The value of the posterior distribution of the epileptic parameters η is always higher than the mean value of the set prior distribution

[lala z]

Hello, 

         I have encountered a very strange problem, that is, from all my results, all the finally predicted epileptic parameters η should be higher than the prior mean value I set, for example, when I set η=η_ mu+0.1*eigen_  vec*  η_  star,  η_  Star~N (0,1), if η_ mu=- 3, then finally predicted η  of the posterior distribution  should be higher than - 3, which will lead to too strong a priori belief.

         Then, I tried to print the posterior sampling value of  η_  star  . I found that the sampled values were all greater than 0, which caused the phenomenon I mentioned above. I don't know whether this is normal.

If you can help me answer this question, I will be very grateful, because this question has troubled me for a long time.

Thanks!

lala

[WOODMAN Michael]

hi

this parametrization is detailed in Jha et al 2022 here

https://iopscience.iop.org/article/10.1088/2632-2153/ac9037/meta

Please have a read to see if it helps.

cheers,

Marmaduke

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From: 'lala z' via TVB Users <tvb-...@googlegroups.com>
Sent: Friday, December 2, 2022 3:23:31 AM
To: TVB Users
Subject: [RESEAUX SOCIAUX] [TVB] The value of the posterior distribution of the epileptic parameters η is always higher than the mean value of the set prior distribution

 

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[lala z]

Hello, 

       I have read the article you said, if  adding eigen_vec, then the value of the predicted parameter η is higher than the mean value η_mu of the prior distribution, because  eigen_vec is an  matrix, And the values ​​of the matrix should be greater than 0, and even if η_ star has sampled negative values,  final eigen_vec* η_ star has a high probability of being a positive value.    So according to   η=η_ mu+0.1*eigen_  vec*  η_  star, the posterior distribution of the last predicted η must be greater than η_mu. I don't know if I understand correctly.

       However, when I set the priori of η as: η=η_mu+η_star, η_star~N(0,1), the same situation will also occur, that is, the posterior sampling value of η_star is still greater than 0, and η must also greater than η_mu.

       I don't know if this phenomenon is normal, if so, then the posterior distribution of η is very dependent on η_mu.

Looking forward to your reply.

thanks.

lala

[WOODMAN Michael]

hi

Yes, what you wrote is correct, but this is by design.  The HMC sampler works best with uncorrelated parameters, and the use of eigen_vec derived from the gain matrix allows the n_star parameters to be uncorrelated, and using n_mu takes into account that the final n values have a non-zero mean.

In other words, if the posterior for n_star is properly sampled, and n is a deterministic transformation of n_star, then we don't need to worry about the distribution of n.

Perhaps I have addressed your question, please try to read the model code and how these parameters interact with the neural mass model, to see if that completes your understanding.

cheers,

Marmaduke

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From: 'lala z' via TVB Users <tvb-...@googlegroups.com>

Sent: Tuesday, December 6, 2022 9:28:38 AM
To: TVB Users
Subject: [RESEAUX SOCIAUX] Re: [RESEAUX SOCIAUX] [TVB] The value of the posterior distribution of the epileptic parameters η is always higher than the mean value of the set prior distribution

 

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[lala z]

Hello, 

        I seem to understand what you said, but if I want to set a weak information prior in combination with the clinical hypothesis, for example, the mean of the prior distribution of the epileptogenicity parameter η of the brain node with the clinical hypothesis as Ez is set to -2.35, while the prior mean of other nodes is set to -3, since the posterior distribution of the  predicted η is always greater than η_mu, so this will lead to a strong prior belief, so if combined with clinical assumptions, it seems that there is no significance. Because if I assume a Hz as Ez, and set its prior mean value to -2.35 or greater, then this node may be predicted as Ez or Pz in the end, and will not be predicted as Hz. In this case,the prior belief is strong.

The variational inference algorithm I use

Looking for your reply,

thanks!

lala