def testDensitySymmetries(self):
# check flipping samples gives flipped density
samps = Gaussian1D(0, 1, xmin=-1, xmax=4).MCSamples(12000)
d = samps.get1DDensity('x')
samps.samples[:, 0] *= -1
samps = MCSamples(samples=samps.samples, names=['x'], ranges={'x': [-4, 1]})
d2 = samps.get1DDensity('x')
self.assertTrue(np.allclose(d.P, d2.P[::-1]))
samps = Gaussian2D([0, 0], np.diagflat([1, 2]), xmin=-1, xmax=2, ymin=0, ymax=3).MCSamples(12000)
d = samps.get2DDensity('x', 'y')
samps.samples[:, 0] *= -1
samps = MCSamples(samples=samps.samples, names=['x', 'y'], ranges={'x': [-2, 1], 'y': [0, 3]})
d2 = samps.get2DDensity('x', 'y')
self.assertTrue(np.allclose(d.P, d2.P[:, ::-1]))
samps.samples[:, 0] *= -1
samps.samples[:, 1] *= -1
samps = MCSamples(samples=samps.samples, names=['x', 'y'], ranges={'x': [-1, 2], 'y': [-3, 0]})
d2 = samps.get2DDensity('x', 'y')
self.assertTrue(np.allclose(d.P, d2.P[::-1, ::], atol=1e-5))
def testDensitySymmetries(self):
# check flipping samples gives flipped density
samps = Gaussian1D(0, 1, xmin=-1, xmax=4).MCSamples(12000)
d = samps.get1DDensity('x')
samps.samples[:, 0] *= -1
samps = MCSamples(samples=samps.samples, names=['x'], ranges={'x': [-4, 1]})
d2 = samps.get1DDensity('x')
self.assertTrue(np.allclose(d.P, d2.P[::-1]))
samps = Gaussian2D([0, 0], np.diagflat([1, 2]), xmin=-1, xmax=2, ymin=0, ymax=3).MCSamples(12000)
d = samps.get2DDensity('x', 'y')
samps.samples[:, 0] *= -1
samps = MCSamples(samples=samps.samples, names=['x', 'y'], ranges={'x': [-2, 1], 'y': [0, 3]})
d2 = samps.get2DDensity('x', 'y')
self.assertTrue(np.allclose(d.P, d2.P[:, ::-1]))
samps.samples[:, 0] *= -1
samps.samples[:, 1] *= -1
samps = MCSamples(samples=samps.samples, names=['x', 'y'], ranges={'x': [-1, 2], 'y': [-3, 0]})
d2 = samps.get2DDensity('x', 'y')
self.assertTrue(np.allclose(d.P, d2.P[::-1, ::], atol=1e-5))
def _add_prior_density(self, plotter, posterior,
ndraws, normalize,
KL_divergence, KL_base,
bootstrap, n_simulate):
""" Crudely estimate the prior density.
Kullback-Leibler divergence estimated in bits for a combined run or
the same run for which the credible intervals are calculated.
"""
run = posterior.subset_to_plot[0]
yield 'Plotting prior for posterior %s...' % posterior.ID
l = posterior.likelihood
if l is None:
return # quietly do nothing
elif not hasattr(l, 'prior'):
return
elif not hasattr(l.prior, 'draw'):
return
elif not callable(l.prior.draw):
return
samples, _ = l.prior.draw(ndraws, transform=True)
color, lw = (run.contours[key] for key in ('color', 'lw'))
quantiles = [None] * 3
with verbose(KL_divergence,
'Estimating 1D marginal KL-divergences in %s' % KL_base,
'Estimated 1D marginal KL-divergences') as condition:
for i, ax in enumerate([plotter.subplots[i,i] \
for i in range(plotter.subplots.shape[0])]):
name = self.params.names[i]
bounds = {name: posterior.bounds[name]}
settings = {'fine_bins': 1024,
'smooth_scale_1D': 0.3,
'boundary_correction_order': 1,
'mult_bias_correction_order': 1} # adopt from posterior settings or take custom input?
idx = l.index(name)
if idx is None: idx = l.prior.index(name)
bcknd = MCSamples(sampler='uncorrelated',
samples=samples[:,idx],
weights=None,
names=[name],
ranges=bounds,
settings=settings)
if normalize:
bcknd.get1DDensity(name).normalize(by='integral',
in_place=True)
x = _np.linspace(ax.xaxis.get_view_interval()[0],
ax.xaxis.get_view_interval()[1],
1000)
ax.plot(x, bcknd.get1DDensity(name).Prob(x),
ls='-.', color=color, lw=lw)
if not condition: continue # go to next iteration if no KL
# a prototype Kullback-Leibler divergence callback
# information in bits
def KL(ns_run, logw):
x = ns_run['theta'][:,posterior.get_index(name)]
w_rel = _np.exp(logw - logw.max())
where = w_rel > run.kde_settings.get('min_weight_ratio',
1.0e-30)
prior = bcknd.get1DDensity(name).Prob(x[where])
p = getdist_kde(x[where], x, w_rel,
ranges=[posterior.bounds[name]],
idx=0,
normalize=normalize,
settings=run.kde_settings)
# Due to spline interpolation, very small densities can be
# negative, so manually give a small postive value which
# does not affect KL integral approximation
p[p<=0.0] = p[p>0.0].min()
KL = _np.sum(w_rel[where] \
* (_np.log(p) - _np.log(prior))) \
/_np.sum(w_rel[where])
if KL_base == 'bits':
return KL / _np.log(2.0)
elif KL_base == 'nats':
return KL
else:
raise ValueError('Invalid base for KL-divergence.')
if bootstrap:
for j, cred_int in enumerate([0.025, 0.5, 0.975]):
quantiles[j] = run_ci_bootstrap(run.nestcheck_backend,
estimator_list=[KL],
cred_int=cred_int,
n_simulate=n_simulate,
simulate_weights=True,
flip_skew=True)
# KL in bits
interval = r'$D_{\mathrm{KL}}=%.2f_{-%.2f}^{+%.2f}$' \
% (quantiles[1],
quantiles[1] - quantiles[0],
quantiles[2] - quantiles[1])
yield ('%s KL-divergence = %.4f/-%.4f/+%.4f'
% (name,
quantiles[1],
quantiles[1] - quantiles[0],
quantiles[2] - quantiles[1]))
if not rcParams['text.usetex']:
fontsize = plotter.settings.lab_fontsize - 1
else:
fontsize = plotter.settings.lab_fontsize
ax.set_title(interval, color=color,
fontsize=fontsize)
else:
where = run.samples[:,0] > 0.0
ns_run = {'theta': run.samples[where,2:]}
divergence = KL(ns_run, _np.log(run.samples[where,0]))
yield ('%s KL-divergence = %.4f' % (name, divergence))
divergence = (r'$D_{\mathrm{KL}}=%.2f$' % divergence)
if not rcParams['text.usetex']:
fontsize = plotter.settings.lab_fontsize - 1
else:
fontsize = plotter.settings.lab_fontsize
ax.set_title(divergence, color=color,
fontsize=fontsize)
yield None