Running ares with emcee

It’s relatively straightforward to call the Markov-Chain Monte Carlo code emcee (Foreman-Mackey et al. (2013)), and perform a fit to the turning points in the global 21-cm signal.

Note

Development of a generalized fitter is currently underway.

The fastest model to fit is one treating the Lyman-\(\alpha\), ionization, and thermal histories as a tanh function:

# These go to every likelihood evaluation
base_pars = \
{
 'tanh_model': True,
 'auto_generate_blobs': True,
}

Now, initialize a fitter:

# Initialize fitter
fit = ares.inference.ModelFit(**base_pars)

and the turning points to be fit:

# Positions of the turning points (nu_B, nu_C, nu_D, T_B, T_C, T_D)
fit.mu = np.array([45, 70, 105, -5, -100, 20])

# Set errors
fit.set_error(error1d=[0.5, 0.5, 0.5, 5., 5., 5.])

# Tells fitter that all frequencies are in MHz, all temperatures in mK.
fit.measurement_units = ('MHz', 'mK')

# Defines order of errors
fit.measurement_map = \
    [('B', 0), ('C', 0), ('D', 0),
     ('B', 1), ('C', 1), ('D', 1)]

Finally, we set the parameters to be varied in the fit and their priors, which in this case we’ll take to be uninformative over a relatively broad range:

# Set axes of parameter space
fit.set_axes(['tanh_xz0', 'tanh_xdz', 'tanh_Tz0', 'tanh_Tdz'],
    is_log=[False]*4)

# Set priors on model parameters (uninformative)
fit.priors = \
{
 'tanh_xz0': ['uniform', 5., 20.],
 'tanh_xdz': ['uniform', 0.1, 20],
 'tanh_Tz0': ['uniform', 5., 20.],
 'tanh_Tdz': ['uniform', 0.1, 20],
}

# Set the number of Goodman-Weare walkers
fit.nwalkers = 128

To finally run it,

fit.run(prefix='test_tanh', burn=10, steps=50, save_freq=10)

This will result in a series of files named test_tanh*.pkl.