[SciPy-Dev] merged scipy.stats.qmc with quasi-Monte Carlo functionality

[Pamphile Roy]

Hi everyone,

First of all, thank you for everyone who helped with adding QMC (scipy.stats.qmc) :).

I wanted to give an overview of the current work in progress and some perspectives.

Waiting for reviews:

* Using QMC in scipy.optimize: https://github.com/scipy/scipy/pull/13469 <https://github.com/scipy/scipy/pull/13469> (had a few reviews, could be shipped fast and blocking Stefan Endres to work on improvements of shgo).
* New QMC method (LHS optimized): https://github.com/scipy/scipy/pull/13471 <https://github.com/scipy/scipy/pull/13471> (code was originally in the QMC PR and received initial reviews thanks to Matt Haberland, but since then nothing more).
* General tutorial: https://github.com/scipy/scipy/pull/13487 <https://github.com/scipy/scipy/pull/13487> (finished but Art Owen might drop in and add things, this could also wait for another PR).
* Small Cython refactoring of an internal function of Sobol’: https://github.com/scipy/scipy/pull/13514 <https://github.com/scipy/scipy/pull/13514> (waiting for a maintainer to be merged).

Work in progress:

* Port to Cython (Pythran is being looked at too) of discrepancy functions (thanks Arthur Volant): https://github.com/scipy/scipy/pull/13576 <https://github.com/scipy/scipy/pull/13576> .

Other Cythonization which have not been looked at yet, see this issue https://github.com/scipy/scipy/issues/13474 <https://github.com/scipy/scipy/issues/13474> .

Perspectives:

* Other scrambling methods (for Halton and Sobol’, but could also have more generic things like randomization of any QMC).
* Use QMC with any distribution from scipy.stats. There is an issue with some initial discussions, would need more opinion for me to continue and propose a PR: https://github.com/scipy/scipy/issues/13368 <https://github.com/scipy/scipy/issues/13368>.
* Add other QMC methods: lattice rules, other low discrepancy sequences, adaptive LHS, etc.
* Add other uniformity criteria: L-inf, minimum spanning tree, discrepancy over sub-spaces, etc.
* General method to construct an optimal design based on a metric. (Similar to what I propose with LHS optimized).
* Your ideas.

Thanks in advance for your help.

Cheers,

Pamphile
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