def main():
print "Initializing SP"
n_walkers = 4
n_dim = 1 # SSP age
n_steps = 1000
n_burn = 50 # burn-in of 50 steps
pset_true = mock_parameters()
bands = ['SDSS_u', 'SDSS_g', 'SDSS_r', 'SDSS_i']
p0 = init_chain(n_walkers)
d = 785 * 1000. # distance in parsecs
sp = fsps.StellarPopulation(**pset_true)
mock_mags = sp.get_mags(bands=bands, tage=pset_true['tage'])
mock_mjy = ab_to_mjy(mock_mags, d)
sigma_mags = np.ones(len(bands)) * 0.1
mock_sigma = (mock_mjy * sigma_mags) / 1.0875
print "Mock data"
for b, mjy, sigma in zip(bands, mock_mjy, mock_sigma):
print "%s %.2e %.2e" % (b, mjy, sigma)
print "Running emcee"
sampler = emcee.EnsembleSampler(n_walkers, n_dim, ln_prob,
args=(mock_mjy, mock_sigma, sp, d, bands))
sampler.run_mcmc(p0, n_steps)
print "chain shape", sampler.flatchain.shape
print "Mean acceptance fraction: {0:.3f}".format(
np.mean(sampler.acceptance_fraction))
fig = Figure(figsize=(3.5, 3.5))
canvas = FigureCanvas(fig)
gs = gridspec.GridSpec(2, 1, left=0.15, right=0.93, bottom=0.12, top=0.95,
wspace=None, hspace=0.4, width_ratios=None, height_ratios=None)
ax_age = fig.add_subplot(gs[0])
ax_chain = fig.add_subplot(gs[1])
steps = np.arange(n_steps)
for i in xrange(n_walkers):
chain = sampler.chain[i, :, 0]
ax_chain.plot(steps, chain, '-', alpha=0.5)
ax_chain.set_xlabel("steps")
ax_chain.set_ylabel(r"$t$ (Gyr)")
burnt_chain = sampler.chain[:, n_burn:, :].reshape((-1, n_dim))
print "burnt_chain shape", burnt_chain.shape
mean_age = burnt_chain.mean()
std_age = burnt_chain.std()
ax_age.hist(burnt_chain, bins=100, range=(0., 5),
histtype='stepfilled', edgecolor='None', facecolor='0.5')
ax_age.text(0.9, 0.9, "Mock Age %.2f Gyr" % pset_true['tage'],
size=8,
transform=ax_age.transAxes, ha='right', va='top')
ax_age.text(0.9, 0.78, "Est. $%.2f \pm %.2f$ Gyr" % (
mean_age, std_age),
size=8,
transform=ax_age.transAxes, ha='right', va='top')
ax_age.axvline(x=pset_true['tage'], linewidth=1, color='r')
ax_age.axvline(x=mean_age, linewidth=1, color='k', ls='--')
ax_age.set_xlabel(r"$t$ (Gyr)")
gs.tight_layout(fig, pad=1.08, h_pad=None, w_pad=None, rect=None)
canvas.print_figure("proto_mcmc_chain.pdf", format="pdf")
def ln_like(theta, obs_mjy, obs_sigma, sp, d, bands):
"""ln-likelihood function"""
model_mags = sp.get_mags(tage=theta, bands=bands)
model_mjy = ab_to_mjy(model_mags, d)
L = -0.5 * np.sum(np.power((model_mjy - obs_mjy) / obs_sigma, 2.))
return L