add the saving of posteriors

[avivajpeyi]

Closes #25

[avivajpeyi]

For easier viewing, main changes in template.ipynb:

#%%

def validate_posterior_filename(filename):
    suffix = Path(filename).suffix
    if suffix != ".h5":
        raise ValueError(f"{suffix} is an invalid extension.")

def save_posteriors(trace, filename):   
    """Save posteriors as a HDF5 file"""
    validate_posterior_filename(filename)
    posteriors = pm.trace_to_dataframe(trace)
    posteriors.to_hdf(filename, mode='w', key='posterior')


def load_posteriors(filename):
    """Load posteriors from HDF5 file and return posteriors as a pd.DataFrame"""
    validate_posterior_filename(filename)
    return pd.read_hdf(filename, key="posterior")

#%%

posterior_filename = os.path.basename(FILENAME.replace(".ipynb", ".h5"))
save_posteriors(trace, posterior_filename)

Note that we could compress the H5 file to save space.

[avivajpeyi]

Changed the above pm.trace_to_dataframe to az.to_netcdf, so we are now storing the trace as an arviz.data.inference_data.InferenceData.

arviz is cool! hadn't come across it until now :)