Algorithms aiming at finding the distribution of the parameters instead of the parameters themselves?

1

Dear all,

Are there algorithms aiming at finding the distribution of the parameters instead of the parameters themselves?

I mean like, just an absolutely and crazily simplied version as below,

y = ax

I have data of (x,y).

The parameter a actually distributed according to some distribution.

Therefore, instead of finding the parameter a itself, I want to find the underline distribution of a.

I wonder are there such algorithms?

I know gaussian mixing model can do things like that, but most of the gaussian mixing model seems is based on clustering the data (x,y), not the parameter a.

Sorry it is not a direct Fortran problem, but I am sure such algorithms can be written in Fortran :slight_smile:

Thanks much in advance!

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Statistical models are often fit by maximum likelihood. The covariance matrix of the parameter estimates is determined by the Hessian matrix of the likelihood wrt the parameters, as explained for example in section 5 of this tutorial.

Since Fortran is fast, it is often feasible to bootstrap the distributions of parameters, as discussed in the Wikipedia article. You just sample with replacement to create many synthetic data sets and use the estimated parameters from each data set to get a multivariate parameter distribution.

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