(t-\Theta )}{\tau _r}}\right]...

I don't understand the following step regarding the (i,j)^{th} element of the Fisher Information Matrix, \textbf{J}: J_{ij}\triangleq\mathcal{E}\left\{ \frac{\partial}{\partial\theta_{i}}L_{\textbf{x}}(\textbf{θ})\frac{\partial}{\partial\theta_{j}} L_{\mathbf{x}}(\textbf{θ})\right\} \\...

Hi everyone. Homework Statement We are given N spins 1/2. A rotation is defined as \rho_\theta=e^{-i\theta J_n}\rho_\theta e^{i\theta J_n} on an Hilbert Space H, with J_n=n_xJ_x+n_yJ_y+n_zJ_z\:,\quad n_x^2+n_y^2+n_z^2=1, and \theta isn't related to any observable. Given a quantum state...

How to understand "fisher information"? Hello, I am trying to understand what "fisher information is." It is defined as V [∂/∂∅(lnf(X,∅)) ]=E[ (∂/∂∅[lnf(X,∅)])^2 ]. From Wikipedia: Can you please help me understand why this is the case? How can this be explained by looking at the...

Fisher matrix=(minus the) average of the second derivative of the log-likelihood with respect to the parameters It seems to me the Fisher matrix for Gaussian data is invariant with respect to any (non-singular) linear transformation of the data; if correct this is a very useful property...

The fisher information matrix for multivariate normal distribution is said at many places to be simplified as: \mathcal{I}_{m,n} = \frac{\partial \mu^\mathrm{T}}{\partial \theta_m} \Sigma^{-1} \frac{\partial \mu}{\partial \theta_n}.\ even on...

Maybe it is a good idea to have mathematical tutorials like in the subforum about Physics. I have no homework anymore :smile: but tend to think that doing mathematics is a skill that always pays back at the end. First thing I want to know what https://en.wikipedia.org/wiki/Fisher_information...

Have some of you read this book by Roy Friedel? What are your comment? I am also interrested in other sources about "information" and "Fisher information" as it could be used in physics. Thanks Michel