Computing fisher Matrix numerically

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 Joined: March 09 2020
 Affiliation: The University of Ferrara
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Computing fisher Matrix numerically
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 parameter). But I am unable to understand how to compute the Fisher matrix when the model is more complicated like the power spectrum which depends on the cosmological parameters in a complicated way. From the exercises that I have done, I understand the Fisher matrix computed around certain model parameters is valid around that set of model parameters but how do you go from varying parameters (and computing the Fisher matrix around each set of parameters) to deducing the covariances between the parameters in parameter space and making the triangle plot.
I have been unable to find the answer to this question all day. Thanks in advance for your help.
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 parameter). But I am unable to understand how to compute the Fisher matrix when the model is more complicated like the power spectrum which depends on the cosmological parameters in a complicated way. From the exercises that I have done, I understand the Fisher matrix computed around certain model parameters is valid around that set of model parameters but how do you go from varying parameters (and computing the Fisher matrix around each set of parameters) to deducing the covariances between the parameters in parameter space and making the triangle plot.
I have been unable to find the answer to this question all day. Thanks in advance for your help.

 Posts: 53
 Joined: August 02 2006
 Affiliation: UC Berkeley
Re: Computing fisher Matrix numerically
You might find useful the notes at https://supernova.lbl.gov/~evlinder/scires.html, specifically https://supernova.lbl.gov/~evlinder/InfoMatrixNotes.pdf.

 Posts: 10
 Joined: March 09 2020
 Affiliation: The University of Ferrara
 Contact:
Re: Computing fisher Matrix numerically
Hi Eric,
Thank you so much for the links. I got my answer!! Thanks a bunch again!
Thank you so much for the links. I got my answer!! Thanks a bunch again!

 Posts: 10
 Joined: March 09 2020
 Affiliation: The University of Ferrara
 Contact:
Re: Computing fisher Matrix numerically
For anyone else looking for the same information and stumbles on to this thread, I also leave this link to the MontePython paper which is a pretty nice description of using the Fisher matrix approximation.
https://arxiv.org/pdf/1804.07261.pdf
https://arxiv.org/pdf/1804.07261.pdf