The HAWC Accelerated Likelihood (HAL) framework

Installation

hawc_hal depends on astromodels, threeML as well as some additional packages (numba, uproot).

If you don't have mamba,install mamba according to the instruction into the base environment.

To install hawc_hal in a conda environment, we recommend to use the following procedure:

mamba create --name new_hal -c conda-forge -c threeml numpy scipy matplotlib ipython numba reproject "astromodels>=2" "threeml>=2" root
conda activate new_hal
pip install git+https://github.com/threeml/hawc_hal.git

For the time being, we recommend updating to the master version of astromodels and threeML from github:

pip install --upgrade git+https://github.com/threeml/astromodels.git
pip install --upgrade git+https://github.com/threeml/threeML.git

The above will install a new python 3 environment. There seem to be version conflicts that currently prevent installing hawc_hal with the newer (>=2.0) versions of threeML and astromodels.

You can also add hawc_hal to an existing environment. If you have conda installed, it is highly reccomended that you install numba through conda like this (simply skip this step if you are not running in a conda environment):

> conda install -c conda-forge numba

You also need root (whether installed through conda or not) and threeML/astromodels and their dependencies.

HAL now has no dependencies relying on ROOT or root-numpy. Instead, it uses uproot. The following are installed along with HAL: uproot, awkward, hist, mplhep

Check installation

Use the following commands to check if your installation was successful. You should be inside your conda environment for this.

• To test threeML: pytest --pyargs threeML
• To test astromodels: pytest --pyargs astromodels
• To test HAL: pytest --pyargs hawc_hal

If you are interested in more detailed output from the tests, learn more about pytest command line options here.

Examples

You can find a worked example relying only on publicly accessible data on the threeML documentation (or download the notebook).

Mrk 421 analysis example

(This example assumes you have access to an all-sky HAWC dataset)

from hawc_hal import HAL, HealpixConeROI
import matplotlib.pyplot as plt
from threeML import *

# Define the ROI
ra_mkn421, dec_mkn421 = 166.113808, 38.208833
data_radius = 3.0
model_radius = 8.0

roi = HealpixConeROI(data_radius=data_radius,
                     model_radius=model_radius,
                     ra=ra_mkn421,
                     dec=dec_mkn421)

# Instance the plugin

maptree = ... # This can be either a ROOT or a hdf5 file
response = ... # This can be either a ROOT or hdf5 file

hawc = HAL("HAWC",
           maptree,
           response,
           roi)

# Use from bin 1 to bin 9
hawc.set_active_measurements(1, 9)

# Display information about the data loaded and the ROI
hawc.display()

# Look at the data
fig = hawc.display_stacked_image(smoothing_kernel_sigma=0.17)
# Save to file
fig.savefig("hal_mkn421_stacked_image.png")

# If you want, you can save the data *within this ROI* and the response
# in hd5 files that can be used again with HAL
# (this is useful if you want to publish only the ROI you
# used for a given paper)
hawc.write("my_response.hd5", "my_maptree.hd5")

# Define model as usual
spectrum = Log_parabola()
source = PointSource("mkn421", ra=ra_mkn421, dec=dec_mkn421, spectral_shape=spectrum)

spectrum.piv = 1 * u.TeV
spectrum.piv.fix = True

spectrum.K = 1e-14 / (u.TeV * u.cm ** 2 * u.s)  # norm (in 1/(keV cm2 s))
spectrum.K.bounds = (1e-25, 1e-19)  # without units energies are in keV

spectrum.beta = 0  # log parabolic beta
spectrum.beta.bounds = (-4., 2.)

spectrum.alpha = -2.5  # log parabolic alpha (index)
spectrum.alpha.bounds = (-4., 2.)

model = Model(source)

data = DataList(hawc)

jl = JointLikelihood(model, data, verbose=False)
jl.set_minimizer("ROOT")
param_df, like_df = jl.fit()

# See the model in counts space and the residuals
fig = hawc.display_spectrum()
# Save it to file
fig.savefig("hal_mkn421_residuals.png")

# See the spectrum fit
fig = plot_point_source_spectra(jl.results,
                                ene_min=0.1,
                                ene_max=100,
                                num_ene=50,
                                energy_unit='TeV',
                                flux_unit='TeV/(s cm2)')
fig.savefig("hal_mkn421_fit_spectrum.png")

# Look at the different energy planes (the columns are model, data, residuals)
fig = hawc.display_fit(smoothing_kernel_sigma=0.3)
fig.savefig("hal_mkn421_fit_planes.png")

# Compute TS
jl.compute_TS("mkn421", like_df)

# Compute goodness of fit with Monte Carlo
gf = GoodnessOfFit(jl)
gof, param, likes = gf.by_mc(100)
# print("Prob. of obtaining -log(like) >= observed by chance if null hypothesis is true: %.2f" % gof['HAWC'])
print(f"Prob. of obtaining -log(like) >= observed by chance if null hypothesis is true: {gof['HAWC']:.2f}")

# it is a good idea to inspect the results of the simulations with some plots
# Histogram of likelihood values
fig, sub = plt.subplots()
likes.hist(ax=sub)
# Overplot a vertical dashed line on the observed value
plt.axvline(jl.results.get_statistic_frame().loc['HAWC', '-log(likelihood)'],
            color='black',
            linestyle='--')
fig.savefig("hal_sim_all_likes.png")

# Plot the value of beta for all simulations (for example)
fig, sub = plt.subplots()
param.loc[(slice(None), ['mkn421.spectrum.main.Log_parabola.beta']), 'value'].plot()
fig.savefig("hal_sim_all_beta.png")

# Free the position of the source
source.position.ra.free = True
source.position.dec.free = True

# Set boundaries (no need to go further than this)
source.position.ra.bounds = (ra_mkn421 - 0.5, ra_mkn421 + 0.5)
source.position.dec.bounds = (dec_mkn421 - 0.5, dec_mkn421 + 0.5)

# Fit with position free
param_df, like_df = jl.fit()

# Make localization contour
a, b, cc, fig = jl.get_contours(model.mkn421.position.dec, 38.15, 38.22, 10,
                                model.mkn421.position.ra, 166.08, 166.18, 10, )

plt.plot([ra_mkn421], [dec_mkn421], 'x')
fig.savefig("hal_mkn421_localization.png")

# Of course we can also do a Bayesian analysis the usual way
# NOTE: here the position is still free, so we are going to obtain marginals about that
# as well
# For this quick example, let's use a uniform prior for all parameters
for parameter in model.parameters.values():

    if parameter.fix:
        continue

    if parameter.is_normalization:

        parameter.set_uninformative_prior(Log_uniform_prior)

    else:

        parameter.set_uninformative_prior(Uniform_prior)

# Let's execute our bayes analysis
bs = BayesianAnalysis(model, data)
samples = bs.sample(30, 100, 100)
fig = bs.results.corner_plot()

fig.savefig("hal_corner_plot.png")

Convert ROOT maptree to hdf5 maptree

from hawc_hal.maptree import map_tree_factory
from hawc_hal import HealpixConeROI

root_map_tree = "maptree_1024.root" # path to your ROOT maptree

# Export the entire map tree (full sky)
m = map_tree_factory(root_map_tree, None)
m.write("full_sky_maptree.hd5")

# Export only the ROI. This is a file only a few Mb in size
# that can be provided as dataset to journals, for example
ra_mkn421, dec_mkn421 = 166.113808, 38.208833
data_radius = 3.0
model_radius = 8.0

roi = HealpixConeROI(data_radius=data_radius,
                     model_radius=model_radius,
                     ra=ra_mkn421,
                     dec=dec_mkn421)

m = map_tree_factory(root_map_tree, roi)
m.write("roi_maptree.hd5")

Radial profile examples will come soon