Add a Maximum Likelihood solver

[raoulcollenteur]

@mbakker7, is it an idea to move the LmFitSolverNew to a separate branch or remove it?

[mbakker7]

This is a first step to add a Maximum Likelihood Function as objective function.
It would be very useful to have that. Maybe we should change the name to MaxLikelihoodSolver.

[raoulcollenteur]

That would indeed be very useful! I also have some scripts already we could merge into that. Going to remove this from the main branch and add it in a separate branch to keep things clean. Changed the title of this Issue.

[raoulcollenteur]

Move LmfitSolveNew to a separate branch: https://github.com/pastas/pastas/tree/364-add-maximum-likelihood-solver

[dbrakenhoff]

Not sure if this could be of any help, but metran uses a Kalman filter and maximum likelihood to optimize the model. It is a slightly different model for decomposing timeseries into specific and common components but could be useful as a reference...?

[raoulcollenteur]

@mbakker7, not sure if this is covered by #559 ? Actually #559 adds MCMC, which is different from a maximum likelihood solver where the negative log likelihood is minimised.

If #559 covers what you want and we don't want a maximum likelihood solver where the negative log likelihood is minimised, perhaps we can close this issue?

[mbakker7]

I propose to have a maxium likelihood solver separate from the MCMC. I guess this doesn't require much work as all that is needed is an objective function that is the negative maximium likelihood function. So rather than a solver it is an objective function. Maybe change the title of the issue?

[raoulcollenteur]

Ok. Then we keep this issues alive. MLE might be easy to add with objective functions from #559, let's look at that after the finishing that one.