Non-identification, local maxima and optimization

Modeling
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1

I have described my model in :

I find that it has some identification problem and I may get the local maxima when I set a very tiny prior for all parameters.
I have two questions:

  1. how can I search the parameters which cause the identification problems. And how can I solve this identification problem
  2. If using kalman filter. I find that researchers usually the procedure of repeatedly generating a random vector of starting values, and maximize the log-likelihood function, by using Nelder-Mead maximization algorithm and choosing 100 largest resulting values. So can stan have some functions to avoid the local maxima?

Some suggestions?
Very thank~

1 Like
2

I have an idea that if I could do this: According to the log posterior by shinystan, look through the parameters diagnose. I restrict the parameters in the area which have a higher log posterior. If I do so, can I jump from the local maxima to the global maxima?

mu1
mu11564×382 104 KB

If I can set the parameters:

parameters{
...
mu1<lower=-10,upper=-5>;
...
}
3

using optimizing mode can’t get the same result for parameters. some parameters have very different values when I use “Newton, BFGS, LBFGS”

4

Unfortunately, there are no general methods - every problematic model is problematic in its own ways and in the end you just need to gain a good understanding of your model and its implications. Some of the suggestions at Divergent transitions - a primer apply to this situation as well. In particular, I would try to find the smallest model that is still problematic and the most complex model that doesn’t have the problems (on data simulated to match the model). Then think hard about what changed between those two models could provide some hints.

Unfortunately, for some of the ODE models people want to fit we couldn’t find a parametrization that would work :-/