def nestle_multi2():
# Run nested sampling
res = nestle.sample(loglike2,
prior_transform2,
3,
method='multi',
npoints=2000)
print(res.summary())
# weighted average and covariance:
pm, covm = nestle.mean_and_cov(res.samples, res.weights)
# re-scale weights to have a maximum of one
nweights = res.weights / np.max(res.weights)
# get the probability of keeping a sample from the weights
keepidx = np.where(np.random.rand(len(nweights)) < nweights)[0]
# get the posterior samples
samples_nestle = res.samples[keepidx, :]
print(np.mean(samples_nestle[:, 0])) # mean of A samples
print(np.std(samples_nestle[:, 0])) # standard deviation of A samples
print(np.mean(samples_nestle[:, 1])) # mean of w samples
print(np.std(samples_nestle[:, 1])) # standard deviation of w samples
print(np.mean(samples_nestle[:, 2])) # mean of t0 samples
print(np.std(samples_nestle[:, 2])) # standard deviation of t0 samples
print(len(samples_nestle)) # number of posterior samples
return res.logz
def store_nestle_output(self, result):
"""
This turns the output fron nestle into a dictionary that can
be output by Taurex
Parameters
----------
result: :obj:`dict`
Result from a nestle sample call
Returns
-------
dict
Formatted dictionary for output
"""
from tabulate import tabulate
nestle_output = {}
nestle_output['Stats'] = {}
nestle_output['Stats']['Log-Evidence'] = result.logz
nestle_output['Stats']['Log-Evidence-Error'] = result.logzerr
nestle_output['Stats']['Peakiness'] = result.h
fit_param = self.fit_names
samples = result.samples
weights = result.weights
mean, cov = nestle.mean_and_cov(samples, weights)
nestle_output['solution'] = {}
nestle_output['solution']['samples'] = samples
nestle_output['solution']['weights'] = weights
nestle_output['solution']['covariance'] = cov
nestle_output['solution']['fitparams'] = {}
max_weight = weights.argmax()
table_data = []
for idx, param_name in enumerate(fit_param):
param = {}
param['mean'] = mean[idx]
param['sigma'] = cov[idx]
trace = samples[:, idx]
q_16, q_50, q_84 = quantile_corner(trace, [0.16, 0.5, 0.84],
weights=np.asarray(weights))
param['value'] = q_50
param['sigma_m'] = q_50 - q_16
param['sigma_p'] = q_84 - q_50
param['trace'] = trace
param['map'] = trace[max_weight]
table_data.append((param_name, q_50, q_50 - q_16))
nestle_output['solution']['fitparams'][param_name] = param
return nestle_output
def test_mean_and_cov():
x = np.random.random((10, 3))
w = np.random.random((10,))
mean, cov = nestle.mean_and_cov(x, w)
# check individual elements
xd = x - np.average(x, weights=w, axis=0)
prefactor = w.sum() / (w.sum()**2 - (w**2).sum())
ans00 = prefactor * np.sum(w * xd[:, 0] * xd[:, 0])
assert_approx_equal(cov[0, 0], ans00)
ans01 = prefactor * np.sum(w * xd[:, 0] * xd[:, 1])
assert_approx_equal(cov[0, 1], ans01)
# If weights are all equal, covariance should come out to simple case
w = np.repeat(0.2, 10)
mean, cov = nestle.mean_and_cov(x, w)
assert_allclose(cov, np.cov(x, rowvar=0))
assert_allclose(mean, np.average(x, axis=0))
def test_mean_and_cov():
x = np.random.random((10, 3))
w = np.random.random((10, ))
mean, cov = nestle.mean_and_cov(x, w)
# check individual elements
xd = x - np.average(x, weights=w, axis=0)
prefactor = w.sum() / (w.sum()**2 - (w**2).sum())
ans00 = prefactor * np.sum(w * xd[:, 0] * xd[:, 0])
assert_approx_equal(cov[0, 0], ans00)
ans01 = prefactor * np.sum(w * xd[:, 0] * xd[:, 1])
assert_approx_equal(cov[0, 1], ans01)
# If weights are all equal, covariance should come out to simple case
w = np.repeat(0.2, 10)
mean, cov = nestle.mean_and_cov(x, w)
assert_allclose(cov, np.cov(x, rowvar=0))
assert_allclose(mean, np.average(x, axis=0))
def nested_sampling_results(ns_object, burnin=0.4, bins=None):
""" Shows the results of the Nested Sampling, summary, parameters with errors,
walk and corner plots.
"""
res = ns_object
nsamples = res.samples.shape[0]
indburnin = np.percentile(np.array(list(range(nsamples))), burnin * 100)
print(res.summary())
print(
'\nNatural log of prior volume and Weight corresponding to each sample')
plt.figure(figsize=(12, 4))
plt.subplot(1, 2, 1)
plt.plot(res.logvol, '.', alpha=0.5, color='gray')
plt.xlabel('samples')
plt.ylabel('logvol')
plt.vlines(indburnin, res.logvol.min(), res.logvol.max(),
linestyles='dotted')
plt.subplot(1, 2, 2)
plt.plot(res.weights, '.', alpha=0.5, color='gray')
plt.xlabel('samples')
plt.ylabel('weights')
plt.vlines(indburnin, res.weights.min(), res.weights.max(),
linestyles='dotted')
plt.show()
print("\nWalk plots before the burnin")
show_walk_plot(np.expand_dims(res.samples, axis=0))
if burnin > 0:
print("\nWalk plots after the burnin")
show_walk_plot(np.expand_dims(res.samples[indburnin:], axis=0))
mean, cov = nestle.mean_and_cov(res.samples[indburnin:],
res.weights[indburnin:])
print("\nWeighted mean +- sqrt(covariance)")
print("Radius = {:.3f} +/- {:.3f}".format(mean[0], np.sqrt(cov[0, 0])))
print("Theta = {:.3f} +/- {:.3f}".format(mean[1], np.sqrt(cov[1, 1])))
print("Flux = {:.3f} +/- {:.3f}".format(mean[2], np.sqrt(cov[2, 2])))
if bins is None:
bins = int(np.sqrt(res.samples[indburnin:].shape[0]))
print("\nHist bins =", bins)
ranges = None
fig = corner.corner(res.samples[indburnin:], bins=bins,
labels=["$r$", r"$\theta$", "$f$"],
weights=res.weights[indburnin:], range=ranges,
plot_contours=True)
fig.set_size_inches(8., 8.)
print('\nConfidence intervals')
_ = confidence(res.samples[indburnin:], cfd=68, bins=bins,
weights=res.weights[indburnin:],
gaussianFit=True, verbose=True, save=False)
def show_results(loglike_NFW, prior_transform_NFW, n):
# n is the dim of theta; for NFW model, n =2
result = nestle.sample(loglike_NFW, prior_transform_NFW, 2)
print('log evidence')
print(result.logz)
print('numerical (sampling) error on logz')
print(result.logzerr)
print('array of sample parameters')
print(result.samples)
print('array of weights associated with each sample')
print(result.weights)
p, cov = nestle.mean_and_cov(result.samples, result.weights)
print("core radius a = {0:5.2f} +/- {1:5.2f} kpc".format(
p[0], np.sqrt(cov[0, 0])))
print("normalization factor = {0:5.2f} +/- {1:5.2f}".format(
p[1], np.sqrt(cov[1, 1])))
print(
"Halo density normalization constant = {0:5.2e} +/- {1:5.2e} Msun/kpc^3"
.format(2.312E5 * p[1], 2.312E5 * np.sqrt(cov[1, 1])))
# Note: in order to convert the model to units of Msun/kpc^3 we multiply its value by 2.312E5.
# See comments in the model definition for details.
print("Halo density in our solor system = {0:5.2e} Msun/kpc^3.".format(
2.312E5 * model_NFW(p, 8)))
# Note: 1 Msun/kpc^3 = 3.817E-2 (GeV/c^2)/m^3 = 3.817E-5 (GeV/c^2)/(dm^3)
# 1 dm^3 = 1 liter.
# 3 WIMPS/liter would be 300 GeV/c^2/liter
print("Halo density in our solor system = {0:5.2e} GeV/c^2/liter.".format(
3.817E-5 * 2.312E5 * model_NFW(p, 8)))
plt.figure()
plt.errorbar(data_x, data_y, data_yerr, data_xerr, fmt='*')
plt.xlabel("r (kpc)")
plt.ylabel('V (km/s)')
plt.title(
"The measured rotational speed of the interstellar medium as a fucntion of the galactocentric radius"
)
plt.plot([5., 200.], model_NFW(p, np.array([5., 200.])))
plt.show()
fig = corner.corner(result.samples,
weights=result.weights,
labels=['a', 'rho0'],
range=[0.99999, 0.99999],
bins=30)
plt.show()
return 0
def nested_sampling_results(ns_object, burnin=0.4, bins=None):
""" Shows the results of the Nested Sampling, summary, parameters with errors,
walk and corner plots.
"""
res = ns_object
nsamples = res.samples.shape[0]
indburnin = np.percentile(np.array(range(nsamples)), burnin * 100)
print(res.summary())
print(
'\nNatural log of prior volume and Weight corresponding to each sample')
plt.figure(figsize=(12, 4))
plt.subplot(1, 2, 1)
plt.plot(res.logvol, '.', alpha=0.5, color='gray')
plt.xlabel('samples')
plt.ylabel('logvol')
plt.vlines(indburnin, res.logvol.min(), res.logvol.max(),
linestyles='dotted')
plt.subplot(1, 2, 2)
plt.plot(res.weights, '.', alpha=0.5, color='gray')
plt.xlabel('samples')
plt.ylabel('weights')
plt.vlines(indburnin, res.weights.min(), res.weights.max(),
linestyles='dotted')
plt.show()
print("\nWalk plots before the burnin")
show_walk_plot(np.expand_dims(res.samples, axis=0))
if burnin > 0:
print("\nWalk plots after the burnin")
show_walk_plot(np.expand_dims(res.samples[indburnin:], axis=0))
mean, cov = nestle.mean_and_cov(res.samples[indburnin:],
res.weights[indburnin:])
print("\nWeighted mean +- sqrt(covariance)")
print("Radius = {:.3f} +/- {:.3f}".format(mean[0], np.sqrt(cov[0, 0])))
print("Theta = {:.3f} +/- {:.3f}".format(mean[1], np.sqrt(cov[1, 1])))
print("Flux = {:.3f} +/- {:.3f}".format(mean[2], np.sqrt(cov[2, 2])))
if bins is None:
bins = int(np.sqrt(res.samples[indburnin:].shape[0]))
print("\nHist bins =", bins)
ranges = None
fig = corner.corner(res.samples[indburnin:], bins=bins,
labels=["$r$", r"$\theta$", "$f$"],
weights=res.weights[indburnin:], range=ranges,
plot_contours=True)
fig.set_size_inches(8, 8)
print('\nConfidence intervals')
_ = confidence(res.samples[indburnin:], cfd=68, bins=bins,
weights=res.weights[indburnin:],
gaussian_fit=True, verbose=True, save=False)
def run_nestle(self,outfile='TEST.dat'):
# initalize outfile
self.outfile = open(outfile,'w')
self.outfile.write('ITER Teff Dist Rad NH arfsc1 arfsc2 log(z) \n')
# Start sampler
print('Start Nestle')
result = nestle.sample(self.calllike,self.prior_trans,self.ndim,method='multi',npoints=1000,callback=self.nestle_callback)
# generate posterior means and covariances
p,cov = nestle.mean_and_cov(result.samples,result.weights)
# close output file
self.outfile.close()
return result,p,cov
def print_results(result, display_params):
means, cov = nestle.mean_and_cov(result.samples, result.weights)
std = np.sqrt(np.diag(cov))
plot_labels = [
make_plot_label(*display_param) for display_param in display_params
]
unit_fracs = [dp[1] for dp in display_params]
shifts = [dp[3] for dp in display_params]
print "\nEstimated parameters :"
for m, s, label, scale, shift in zip(means, std, plot_labels, unit_fracs,
shifts):
m1 = m / scale - shift
s1 = s / scale
lbl = latex.latex_to_text(label)
print "%s = %0.6f +/- %0.6f" % (lbl, m1, s1)
def nestle_multi2():
# Run nested sampling
res = nestle.sample(loglike2,
prior_transform2,
2,
method='multi',
npoints=2000)
# weighted average and covariance:
pm, covm = nestle.mean_and_cov(res.samples, res.weights)
# re-scale weights to have a maximum of one
nweights = res.weights / np.max(res.weights)
# get the probability of keeping a sample from the weights
keepidx = np.where(np.random.rand(len(nweights)) < nweights)[0]
# get the posterior samples
samples_nestle = res.samples[keepidx, :]
return res.logz
def get_summary(self):
self.log.info(f'NestedSamplerStatModel::\tgetting the summary (or at'
f"least trying) let's first see if I did run")
self.check_did_run()
self.log.info(
f"NestedSamplerStatModel::\t{utils.now()}\n\tAlright, that's done. Let's get some "
f"info. I'm not going to print too much here")
# keep a dictionary of all the results
resdict = {}
if self.config["sampler"] == 'multinest':
# Do the import of multinest inside the class such that the package can be
# loaded without multinest
try:
from pymultinest.solve import run, Analyzer, solve
except ModuleNotFoundError:
raise ModuleNotFoundError(
'package pymultinest not found. See README for installation')
self.log.info(
'NestedSamplerStatModel::\tget_summary::\tstart analyzer of results')
analyzer = Analyzer(len(self.config['fit_parameters']),
outputfiles_basename=self.result_file)
# Taken from multinest.solve
self.result = analyzer.get_stats()
samples = analyzer.get_equal_weighted_posterior()[:, :-1]
self.log.info('parameter values:')
for name, col in zip(
self.config['fit_parameters'], samples.transpose()):
self.log.info(
'%15s : %.3f +- %.3f' %
(name, col.mean(), col.std()))
resdict[name +
'_fit_res'] = ('{0:5.2f} +/- {1:5.2f}'.format(col.mean(), col.std()))
if 'log_' in name:
resdict[name[4:] + '_fit_res'] = '%.3g +/- %.2g' % (
10. ** col.mean(), 10. ** (col.mean()) * np.log(10.) * col.std())
self.log.info(
f'\t {name[4:]}, {resdict[name[4:] + "_fit_res"]}')
resdict['n_samples'] = len(samples.transpose()[0])
# Pass the samples to the self.result to be saved.
self.result['samples'] = samples
elif self.config["sampler"] == 'nestle':
# Do the import of nestle inside the class such that the package can be
# loaded without nestle
try:
import nestle
except ModuleNotFoundError:
raise ModuleNotFoundError(
'package nestle not found. See README for installation')
# taken from mattpitkin.github.io/samplers-demo/pages/samplers-samplers-everywhere/#Nestle
# estimate of the statistical uncertainty on logZ
logZerrnestle = np.sqrt(self.result.h / self.config['nlive'])
# re-scale weights to have a maximum of one
nweights = self.result.weights / np.max(self.result.weights)
# get the probability of keeping a sample from the weights
keepidx = np.where(np.random.rand(len(nweights)) < nweights)[0]
# get the posterior samples
samples_nestle = self.result.samples[keepidx, :]
# estimate of the statistcal uncertainty on logZ
resdict['nestle_nposterior'] = len(samples_nestle)
resdict['nestle_time'] = self.config['fit_time'] # run time
# log marginalised likelihood
resdict['nestle_logZ'] = self.result.logz
resdict['nestle_logZerr'] = logZerrnestle # uncertainty on log(Z)
resdict['summary'] = self.result.summary()
p, cov = nestle.mean_and_cov(
self.result.samples, self.result.weights)
for i, key in enumerate(self.config['fit_parameters']):
resdict[key + '_fit_res'] = (
'{0:5.2f} +/- {1:5.2f}'.format(p[i], np.sqrt(cov[i, i])))
self.log.info(f'\t, {key}, {resdict[key + "_fit_res"]}')
if 'log_' in key:
resdict[key[4:] + '_fit_res'] = '%.3g +/- %.2g' % (
10. ** p[i], 10. ** (p[i]) * np.log(10) * np.sqrt(cov[i, i]))
self.log.info(
f'\t, {key[4:]}, {resdict[key[4:] + "_fit_res"]}')
self.log.info(
f'NestedSamplerStatModel::\tAlright we got all the info we need, '
f"let's return it to whomever asked for it")
return resdict
def nested_sampling_results(ns_object,
burnin=0.4,
bins=None,
save=False,
output_dir='/'):
""" Shows the results of the Nested Sampling, summary, parameters with errors,
walk and corner plots.
"""
res = ns_object
nsamples = res.samples.shape[0]
indburnin = int(np.percentile(np.array(range(nsamples)), burnin * 100))
print(res.summary())
print(
'\nNatural log of prior volume and Weight corresponding to each sample'
)
plt.figure(figsize=(12, 4))
plt.subplot(1, 2, 1)
plt.plot(res.logvol, '.', alpha=0.5, color='gray')
plt.xlabel('samples')
plt.ylabel('logvol')
plt.vlines(indburnin,
res.logvol.min(),
res.logvol.max(),
linestyles='dotted')
plt.subplot(1, 2, 2)
plt.plot(res.weights, '.', alpha=0.5, color='gray')
plt.xlabel('samples')
plt.ylabel('weights')
plt.vlines(indburnin,
res.weights.min(),
res.weights.max(),
linestyles='dotted')
plt.show()
if save:
plt.savefig(output_dir + 'Nested_results.pdf')
print("\nWalk plots before the burnin")
show_walk_plot(np.expand_dims(res.samples, axis=0))
if burnin > 0:
print("\nWalk plots after the burnin")
show_walk_plot(np.expand_dims(res.samples[indburnin:], axis=0))
if save:
plt.savefig(output_dir + 'Nested_walk_plots.pdf')
mean, cov = nestle.mean_and_cov(res.samples[indburnin:],
res.weights[indburnin:])
print("\nWeighted mean +- sqrt(covariance)")
print("Radius = {:.3f} +/- {:.3f}".format(mean[0], np.sqrt(cov[0, 0])))
print("Theta = {:.3f} +/- {:.3f}".format(mean[1], np.sqrt(cov[1, 1])))
print("Flux = {:.3f} +/- {:.3f}".format(mean[2], np.sqrt(cov[2, 2])))
if save:
with open(output_dir + 'Nested_sampling.txt', "w") as f:
f.write('#################################\n')
f.write('#### CONFIDENCE INTERVALS ###\n')
f.write('#################################\n')
f.write(' \n')
f.write('Results of the NESTED SAMPLING fit\n')
f.write('----------------------------------\n ')
f.write(' \n')
f.write("\nWeighted mean +- sqrt(covariance)\n")
f.write("Radius = {:.3f} +/- {:.3f}\n".format(
mean[0], np.sqrt(cov[0, 0])))
f.write("Theta = {:.3f} +/- {:.3f}\n".format(
mean[1], np.sqrt(cov[1, 1])))
f.write("Flux = {:.3f} +/- {:.3f}\n".format(
mean[2], np.sqrt(cov[2, 2])))
if bins is None:
bins = int(np.sqrt(res.samples[indburnin:].shape[0]))
print("\nHist bins =", bins)
ranges = None
fig = corner.corner(res.samples[indburnin:],
bins=bins,
labels=["$r$", r"$\theta$", "$f$"],
weights=res.weights[indburnin:],
range=ranges,
plot_contours=True)
fig.set_size_inches(8, 8)
if save:
plt.savefig(output_dir + 'Nested_corner.pdf')
print('\nConfidence intervals')
_ = confidence(res.samples[indburnin:],
cfd=68,
bins=bins,
weights=res.weights[indburnin:],
gaussian_fit=True,
verbose=True,
save=False)
if save:
plt.savefig(output_dir + 'Nested_confi_hist_flux_r_theta_gaussfit.pdf')
final_res = np.array([[mean[0], np.sqrt(cov[0, 0])],
[mean[1], np.sqrt(cov[1, 1])],
[mean[2], np.sqrt(cov[1, 1])]])
return final_res
def run_nestle(self,samplertype=None,npoints=None,restart=None,weightrestart=True,maxrejcall=None):
if samplertype == None:
samplertype = 'multi'
if npoints == None:
npoints = 100
if restart == None:
# generate initial random sample within Nestle volume
modind = np.array(range(0,len(self.MODPARS)),dtype=int)
selind = modind[np.random.choice(len(modind),npoints,replace=False)]
if ('Tycho_V' in self.bfpar.keys()) & ('Tycho_B' in self.bfpar.keys()):
cond = (
(self.PHOT['Tycho_V']+self.DM(self.mindist+0.5*self.distran) > self.bfpar['Tycho_V']-1.0) &
(self.PHOT['Tycho_V']+self.DM(self.mindist+0.5*self.distran) < self.bfpar['Tycho_V'] + 1.0) &
(self.PHOT['Tycho_B']+self.DM(self.mindist+0.5*self.distran) > self.bfpar['Tycho_B']-1.0) &
(self.PHOT['Tycho_B']+self.DM(self.mindist+0.5*self.distran) < self.bfpar['Tycho_B'] + 1.0)
)
addind = modind[cond][np.random.choice(len(modind[cond]),int(npoints*0.25),replace=False)]
finind = np.hstack([selind,addind])
finind = np.unique(finind)
else:
finind = selind
initsample = self.MODPARS[finind]
initsample_v = np.empty((len(initsample), self.ndim), dtype=np.float64)
initsample_u = np.empty((len(initsample), self.ndim), dtype=np.float64)
for i in range(len(initsample)):
initsample_v_i = [float(initsample['EEP'][i]),10.0**(float(initsample['log_age'][i])-9.0),float(initsample['[Fe/H]in'][i])]
if self.fitphotbool:
# initsample_v_i.append(self.distran*np.random.rand()+self.mindist)
# initsample_v_i.append(self.Avran*np.random.rand()+self.minAv)
if 'Para' in self.priordict.keys():
distmean = 1000.0/self.priordict['Para'][0]
parashift = self.priordict['Para'][0]-3.0*self.priordict['Para'][1]
distsig = (1000.0/parashift)-distmean
initsample_v_i.append(distsig*np.random.randn()+distmean)
else:
initsample_v_i.append(self.distran*np.random.rand()+self.mindist)
initsample_v_i.append(self.Avran*np.random.rand()+self.minAv)
initsample_u_i = self.prior_inversetrans(initsample_v_i)
initsample_v[i,:] = initsample_v_i
initsample_u[i,:] = initsample_u_i
else:
restart_from = Table.read(restart,format='ascii')
if len(restart_from) > npoints:
if weightrestart:
restart_ind = np.random.choice(range(0,len(restart_from)),npoints,replace=False,p=np.exp(restart_from['logwt']-restart_from['logz'][-1]))
else:
restart_ind = np.random.choice(range(0,len(restart_from)),npoints,replace=False)
restart_sel = restart_from[restart_ind]
addind = np.random.choice(len(self.MODPARS),int(0.25*npoints),replace=False)
addsel = self.MODPARS[addind]
else:
restart_sel = restart_from
numbadd = 1.25*npoints-len(restart_sel)
addind = np.random.choice(len(self.MODPARS),numbadd,replace=False)
addsel = self.MODPARS[addind]
initsample_v = np.empty((len(restart_sel)+len(addsel),self.ndim), dtype=np.float64)
initsample_u = np.empty((len(restart_sel)+len(addsel),self.ndim), dtype=np.float64)
for i in range(len(restart_sel)):
initsample_v_i = [float(restart_sel['EEP'][i]),float(restart_sel['Age'][i]),float(restart_sel['[Fe/H]in'][i])]
if self.fitphotbool:
initsample_v_i.append(float(restart_sel['Dist'][i]))
initsample_v_i.append(float(restart_sel['Av'][i]))
initsample_u_i = self.prior_inversetrans(initsample_v_i)
initsample_v[i,:] = initsample_v_i
initsample_u[i,:] = initsample_u_i
for i in range(len(addsel)):
initsample_v_i = [float(addsel['EEP'][i]),10.0**(float(addsel['log_age'][i])-9.0),float(addsel['[Fe/H]in'][i])]
if self.fitphotbool:
# initsample_v_i.append(self.distran*np.random.rand()+self.mindist)
# initsample_v_i.append(self.Avran*np.random.rand()+self.minAv)
distmean = 1000.0/self.priordict['Para'][0]
parashift = self.priordict['Para'][0]-3.0*self.priordict['Para'][1]
distsig = (1000.0/parashift)-distmean
initsample_v_i.append(distsig*np.random.randn()+distmean)
initsample_v_i.append(self.Avran*np.random.rand()+self.minAv)
initsample_u_i = self.prior_inversetrans(initsample_v_i)
initsample_v[i+len(restart_sel),:] = initsample_v_i
initsample_u[i+len(restart_sel),:] = initsample_u_i
print 'Start Nestle w/ {0} number of samples'.format(len(initsample_v))
self.startmct = datetime.now()
self.stept = datetime.now()
self.ncallt = 0
self.maxcallnum = 0
sys.stdout.flush()
result = nestle.sample(
self.lnp_call_nestle,self.prior_trans,self.ndim,method=samplertype,
npoints=len(initsample_v),callback=self.nestle_callback,user_sample=initsample_u,
# dlogz=1.0,
# update_interval=1,
maxrejcall=maxrejcall,
)
p,cov = nestle.mean_and_cov(result.samples,result.weights)
return result,p,cov
def nest_lc(data,
model,
vparam_names,
bounds,
guess_amplitude_bound=False,
minsnr=5.,
priors=None,
ppfs=None,
npoints=100,
method='single',
maxiter=None,
maxcall=None,
modelcov=False,
rstate=None,
verbose=False,
warn=True,
**kwargs):
"""Run nested sampling algorithm to estimate model parameters and evidence.
Parameters
----------
data : `~astropy.table.Table` or `~numpy.ndarray` or `dict`
Table of photometric data. Must include certain columns.
See the "Photometric Data" section of the documentation for
required columns.
model : `~sncosmo.Model`
The model to fit.
vparam_names : list
Model parameters to vary in the fit.
bounds : `dict`
Bounded range for each parameter. Bounds must be given for
each parameter, with the exception of ``t0``: by default, the
minimum bound is such that the latest phase of the model lines
up with the earliest data point and the maximum bound is such
that the earliest phase of the model lines up with the latest
data point.
guess_amplitude_bound : bool, optional
If true, bounds for the model's amplitude parameter are determined
automatically based on the data and do not need to be included in
`bounds`. The lower limit is set to zero and the upper limit is 10
times the amplitude "guess" (which is based on the highest-flux
data point in any band). Default is False.
minsnr : float, optional
Minimum signal-to-noise ratio of data points to use when guessing
amplitude bound. Default is 5.
priors : `dict`, optional
Prior probability distribution function for each parameter. The keys
should be parameter names and the values should be callables that
accept a float. If a parameter is not in the dictionary, the prior
defaults to a flat distribution between the bounds.
ppfs : `dict`, optional
Prior percent point function (inverse of the cumulative distribution
function) for each parameter. If a parameter is in this dictionary,
the ppf takes precedence over a prior pdf specified in ``priors``.
npoints : int, optional
Number of active samples to use. Increasing this value increases
the accuracy (due to denser sampling) and also the time
to solution.
method : {'classic', 'single', 'multi'}, optional
Method used to select new points. Choices are 'classic',
single-ellipsoidal ('single'), multi-ellipsoidal ('multi'). Default
is 'single'.
maxiter : int, optional
Maximum number of iterations. Iteration may stop earlier if
termination condition is reached. Default is no limit.
maxcall : int, optional
Maximum number of likelihood evaluations. Iteration may stop earlier
if termination condition is reached. Default is no limit.
modelcov : bool, optional
Include model covariance when calculating chisq. Default is False.
rstate : `~numpy.random.RandomState`, optional
RandomState instance. If not given, the global random state of the
``numpy.random`` module will be used.
verbose : bool, optional
Print running evidence sum on a single line.
warn : bool, optional
Issue warning when dropping bands outside the model range. Default is
True.
*New in version 1.5.0*
Returns
-------
res : Result
Attributes are:
* ``niter``: total number of iterations
* ``ncall``: total number of likelihood function calls
* ``time``: time in seconds spent in iteration loop.
* ``logz``: natural log of the Bayesian evidence Z.
* ``logzerr``: estimate of uncertainty in logz (due to finite sampling)
* ``h``: Bayesian information.
* ``vparam_names``: list of parameter names varied.
* ``samples``: 2-d `~numpy.ndarray`, shape is (nsamples, nparameters).
Each row is the parameter values for a single sample. For example,
``samples[0, :]`` is the parameter values for the first sample.
* ``logprior``: 1-d `~numpy.ndarray` (length=nsamples);
log(prior volume) for each sample.
* ``logl``: 1-d `~numpy.ndarray` (length=nsamples); log(likelihood)
for each sample.
* ``weights``: 1-d `~numpy.ndarray` (length=nsamples);
Weight corresponding to each sample. The weight is proportional to
the prior * likelihood for the sample.
* ``parameters``: 1-d `~numpy.ndarray` of weighted-mean parameter
values from samples (including fixed parameters). Order corresponds
to ``model.param_names``.
* ``covariance``: 2-d `~numpy.ndarray` of parameter covariance;
indicies correspond to order of ``vparam_names``. Calculated from
``samples`` and ``weights``.
* ``errors``: OrderedDict of varied parameter uncertainties.
Corresponds to square root of diagonal entries in covariance matrix.
* ``ndof``: Number of degrees of freedom (len(data) -
len(vparam_names)).
* ``bounds``: Dictionary of bounds on varied parameters (including
any automatically determined bounds).
* ``data_mask``: Boolean array the same length as data specifying
whether each observation was used.
*New in version 1.5.0.*
estimated_model : `~sncosmo.Model`
A copy of the model with parameters set to the values in
``res.parameters``.
"""
try:
import nestle
except ImportError:
raise ImportError("nest_lc() requires the nestle package.")
# warnings
if "nobj" in kwargs:
warnings.warn("The nobj keyword is deprecated and will be removed in "
"sncosmo v2.0. Use `npoints` instead.")
npoints = kwargs.pop("nobj")
# experimental parameters
tied = kwargs.get("tied", None)
data = photometric_data(data)
# sort by time
if not np.all(np.ediff1d(data.time) >= 0.0):
sortidx = np.argsort(data.time)
data = data[sortidx]
else:
sortidx = None
model = copy.copy(model)
bounds = copy.copy(bounds) # need to copy this b/c we modify it below
# Order vparam_names the same way it is ordered in the model:
vparam_names = [s for s in model.param_names if s in vparam_names]
# Drop data that the model doesn't cover.
fitdata, data_mask = cut_bands(data,
model,
z_bounds=bounds.get('z', None),
warn=warn)
if guess_amplitude_bound:
if model.param_names[2] not in vparam_names:
raise ValueError("Amplitude bounds guessing enabled but "
"amplitude parameter {0!r} is not varied".format(
model.param_names[2]))
if model.param_names[2] in bounds:
raise ValueError("cannot supply bounds for parameter {0!r}"
" when guess_amplitude_bound=True".format(
model.param_names[2]))
# If redshift is bounded, set model redshift to midpoint of bounds
# when doing the guess.
if 'z' in bounds:
model.set(z=sum(bounds['z']) / 2.)
_, amplitude = guess_t0_and_amplitude(fitdata, model, minsnr)
bounds[model.param_names[2]] = (0., 10. * amplitude)
# Find t0 bounds to use, if not explicitly given
if 't0' in vparam_names and 't0' not in bounds:
bounds['t0'] = t0_bounds(fitdata, model)
if ppfs is None:
ppfs = {}
if tied is None:
tied = {}
# Convert bounds/priors combinations into ppfs
if bounds is not None:
for key, val in six.iteritems(bounds):
if key in ppfs:
continue # ppfs take priority over bounds/priors
a, b = val
if priors is not None and key in priors:
# solve ppf at discrete points and return interpolating
# function
x_samples = np.linspace(0., 1., 101)
ppf_samples = ppf(priors[key], x_samples, a, b)
f = Interp1D(0., 1., ppf_samples)
else:
f = Interp1D(0., 1., np.array([a, b]))
ppfs[key] = f
# NOTE: It is important that iparam_names is in the same order
# every time, otherwise results will not be reproducible, even
# with same random seed. This is because iparam_names[i] is
# matched to u[i] below and u will be in a reproducible order,
# so iparam_names must also be.
iparam_names = [key for key in vparam_names if key in ppfs]
ppflist = [ppfs[key] for key in iparam_names]
npdim = len(iparam_names) # length of u
ndim = len(vparam_names) # length of v
# Check that all param_names either have a direct prior or are tied.
for name in vparam_names:
if name in iparam_names:
continue
if name in tied:
continue
raise ValueError(
"Must supply ppf or bounds or tied for parameter '{}'".format(
name))
def prior_transform(u):
d = {}
for i in range(npdim):
d[iparam_names[i]] = ppflist[i](u[i])
v = np.empty(ndim, dtype=np.float)
for i in range(ndim):
key = vparam_names[i]
if key in d:
v[i] = d[key]
else:
v[i] = tied[key](d)
return v
# Indicies of the model parameters in vparam_names
idx = np.array([model.param_names.index(name) for name in vparam_names])
def loglike(parameters):
model.parameters[idx] = parameters
return -0.5 * chisq(fitdata, model, modelcov=modelcov)
t0 = time.time()
res = nestle.sample(loglike,
prior_transform,
ndim,
npdim=npdim,
npoints=npoints,
method=method,
maxiter=maxiter,
maxcall=maxcall,
rstate=rstate,
callback=(nestle.print_progress if verbose else None))
elapsed = time.time() - t0
# estimate parameters and covariance from samples
vparameters, cov = nestle.mean_and_cov(res.samples, res.weights)
# update model parameters to estimated ones.
model.set(**dict(zip(vparam_names, vparameters)))
# If we need to, unsort the mask so mask applies to input data
if sortidx is not None:
unsort_idx = np.argsort(sortidx) # indicies that will unsort array
data_mask = data_mask[unsort_idx]
# `res` is a nestle.Result object. Collect result into a sncosmo.Result
# object for consistency, and add more fields.
res = Result(
niter=res.niter,
ncall=res.ncall,
logz=res.logz,
logzerr=res.logzerr,
h=res.h,
samples=res.samples,
weights=res.weights,
logvol=res.logvol,
logl=res.logl,
vparam_names=copy.copy(vparam_names),
ndof=len(fitdata) - len(vparam_names),
bounds=bounds,
time=elapsed,
parameters=model.parameters.copy(),
covariance=cov,
errors=OrderedDict(zip(vparam_names, np.sqrt(np.diagonal(cov)))),
param_dict=OrderedDict(zip(model.param_names, model.parameters)),
data_mask=data_mask)
# Deprecated result fields.
depmsg = ("The `param_names` attribute is deprecated in sncosmo v1.0 "
"and will be removed in sncosmo v2.0."
"Use `vparam_names` instead.")
res.__dict__['deprecated']['param_names'] = (res.vparam_names, depmsg)
depmsg = ("The `logprior` attribute is deprecated in sncosmo v1.2 "
"and will be changed in sncosmo v2.0."
"Use `logvol` instead.")
res.__dict__['deprecated']['logprior'] = (res.logvol, depmsg)
return res, model
def print_nestle(res, par, model, x, y, yerror, outfile=None):
print(res.summary)
print(nestle.mean_and_cov(res.samples, res.weights))
plot_triangle(res.samples, par, model, x, y, yerror, weights=res.weights)
if outfile is not None:
plt.savefig(outfile)
def nested_sampling_results(ns_object,
burnin=0.4,
bins=None,
cfd=68.27,
save=False,
output_dir='/',
plot=False):
""" Shows the results of the Nested Sampling, summary, parameters with
errors, walk and corner plots.
Parameters
----------
ns_object: numpy.array
The nestle object returned from `nested_spec_sampling`.
burnin: float, default: 0
The fraction of a walker we want to discard.
bins: int, optional
The number of bins used to sample the posterior distributions.
cfd: float, optional
The confidence level given in percentage.
save: boolean, default: False
If True, a pdf file is created.
output_dir: str, optional
The name of the output directory which contains the output files in the
case ``save`` is True.
plot: bool, optional
Whether to show the plots (instead of saving them).
Returns
-------
final_res: numpy ndarray
Best-fit parameters and uncertainties (corresponding to 68% confidence
interval). Dimensions: nparams x 2.
"""
res = ns_object
nsamples = res.samples.shape[0]
indburnin = int(np.percentile(np.array(range(nsamples)), burnin * 100))
print(res.summary())
print(
'\nNatural log of prior volume and Weight corresponding to each sample'
)
if save or plot:
plt.figure(figsize=(12, 4))
plt.subplot(1, 2, 1)
plt.plot(res.logvol, '.', alpha=0.5, color='gray')
plt.xlabel('samples')
plt.ylabel('logvol')
plt.vlines(indburnin,
res.logvol.min(),
res.logvol.max(),
linestyles='dotted')
plt.subplot(1, 2, 2)
plt.plot(res.weights, '.', alpha=0.5, color='gray')
plt.xlabel('samples')
plt.ylabel('weights')
plt.vlines(indburnin,
res.weights.min(),
res.weights.max(),
linestyles='dotted')
if plot:
plt.show()
plt.savefig(output_dir + 'Nested_results.pdf')
print("\nWalk plots before the burnin")
show_walk_plot(np.expand_dims(res.samples, axis=0))
if burnin > 0:
print("\nWalk plots after the burnin")
show_walk_plot(np.expand_dims(res.samples[indburnin:], axis=0))
plt.savefig(output_dir + 'Nested_walk_plots.pdf')
mean, cov = nestle.mean_and_cov(res.samples[indburnin:],
res.weights[indburnin:])
print("\nWeighted mean +- sqrt(covariance)")
print("Radius = {:.3f} +/- {:.3f}".format(mean[0], np.sqrt(cov[0, 0])))
print("Theta = {:.3f} +/- {:.3f}".format(mean[1], np.sqrt(cov[1, 1])))
print("Flux = {:.3f} +/- {:.3f}".format(mean[2], np.sqrt(cov[2, 2])))
if save:
with open(output_dir + 'Nested_sampling.txt', "w") as f:
f.write('#################################\n')
f.write('#### CONFIDENCE INTERVALS ###\n')
f.write('#################################\n')
f.write(' \n')
f.write('Results of the NESTED SAMPLING fit\n')
f.write('----------------------------------\n ')
f.write(' \n')
f.write("\nWeighted mean +- sqrt(covariance)\n")
f.write("Radius = {:.3f} +/- {:.3f}\n".format(
mean[0], np.sqrt(cov[0, 0])))
f.write("Theta = {:.3f} +/- {:.3f}\n".format(
mean[1], np.sqrt(cov[1, 1])))
f.write("Flux = {:.3f} +/- {:.3f}\n".format(
mean[2], np.sqrt(cov[2, 2])))
if bins is None:
bins = int(np.sqrt(res.samples[indburnin:].shape[0]))
print("\nHist bins =", bins)
if save or plot:
ranges = None
fig = corner.corner(res.samples[indburnin:],
bins=bins,
labels=["$r$", r"$\theta$", "$f$"],
weights=res.weights[indburnin:],
range=ranges,
plot_contours=True)
fig.set_size_inches(8, 8)
if save:
plt.savefig(output_dir + 'Nested_corner.pdf')
print('\nConfidence intervals')
if save or plot:
_ = confidence(res.samples[indburnin:],
cfd=68,
bins=bins,
weights=res.weights[indburnin:],
gaussian_fit=True,
verbose=True,
save=False)
if save:
plt.savefig(output_dir + 'Nested_confi_hist_flux_r_theta_gaussfit.pdf')
final_res = np.array([[mean[0], np.sqrt(cov[0, 0])],
[mean[1], np.sqrt(cov[1, 1])],
[mean[2], np.sqrt(cov[2, 2])]])
return final_res
# The likelihood function:
def loglike(theta):
return -0.5 * (np.sum((y - model(theta, x))**2 / yerr**2))
# Defines a flat prior in 0 < m < 1, 0 < b < 100:
def prior_transform(theta):
return np.array([1., 100.]) * theta
# Run nested sampling
res = nestle.sample(loglike, prior_transform, 2, method='single', npoints=1000)
print(res.summary())
# weighted average and covariance:
p, cov = nestle.mean_and_cov(res.samples, res.weights)
print("m = {0:5.2f} +/- {1:5.2f}".format(p[0], np.sqrt(cov[0, 0])))
print("b = {0:5.2f} +/- {1:5.2f}".format(p[1], np.sqrt(cov[1, 1])))
plt.figure()
plt.errorbar(x, y, yerr=yerr, capsize=0, fmt='k.', ecolor='.7')
plt.plot([0., 10.], model(p, np.array([0., 10.])), c='k')
plt.show()
###############################################################################
# Plot samples to see the full posterior surface.
fig = corner.corner(res.samples,
weights=res.weights,
labels=['m', 'b'],
def __load_mean_and_covariance(self, results):
self.__means, self.__covariance = nestle.mean_and_cov(
results.samples, results.weights
)
def nest_lc(data, model, vparam_names, bounds, guess_amplitude_bound=False,
minsnr=5., priors=None, ppfs=None, npoints=100, method='single',
maxiter=None, maxcall=None, modelcov=False, rstate=None,
verbose=False, **kwargs):
"""Run nested sampling algorithm to estimate model parameters and evidence.
Parameters
----------
data : `~astropy.table.Table` or `~numpy.ndarray` or `dict`
Table of photometric data. Must include certain columns.
See the "Photometric Data" section of the documentation for
required columns.
model : `~sncosmo.Model`
The model to fit.
vparam_names : list
Model parameters to vary in the fit.
bounds : `dict`
Bounded range for each parameter. Bounds must be given for
each parameter, with the exception of ``t0``: by default, the
minimum bound is such that the latest phase of the model lines
up with the earliest data point and the maximum bound is such
that the earliest phase of the model lines up with the latest
data point.
guess_amplitude_bound : bool, optional
If true, bounds for the model's amplitude parameter are determined
automatically based on the data and do not need to be included in
`bounds`. The lower limit is set to zero and the upper limit is 10
times the amplitude "guess" (which is based on the highest-flux
data point in any band). Default is False.
minsnr : float, optional
Minimum signal-to-noise ratio of data points to use when guessing
amplitude bound. Default is 5.
priors : `dict`, optional
Prior probability distribution function for each parameter. The keys
should be parameter names and the values should be callables that
accept a float. If a parameter is not in the dictionary, the prior
defaults to a flat distribution between the bounds.
ppfs : `dict`, optional
Prior percent point function (inverse of the cumulative distribution
function) for each parameter. If a parameter is in this dictionary,
the ppf takes precedence over a prior pdf specified in ``priors``.
npoints : int, optional
Number of active samples to use. Increasing this value increases
the accuracy (due to denser sampling) and also the time
to solution.
method : {'classic', 'single', 'multi'}, optional
Method used to select new points. Choices are 'classic',
single-ellipsoidal ('single'), multi-ellipsoidal ('multi'). Default
is 'single'.
maxiter : int, optional
Maximum number of iterations. Iteration may stop earlier if
termination condition is reached. Default is no limit.
maxcall : int, optional
Maximum number of likelihood evaluations. Iteration may stop earlier
if termination condition is reached. Default is no limit.
modelcov : bool, optional
Include model covariance when calculating chisq. Default is False.
rstate : `~numpy.random.RandomState`, optional
RandomState instance. If not given, the global random state of the
``numpy.random`` module will be used.
verbose : bool, optional
Print running evidence sum on a single line.
Returns
-------
res : Result
Attributes are:
* ``niter``: total number of iterations
* ``ncall``: total number of likelihood function calls
* ``time``: time in seconds spent in iteration loop.
* ``logz``: natural log of the Bayesian evidence Z.
* ``logzerr``: estimate of uncertainty in logz (due to finite sampling)
* ``h``: Bayesian information.
* ``vparam_names``: list of parameter names varied.
* ``samples``: 2-d `~numpy.ndarray`, shape is (nsamples, nparameters).
Each row is the parameter values for a single sample. For example,
``samples[0, :]`` is the parameter values for the first sample.
* ``logprior``: 1-d `~numpy.ndarray` (length=nsamples);
log(prior volume) for each sample.
* ``logl``: 1-d `~numpy.ndarray` (length=nsamples); log(likelihood)
for each sample.
* ``weights``: 1-d `~numpy.ndarray` (length=nsamples);
Weight corresponding to each sample. The weight is proportional to
the prior * likelihood for the sample.
* ``parameters``: 1-d `~numpy.ndarray` of weighted-mean parameter
values from samples (including fixed parameters). Order corresponds
to ``model.param_names``.
* ``covariance``: 2-d `~numpy.ndarray` of parameter covariance;
indicies correspond to order of ``vparam_names``. Calculated from
``samples`` and ``weights``.
* ``errors``: OrderedDict of varied parameter uncertainties.
Corresponds to square root of diagonal entries in covariance matrix.
* ``ndof``: Number of degrees of freedom (len(data) -
len(vparam_names)).
* ``bounds``: Dictionary of bounds on varied parameters (including
any automatically determined bounds).
estimated_model : `~sncosmo.Model`
A copy of the model with parameters set to the values in
``res.parameters``.
"""
try:
import nestle
except ImportError:
raise ImportError("nest_lc() requires the nestle package.")
if "nobj" in kwargs:
warn("The nobj keyword is deprecated and will be removed in a future "
"sncosmo release. Use `npoints` instead.")
npoints = kwargs.pop("nobj")
# experimental parameters
tied = kwargs.get("tied", None)
data = photometric_data(data)
data.sort_by_time()
model = copy.copy(model)
bounds = copy.copy(bounds) # need to copy this b/c we modify it below
# Order vparam_names the same way it is ordered in the model:
vparam_names = [s for s in model.param_names if s in vparam_names]
# Drop data that the model doesn't cover.
data = cut_bands(data, model, z_bounds=bounds.get('z', None))
if guess_amplitude_bound:
if model.param_names[2] not in vparam_names:
raise ValueError("Amplitude bounds guessing enabled but "
"amplitude parameter {0!r} is not varied"
.format(model.param_names[2]))
if model.param_names[2] in bounds:
raise ValueError("cannot supply bounds for parameter {0!r}"
" when guess_amplitude_bound=True"
.format(model.param_names[2]))
# If redshift is bounded, set model redshift to midpoint of bounds
# when doing the guess.
if 'z' in bounds:
model.set(z=sum(bounds['z']) / 2.)
_, amplitude = guess_t0_and_amplitude(data, model, minsnr)
bounds[model.param_names[2]] = (0., 10. * amplitude)
# Find t0 bounds to use, if not explicitly given
if 't0' in vparam_names and 't0' not in bounds:
bounds['t0'] = t0_bounds(data, model)
if ppfs is None:
ppfs = {}
if tied is None:
tied = {}
# Convert bounds/priors combinations into ppfs
if bounds is not None:
for key, val in six.iteritems(bounds):
if key in ppfs:
continue # ppfs take priority over bounds/priors
a, b = val
if priors is not None and key in priors:
# solve ppf at discrete points and return interpolating
# function
x_samples = np.linspace(0., 1., 101)
ppf_samples = ppf(priors[key], x_samples, a, b)
f = Interp1D(0., 1., ppf_samples)
else:
f = Interp1D(0., 1., np.array([a, b]))
ppfs[key] = f
# NOTE: It is important that iparam_names is in the same order
# every time, otherwise results will not be reproducible, even
# with same random seed. This is because iparam_names[i] is
# matched to u[i] below and u will be in a reproducible order,
# so iparam_names must also be.
iparam_names = [key for key in vparam_names if key in ppfs]
ppflist = [ppfs[key] for key in iparam_names]
npdim = len(iparam_names) # length of u
ndim = len(vparam_names) # length of v
# Check that all param_names either have a direct prior or are tied.
for name in vparam_names:
if name in iparam_names:
continue
if name in tied:
continue
raise ValueError("Must supply ppf or bounds or tied for parameter '{}'"
.format(name))
def prior_transform(u):
d = {}
for i in range(npdim):
d[iparam_names[i]] = ppflist[i](u[i])
v = np.empty(ndim, dtype=np.float)
for i in range(ndim):
key = vparam_names[i]
if key in d:
v[i] = d[key]
else:
v[i] = tied[key](d)
return v
# Indicies of the model parameters in vparam_names
idx = np.array([model.param_names.index(name) for name in vparam_names])
def loglike(parameters):
model.parameters[idx] = parameters
return -0.5 * chisq(data, model, modelcov=modelcov)
t0 = time.time()
res = nestle.sample(loglike, prior_transform, ndim, npdim=npdim,
npoints=npoints, method=method, maxiter=maxiter,
maxcall=maxcall, rstate=rstate,
callback=(nestle.print_progress if verbose else None))
elapsed = time.time() - t0
# estimate parameters and covariance from samples
vparameters, cov = nestle.mean_and_cov(res.samples, res.weights)
# update model parameters to estimated ones.
model.set(**dict(zip(vparam_names, vparameters)))
# `res` is a nestle.Result object. Collect result into a sncosmo.Result
# object for consistency, and add more fields.
res = Result(niter=res.niter,
ncall=res.ncall,
logz=res.logz,
logzerr=res.logzerr,
h=res.h,
samples=res.samples,
weights=res.weights,
logvol=res.logvol,
logl=res.logl,
vparam_names=copy.copy(vparam_names),
ndof=len(data) - len(vparam_names),
bounds=bounds,
time=elapsed,
parameters=model.parameters.copy(),
covariance=cov,
errors=OrderedDict(zip(vparam_names,
np.sqrt(np.diagonal(cov)))),
param_dict=OrderedDict(zip(model.param_names,
model.parameters)))
# Deprecated result fields.
depmsg = ("The `param_names` attribute is deprecated in sncosmo v1.0 "
"and will be removed in a future release. "
"Use `vparam_names` instead.")
res.__dict__['deprecated']['param_names'] = (res.vparam_names, depmsg)
depmsg = ("The `logprior` attribute is deprecated in sncosmo v1.2 "
"and will be changed in a future release. "
"Use `logvol` instead.")
res.__dict__['deprecated']['logprior'] = (res.logvol, depmsg)
return res, model
def __load_mean_and_covariance(self, results):
self.__means, self.__covariance = nestle.mean_and_cov(
results.samples, results.weights)
def __save_cov_data(save_name, results):
mean, cov = nestle.mean_and_cov(results.samples, results.weights)
numpy.save(save_name + ".npy", {"mean": mean, "cov": cov})
def loglike(theta):
return -0.5*(np.sum((y-model(theta, x))**2/yerr**2))
# Defines a flat prior in 0 < m < 1, 0 < b < 100:
def prior_transform(theta):
return np.array([1., 100.]) * theta
# Run nested sampling
res = nestle.sample(loglike, prior_transform, 2, method='single',
npoints=1000)
print(res.summary())
# weighted average and covariance:
p, cov = nestle.mean_and_cov(res.samples, res.weights)
print("m = {0:5.2f} +/- {1:5.2f}".format(p[0], np.sqrt(cov[0, 0])))
print("b = {0:5.2f} +/- {1:5.2f}".format(p[1], np.sqrt(cov[1, 1])))
plt.figure()
plt.errorbar(x, y, yerr=yerr, capsize=0, fmt='k.', ecolor='.7')
plt.plot([0., 10.], model(p, np.array([0., 10.])), c='k')
plt.show()
###############################################################################
# Plot samples to see the full posterior surface.
fig = corner.corner(res.samples, weights=res.weights, labels=['m', 'b'],
range=[0.99999, 0.99999], truths=theta_true, bins=30)
plt.show()
def __save_cov_data(save_name, results):
mean, cov = nestle.mean_and_cov(results.samples, results.weights)
numpy.save(save_name + ".npy", {"mean": mean, "cov": cov})