Revised LGCP notebook

[ckrapu]

This PR updates the log Gaussian Cox process notebook to conform to best practices for documentation as documented in #57 . The following changes were made:

• The GP model formulation was changed from ExpQuad covariance kernel to Matern52 and the diagonal variance prior was changed from HalfCauchy over the standard deviation to InverseGamma over the variance. This solved an issue with the earlier formulation in which some parameter draws corresponded to nonviable covariance matrices.
• As a consequence of the above, the code for filtering posterior samples for NaNs is no longer needed and was therefore removed.
• The usage of np.random.randn was replaced with the rng.standard_normal generator for random numbers.

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OriolAbril commented on 2021-04-02T14:36:38Z
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I think we can delete setting the global seed here.

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OriolAbril commented on 2021-04-02T14:36:38Z
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I would use chains=4 instead to indicate we want 4 chains, it will then default to 4 cores unless the cpu has less in which it would use all cores available.

ckrapu commented on 2021-04-03T17:27:44Z
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Got it - changed the setting.

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OriolAbril commented on 2021-04-02T14:36:39Z
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Can we use

spp_trace = pm.sample_posterior_predictive(trace, var_names=["intensity_new"], keep_size=True)
trace.extend(az.from_dict(posterior_predictive=spp_trace, dims={"intensity_new": ["sample"]}))
intensity_samples = trace.posterior_predictive["intensity_new"]

Maybe even exponentiate here when defining intensity_samples?

Using this will allow to subset with intensity_samples.sel(sample=3) and to average with intensity_samples.mean(("chain", "draw")) 

ckrapu commented on 2021-04-03T17:28:19Z
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Thanks for the tip! I replaced the subsetting with the relevant Arviz methods.

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OriolAbril commented on 2021-04-02T14:36:39Z
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I would leave that you are the author of the notebook, and add to that that you updated it too

[OriolAbril]

Also note that you have to make sure to run the style checks: https://github.com/pymc-devs/pymc3/wiki/PyMC3-Jupyter-Notebook-Style-Guide

[ckrapu]

Got it - changed the setting.

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[ckrapu]

Thanks for the tip! I replaced the subsetting with the relevant Arviz methods.

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