Simulated Method of Moments / Indirect inference: how might ModelingToolkit be extended to provide convenient user inteface?

[ChrisRackauckas]

@mcreel

Approximation methods such as quadrature, etc., are also often unavailable due to curse of dimensionality considerations

Standard quadrature methods, yes, but there are symbolic-numeric techniques for deriving problem-specific sparse quadratures.

https://dl.acm.org/doi/10.1145/1073884.1073898

The whole point is to derive isometries and build problem-specific quadratures based on the symmetries. If your argument is that standard methods don’t work, that okay I agree but that’s why no one suggested doing that.

@mcreel

What I don’t see is how a symbolic system to describe the model can help to discover informative statistics, when the data is generated from the model in a way such that the density or moments of the data are not available.

If you have numerical methods solving equations, symbolic systems can help improve it. Automatic parallelization of code, sparsity handling, tearing, etc. I’m not sure what the hold up is? Is parallelism not good? I’m confused by your argument.

@mcreel

It may be that simple, not very informative moments can fit into a symbolic system, but more complicated, tailor made moments seem unlikely, to me, to be workable with such a system. So, my question is how a symbolic system could help.

Quite the opposite. The whole purpose is to help the derivation of tailor made moments and expansions in special ways no one would ever want to write out by hand. In the same way, would you ever want to tear nonlinear systems by hand?

I don’t think you’re quite understanding the symbolic-numeric approach and instead are thinking about some pure symbolic world. This isn’t SymPy. It’s more akin to generalized automatic differentiation to problems other than differentiation.