add start of hawkes MLE

[ljwolf]

This adds the start of a spatiotemporal Hawkes process estimator. I'm trying to finish the single-dimension case first.

A Hawkes process is a kind of spatially-and-temporally dependent point process. Points that arrive at time t at location s make other arrivals near s and shortly after t more likely. Thus, Hawkes processes are sometimes called self-exciting.

Some existing implementations exist, and I'm hopeful to make both an MLE estimator and a simulator.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 74.8%. Comparing base (374de06) to head (28ab8db).
⚠️ Report is 92 commits behind head on main.

Additional details and impacted files

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+ Coverage   74.8%   74.8%   +0.1%     
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  Files         12      12             
  Lines       1938    1942      +4     
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+ Hits        1449    1453      +4     
  Misses       489     489             

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[ljwolf]

One open question is on estimation strategy.

While we can use pure python and MLE to recover the parameters, this will likely be quite slow/inefficient. So three strategies get us out of this:

1. We could try to numba/cythonize the pairwise dependence loop,
2. We could do something nonparametric with Graph/W to sparsify the pairwise dependence loop

Alternatively, I think this would be case where moving to a Bayesian estimator might kill two birds with one stone.... I also don't know yet how to do inference on the parameters in MLE using a permutation approach yet. Any permutation-based inference will be seriously expensive, since we have to deal with randomizing over space, time, and mark.

But, if we implement this log likelihood in stan/pymc, we could get estimation (only) using their MAP estimators, or also support inference using sampling.