def run_mcmc(meas, x, nsamples, covm=None, scales=None):
"""
Sample the likelihood space with a Markov Chain Monte Carlo.
:param meas: TemplateMeasurement
measurement whose spectrum likelihood space is to be probe
:param x: [float]
parameter values where to start the chain
:param covm: [[float]]
covariance matrix values if sampling transformed space
:param scales: [float]
parameter scales if not sampling transformed space
:return: [float], [float], [float], pymcmc.MCMC
posterior mean, lower CI, upper CI for each parameter, and the MCMC
object used for sampling
"""
mcmc = MCMC(meas.spec.npars)
mcmc.set_values(x)
if covm is not None and scales is None:
mcmc.set_covm(covm)
elif scales is not None:
mcmc.set_scales(scales)
else:
raise ValueError("Must provide covariance OR scales")
mcmc.rescale = 2 # good starting point
mcmc.learn_scale(meas.spec.ll, 1000)
mcmc.run(meas.spec.ll, nsamples)
mean = list()
mean_down = list()
mean_up = list()
for ipar in range(meas.spec.npars):
mean.append(np.mean(mcmc.data[:, ipar]))
low, high, _, _ = npinterval.interval(mcmc.data[:, ipar], 0.6827)
mean_down.append(low-mean[-1])
mean_up.append(high-mean[-1])
return mean, mean_down, mean_up, mcmc
def probe_results(scales, ntrials, ndims, mode):
"""
Probe a grid of results at various scales.
:param scales: iterable
rescale values at which to run MCMCs
:param ntrials: int
number of trials at each scale
:param ndims: int
dimension of space to probe
:param mode: str
{var, over, pca}
var: scale by the known variance of each parameter
over: over-estimate the variance of each parameter
pca: tranform to the PCA space
"""
if mode not in {'var', 'over', 'pca'}:
raise ValueError("Unknown probe mode: %s" % mode)
results = list()
for scale in scales:
for _ in range(ntrials):
norm = MultiNorm(ndims)
mcmc = MCMC(norm._ndims)
mcmc.verbose = False
mcmc.rescale = scale
if mode == 'var':
# Use the know variance of each paramete as the proposal scale
mcmc.set_scales(norm._sigs)
elif mode == 'over':
# Overestimate the variances by up to 50% (typical)
mcmc.set_scales(
norm._sigs *
(np.random.rand(norm._ndims)/2.+1))
elif mode == 'pca':
# Transform the proposal to a space of independent variables
mcmc.set_covm(norm._cov)
mcmc.run(norm.loglikelihood, 10000)
data = mcmc.data[0::1]
results.append((scale, performance(norm, data), mcmc.getrate()))
print('%.1f: %.3f, %.2f' % results[-1])
results = np.array(results)
plt.xlabel(r'scale')
plt.ylabel(r'$\langle |\Delta\sigma| / \sigma \rangle$')
plt.plot(results[:, 0], results[:, 1], 'o')
plt.savefig('%d_%s_scale.pdf' % (ndims, mode), format='pdf')
plt.clf()
plt.xlabel(r'acceptance rate')
plt.ylabel(r'$\langle |\Delta\sigma| / \sigma \rangle$')
plt.plot(results[:, 2], results[:, 1], 'o')
plt.savefig('%d_%s_accept.pdf' % (ndims, mode), format='pdf')
plt.clf()
def run_mcmc(meas, x, nsamples, covm=None, scales=None):
"""
Sample the likelihood space with a Markov Chain Monte Carlo.
:param meas: TemplateMeasurement
measurement whose spectrum likelihood space is to be probe
:param x: [float]
parameter values where to start the chain
:param covm: [[float]]
covariance matrix values if sampling transformed space
:param scales: [float]
parameter scales if not sampling transformed space
:return: [float], [float], [float], pymcmc.MCMC
posterior mean, lower CI, upper CI for each parameter, and the MCMC
object used for sampling
"""
mcmc = MCMC(meas.spec.npars)
mcmc.set_values(x)
if covm is not None and scales is None:
mcmc.set_covm(covm)
elif scales is not None:
mcmc.set_scales(scales)
else:
raise ValueError("Must provide covariance OR scales")
mcmc.rescale = 2 # good starting point
mcmc.learn_scale(meas.spec.ll, 1000)
mcmc.run(meas.spec.ll, nsamples)
mean = list()
mean_down = list()
mean_up = list()
for ipar in range(meas.spec.npars):
mean.append(np.mean(mcmc.data[:, ipar]))
low, high, _, _ = npinterval.interval(mcmc.data[:, ipar], 0.6827)
mean_down.append(low - mean[-1])
mean_up.append(high - mean[-1])
return mean, mean_down, mean_up, mcmc
plt.ylabel(r'$\langle |\Delta\sigma| / \sigma \rangle$')
plt.plot(results[:, 2], results[:, 1], 'o')
plt.savefig('%d_%s_accept.pdf' % (ndims, mode), format='pdf')
plt.clf()
# Set some formatting options for numpy and pyplot
np.set_printoptions(precision=2, suppress=True)
plt.rc('text', usetex=True)
plt.rc('font', family='serif')
rescale = 2.5
# 1D simple calse
norm = MultiNorm(1)
mcmc = MCMC(norm._ndims)
mcmc.rescale = rescale
mcmc.set_scales(norm._sigs)
mcmc.run(norm.loglikelihood, 10000)
data = mcmc.data[0::1]
draw_axis(norm, 0, data)
plt.savefig('axis_1D.pdf', format='pdf')
plt.clf()
trace_axis(norm, 0, data[:1000])
plt.savefig('trace_1D.pdf', format='pdf')
plt.clf()
# 1D asymmetric case
norm = MultiNorm(1, mus=[0], sigs=[1], cut=(float('-inf'), 0))
mcmc = MCMC(norm._ndims)
mcmc.rescale = rescale