1. ### Python Invert a matrix from a 4D array : equivalence or difference with indexes

I have a 4D array of dimension ##100\text{x}100\text{x}3\text{x}3##. I am working with `Python Numpy. This 4D array is used since I want to manipulate 2D array of dimensions ##100\text{x}100## for the following equation (it allows to compute the ##(i,j)## element ##F_{ij}## of Fisher matrix) ...
2. ### A Covariance matrix size: 3x3 or 4x4?

Hello, I follow the post https://www.physicsforums.com/threads/cross-correlations-what-size-to-select-for-the-matrix.967222/#post-6141227 . It talks about the constraints on cosmological parameters and forecast on futur Dark energy surveys with Fisher's matrix formalism. Below a capture of...
3. ### I Cross-correlations: what size to select for the matrix?

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...
4. ### I Fisher matrix - equivalence or not between sequences

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...
5. ### I Conf.intervals for fitted parameters: divide by sqrt(n)?

If you fit a parametrized model (i.e. y = a log(x + b) + c) to some data points the output is typically the optimized parameters (i.e. a, b, c) and the covariance matrix. The squares of the diagonal elements of this matrix are the standard errors of the optimized parameters. (i.e. sea, seb...
6. ### I Covariance Matrices and Standard form

Hi. I have a question about covariance matrices (CMs) and a standard form. In Ref. [Inseparability Criterion for Continuous Variable Systems], it is mentioned that CMs ##M## for two-mode Gaussian states can be symplectic transformed to the standard form ##M_s##: ## M= \left[ \begin{array}{cc}...
7. ### I Uncertainty of coefficients after a least square fit

Fitting data to a linear function (y=a0+a1*x) with least square gives the coefficients a0 and a1. I am having trouble with calculating the uncertainty of a0. I understand that the diagonal elements of the covariance matrix C is the square of the uncertainty of each coefficient if there are no...
8. ### I Covariance in fitting function

Hello! I have to calculate the covariance between 2 parameters from a fit function. I found this package in Python called iminuit that did a good fit and also calculate the covariance matrix of the parameters. I tested the package on a simple function and I am not sure I understand the result...
9. ### Valid Covariance Matrices

I'm trying to understand what makes a valid covariance matrix valid. Wikipedia tells me all covariance matrices are positive semidefinite (and, in fact, they're positive definite unless one signal is an exact linear combination of others). I don't have a very good idea of what this means in...