Dear Stan devolopers and community,

for a validation and inference of the parameters of a Markov model I need to solve an eigenvalue problem of the ratematrix.

Browsing the old google Group.

https://groups.google.com/forum/#!msg/stan-users/QJe1TNioiyg/7VI2hBhRk8oJ.

I found some discussion which did not really solve the issue. Of course there are classes of matrixes which have only real valued Eigenvalues such as rate matrixes of time reversible markov processes. They are similar to symmetric matrix thus they share the same eigenvalues. Therefore they are all real numbers and they are all smaller then 1 etc…

On page 69 of that link the talk about that. Finding that similar Matrix then requires to transform the ratematrix to its jordan normal form and I guess thats not yet written in the set algrebra functions in Stan.

It would be cool if Stan gets a function for that type of ratematrix. I guess many users would benefit since infering Markov models is a popular task :).

What do you think?

Thanks a lot in advance

Jan