Feature normal approximation

[ckoerber]

This PR extends the previous normal approximations PR (#49) by adding a command-line interface. It aims to follow the logic of existing CLI interfaces.

New Feature

After reinstalling this module

pip install [--user] [-e] .

the command-line tool bayeschime will be present.

This script reads in inputs, runs a fit, and dumps results to an output folder.

Example usage:

> bayeschime -p data/Downtown_parameters.csv -d data/Downtown_ts.csv \
    -y data/data_errors.csv -o output/ -v

Notes about data uncertainties

The posterior estimations need to know about uncertainties in the data. These uncertainties are defined in data/data_errors.csv and used in the get_yy method in bayes_chime/normal/scripts/cli.py:

yy_sdev = yy_mean * rel_err + abs_err

If no y-error file is provided, the script runs an empirical Bayes check to infer the abs_err size for rel_err=0.

For now, I do not have a solid understanding of the size of these errors. In studies of the NYC data, binning dates in the range of 1-4 days and looking at fluctuations of new admissions suggested that relative errors in admissions are at the order of 10%. Setting the abs_err to ~10 is important to not emphasize early dates too much (as the routine focuses on points with smaller errors).

Further updates

• Normal data plotting functions plot_gvar and plot_band now have a y_min argument which cuts off the error band when values are smaller than y_min. Note that this is only visual and does not change computations.

[cjbayesian]

This LGTM. Is this ready to be merged ahead of #62 ?