def plot_eta_earth_histogram(eta_earths, outdir=None):
pu.plot_histogram_posterior(eta_earths.flatten(), normed=True, histtype='step', color='k')
pp.xlabel(r'$\eta_\oplus$')
pp.ylabel(r'$p\left(\eta_\oplus\right)$')
pp.axvline(np.percentile(eta_earths, 5), color='k')
pp.axvline(np.percentile(eta_earths, 95), color='k')
if outdir is not None:
pp.savefig(op.join(outdir, 'eta-earth.pdf'))
def plot_1d(chain, inj, name, lname, outdir, show):
pp.clf()
pu.plot_histogram_posterior(chain[name].view(float).flatten(), normed=True, histtype='step')
if inj is not None:
pp.axvline(inj[name])
pp.xlabel('$' + lname + '$')
pp.ylabel(r'$p\left( ' + lname + r' \right)$')
pp.savefig(op.join(outdir, '{0:s}.pdf'.format(name)))
if show:
pp.show()
def plot_nplanets_histogram(chain, outdir=None):
tau = ac.autocorrelation_length_estimate(np.mean(chain[:,:,0], axis=0))
if tau is None:
nps = chain[:,:,0].flatten()
else:
nps = chain[:,::tau,0].flatten()
pu.plot_histogram_posterior(nps, normed=True, color='k', histtype='step')
pp.xlabel(r'$\Lambda_\mathrm{pl}$')
pp.ylabel(r'$p(\Lambda_\mathrm{pl})$')
pp.axvline(np.percentile(nps, 5), color='k')
pp.axvline(np.percentile(nps, 95), color='k')
if outdir is not None:
pp.savefig(op.join(outdir, 'npl.pdf'))
def plot_correlation_coefficient(logpost, chain, outdir=None):
fchain = chain.reshape((-1, chain.shape[2]))
rs = []
for p in fchain:
cm = logpost.covariance_matrix(p)
rs.append(cm[0,1] / np.sqrt(cm[0,0]*cm[1,1]))
rs = np.array(rs)
pu.plot_histogram_posterior(rs, normed=True, histtype='step', color='k')
pp.xlabel(r'$r$')
pp.ylabel(r'$p(r)$')
pp.axvline(np.percentile(rs, 5), color='k')
pp.axvline(np.percentile(rs, 95), color='k')
if outdir is not None:
pp.savefig(op.join(outdir, 'corr.pdf'))
def plot_parameters(logpost, chain, eta_earths, outdir=None):
pp.subplot(2,1,1)
pu.plot_histogram_posterior(eta_earths.flatten(), normed=True, histtype='step', color='k')
pp.xlabel(r'$\eta_\oplus$')
pp.ylabel(r'$p\left(\eta_\oplus\right)$')
pp.axvline(np.percentile(eta_earths, 5), color='k')
pp.axvline(np.percentile(eta_earths, 95), color='k')
pp.subplot(2,1,2)
nps = chain[:,:,0].flatten()
pu.plot_histogram_posterior(nps, normed=True, color='k', histtype='step')
pp.xlabel(r'$\Lambda_\mathrm{pl}$')
pp.ylabel(r'$p(\Lambda_\mathrm{pl})$')
pp.axvline(np.percentile(nps, 5), color='k')
pp.axvline(np.percentile(nps, 95), color='k')
pp.tight_layout()
if outdir is not None:
pp.savefig(op.join(outdir, 'pars.pdf'))
ea_col = fits.Column(name='eta_earth', format='E', array=eta_earths.flatten())
npl_col = fits.Column(name='Lambda_pl', format='E', array=nps)
cols = fits.ColDefs([ea_col, npl_col])
tbhdu = fits.BinTableHDU.from_columns(cols)
hdr = fits.Header()
hdr['COMMENT'] = 'Farr, et al (2015) Figure 2'
hdr['COMMENT'] = 'Posterior samples from eta_earth and Lambda_pl'
hdr['COMMENT'] = 'eta_earth is the number density of planets per star'
hdr['COMMENT'] = 'per natural-logarithmic interval in P and R'
hdr['COMMENT'] = 'at P = 1 yr and R = 1 REarth'
hdr['COMMENT'] = 'Lambda_pl is the Poisson mean number of planets'
hdr['COMMENT'] = 'per star'
prihdu = fits.PrimaryHDU(header=hdr)
hdus = fits.HDUList([prihdu, tbhdu])
hdus.writeto(op.join(outdir, 'pars.fits'), clobber=True)
def plot_selection(logpost, chain, Ndraw=100, outdir=None):
fchain = chain.reshape((-1, chain.shape[2]))
all_draws = []
draws = []
psel = 0
for p in fchain[np.random.randint(fchain.shape[0], size=Ndraw), :]:
dcands = logpost.draw(p, logpost.systems['Kepler_ID'],
logpost.systems['Mass'],
logpost.systems['Radius'],
logpost.systems['SNR0'])
all_draws.append(dcands)
draws.append(dcands[np.random.random(size=dcands.shape[0]) < 1.0/Ndraw])
psel += logpost.ptransit(logpost.candidates['Period'],
logpost.candidates['Stellar_Mass'],
logpost.candidates['Stellar_Radius']) * \
logpost.pdetect(p, logpost.candidates['Period'],
logpost.candidates['Radius'],
logpost.candidates['SNR0'])
psel /= Ndraw
all_candidates = np.concatenate(all_draws)
candidates = np.concatenate(draws)
pp.subplot(2,2,1)
pu.plot_histogram_posterior(logpost.candidates['Radius'], color='k', normed=True, histtype='step', log=True)
pu.plot_histogram_posterior(all_candidates['Radius'], color='b', normed=True, histtype='step', log=True)
pp.yscale('log')
pp.axis(xmin=min(np.min(candidates['Radius']), np.min(logpost.candidates['Radius'])),
xmax=max(np.max(candidates['Radius']), np.max(logpost.candidates['Radius'])),
ymin=1e-4)
pp.xlabel(r'$R$ ($R_\oplus$)')
pp.ylabel(r'$p(\ln R)$')
pp.subplot(2,2,2)
pp.scatter(logpost.candidates['Period'], logpost.candidates['Radius'], color='k', alpha=0.05)
pp.scatter(candidates['Period'], candidates['Radius'], color='b', alpha=0.05)
pp.axis(xmin=min(np.min(candidates['Period']), np.min(logpost.candidates['Period'])),
xmax=max(np.max(candidates['Period']), np.max(logpost.candidates['Period'])),
ymin=min(np.min(candidates['Radius']), np.min(logpost.candidates['Radius'])),
ymax=max(np.max(candidates['Radius']), np.max(logpost.candidates['Radius'])))
pp.ylabel(r'$R$ ($R_\oplus$)')
pp.xlabel(r'$P$ ($\mathrm{yr}$)')
pp.xscale('log')
pp.yscale('log')
pp.subplot(2,2,3)
pp.scatter(logpost.candidates['Period'], logpost.candidates['Radius'], c=psel,
norm=mc.LogNorm())
pp.axis(xmin=min(np.min(candidates['Period']), np.min(logpost.candidates['Period'])),
xmax=max(np.max(candidates['Period']), np.max(logpost.candidates['Period'])),
ymin=min(np.min(candidates['Radius']), np.min(logpost.candidates['Radius'])),
ymax=max(np.max(candidates['Radius']), np.max(logpost.candidates['Radius'])))
pp.xscale('log')
pp.yscale('log')
pp.ylabel(r'$R$ ($R_\oplus$)')
pp.xlabel(r'$P$ ($\mathrm{yr}$)')
pp.colorbar()
pp.subplot(2,2,4)
pu.plot_histogram_posterior(logpost.candidates['Period'], color='k', normed=True, histtype='step', log=True)
pu.plot_histogram_posterior(all_candidates['Period'], color='b', normed=True, histtype='step', log=True)
pp.yscale('log')
pp.axis(xmin=min(np.min(candidates['Period']), np.min(logpost.candidates['Period'])),
xmax=max(np.max(candidates['Period']), np.max(logpost.candidates['Period'])),
ymin=1e-4)
pp.xlabel(r'$P$ ($\mathrm{yr}$)')
pp.ylabel(r'$p(\ln P)$')
pp.tight_layout()
if outdir is not None:
pp.savefig(op.join(outdir, 'selection.pdf'))
hdr = fits.Header()
hdr['COMMENT'] = 'Farr et al (2015) Figure 4'
hdr['COMMENT'] = 'Posterior predictive distribution of observed periods and radii'
hdr['COMMENT'] = 'from the model in that paper fit to the candidate data set.'
hdr['COMMENT'] = 'Also, the inferred selection function at each of the candidates.'
hdu = fits.PrimaryHDU(header=hdr)
hdulist = fits.HDUList([hdu])
pers = fits.Column(name='P', format='E', unit='yr', array=all_candidates['Period'])
rads = fits.Column(name='R', format='E', unit='REarth', array=all_candidates['Radius'])
hdulist.append(fits.BinTableHDU.from_columns(fits.ColDefs([pers, rads])))
ids = fits.Column(name='ID', format='D', array=logpost.candidates['Kepler_ID'])
pers = fits.Column(name='P', format='E', unit='yr', array=logpost.candidates['Period'])
rads = fits.Column(name='R', format='E', unit='REarth', array=logpost.candidates['Radius'])
pselect = fits.Column(name='psel', format='E', array=psel)
hdulist.append(fits.BinTableHDU.from_columns(fits.ColDefs([ids, pers, rads, pselect])))
hdulist.writeto(op.join(outdir, 'selection.fits'), clobber=True)
# parameters you are interested in.
ys = zeros(xs.shape)
for mu, sigma in zip(pchain['mu'].flatten(), pchain['sigma'].flatten()):
ys += ss.norm.pdf(xs, loc=mu, scale=sigma)
ys /= 12000.0
# Here's the plot
plot(xs, ys, '-b')
xlabel(r'$\mu_j$')
ylablel(r'$p\left( \mu_j \right)$')
ylabel(r'$p\left( \mu_j \right)$')
savefig('muj.pdf')
# Now just plot some posterior distributions of the mu and sigma
# parameters.
pu.plot_histogram_posterior(pchain['mu'].flatten(), normed=True, histtype='step')
axis(ymax=1)
axis(ymax=0.2
)
axis(ymax=0.07)
axis(ymax=0.06)
axvline(p0['mu'])
axvline(p0['mu'], color='k')
xlabel(r'$\mu$')
ylabel(r'$p(\mu)$')
savefig('mu.pdf')
pu.plot_histogram_posterior(pchain['sigma'].flatten(), normed=True, histtype='step')
axis(ymax=0.07)
axis(ymax=0.1)
axis(ymax=0.09)
axvline(p0['sigma'])
