log gaussian cox process

File: https://nbviewer.jupyter.org/github/pymc-devs/pymc-examples/blob/main/examples/case_studies/log-gaussian-cox-process.ipynb
Reviewers: @ckrapu

Context

Known changes needed

Changes listed in this section should all be done at some point in order to get this
notebook to a "Best Practices" state. However, these are probably not enough!
Make sure to thoroughly review the notebook and search for other updates.

General updates

• use numpy Generator. See also https://numpy.org/doc/stable/reference/random/index.html?highlight=random%20sampling%20numpy%20random#quick-start

Changes for discussion

Changes listed in this section are up for discussion, these are ideas on how to improve
the notebook but may not have a clear implementation, or fix some know issue only partially.

ArviZ related

• Use xarray and from_pymc3_predictions to filter nans and slice/reduce intensity_samples

Notes

Exotic dependencies

None

Computing requirements

Model takes roughly 5 mins to sample.

The target is examples/case_studies/log-gaussian-cox-process.ipynb; start by reading and running the notebook, then review its random-number usage against NumPy Generator guidance. Update the notebook toward a Best Practices state, investigate the xarray/from_pymc3_predictions discussion item, and confirm the roughly five-minute sampling workflow still works.