def test_lnsigma(self):
# check that lnsigma works correctly
def lnprior(theta, x, y, yerr):
m, b, lnf = theta
if -5.0 < m < 0.5 and 0.0 < b < 10.0 and -10.0 < lnf < 1.0:
return 0.0
return -np.inf
def lnlike(theta, x, y, yerr):
m, b, lnf = theta
model = m * x + b
inv_sigma2 = 1.0 / (yerr**2 + model**2 * np.exp(2 * lnf))
print(inv_sigma2)
return -0.5 * (np.sum((y - model)**2 * inv_sigma2 -
np.log(inv_sigma2)))
x, y, yerr, _ = self.data.data
theta = [self.m_true, self.b_true, np.log(self.f_true)]
bo = BaseObjective(theta,
lnlike,
lnprior=lnprior,
fcn_args=(x, y, yerr))
lnsigma = Parameter(np.log(self.f_true),
'lnsigma',
bounds=(-10, 1),
vary=True)
self.objective.setp(np.array([self.b_true, self.m_true]))
self.objective.lnsigma = lnsigma
assert_allclose(self.objective.lnlike(), bo.lnlike())
def test_lnsigma(self):
# check that lnsigma works correctly, by using the emcee line fit
# example
def logp(theta, x, y, yerr):
m, b, lnf = theta
if -5.0 < m < 0.5 and 0.0 < b < 10.0 and -10.0 < lnf < 1.0:
return 0.0
return -np.inf
def logl(theta, x, y, yerr):
m, b, lnf = theta
model = m * x + b
inv_sigma2 = 1.0 / (yerr**2 + model**2 * np.exp(2 * lnf))
print(inv_sigma2)
return -0.5 * (np.sum((y - model)**2 * inv_sigma2 -
np.log(inv_sigma2)))
x, y, yerr, _ = self.data.data
theta = [self.m_true, self.b_true, np.log(self.f_true)]
bo = BaseObjective(theta, logl, logp=logp, fcn_args=(x, y, yerr))
lnsigma = Parameter(np.log(self.f_true),
'lnsigma',
bounds=(-10, 1),
vary=True)
self.objective.setp(np.array([self.b_true, self.m_true]))
self.objective.lnsigma = lnsigma
# amendment factor because dfm emcee example does not include 2pi
amend = 0.5 * self.objective.npoints * np.log(2 * np.pi)
assert_allclose(self.objective.logl() + amend, bo.logl())
def test_base_emcee(self):
# check that the base objective works against the emcee example.
def lnprior(theta, x, y, yerr):
m, b, lnf = theta
if -5.0 < m < 0.5 and 0.0 < b < 10.0 and -10.0 < lnf < 1.0:
return 0.0
return -np.inf
def lnlike(theta, x, y, yerr):
m, b, lnf = theta
model = m * x + b
inv_sigma2 = 1.0 / (yerr**2 + model**2 * np.exp(2 * lnf))
return -0.5 * (np.sum((y - model)**2 * inv_sigma2 -
np.log(inv_sigma2)))
x, y, yerr, _ = self.data.data
theta = [self.m_true, self.b_true, np.log(self.f_true)]
bo = BaseObjective(theta,
lnlike,
lnprior=lnprior,
fcn_args=(x, y, yerr))
# test that the wrapper gives the same lnlike as the direct function
assert_almost_equal(bo.lnlike(theta), lnlike(theta, x, y, yerr))
assert_almost_equal(bo.lnlike(theta), -bo.nll(theta))
assert_almost_equal(bo.nll(theta), 12.8885352412)
# Find the maximum likelihood value.
result = minimize(bo.nll, theta)
# for repeatable sampling
np.random.seed(1)
ndim, nwalkers = 3, 100
pos = [
result["x"] + 1e-4 * np.random.randn(ndim) for i in range(nwalkers)
]
sampler = emcee.EnsembleSampler(nwalkers, ndim, bo.lnprob)
sampler.run_mcmc(pos, 800, rstate0=np.random.get_state())
burnin = 200
samples = sampler.chain[:, burnin:, :].reshape((-1, ndim))
samples[:, 2] = np.exp(samples[:, 2])
m_mc, b_mc, f_mc = map(
lambda v: (v[1], v[2] - v[1], v[1] - v[0]),
zip(*np.percentile(samples, [16, 50, 84], axis=0)))
assert_allclose(m_mc, (-1.0071664, 0.0809444, 0.0784894), rtol=0.04)
assert_allclose(b_mc, (4.5428107, 0.3549174, 0.3673304), rtol=0.04)
assert_allclose(f_mc, (0.4610898, 0.0823304, 0.0640812), rtol=0.06)
# # smoke test for covariance matrix
bo.parameters = np.array(result['x'])
covar1 = bo.covar()
uncertainties = np.sqrt(np.diag(covar1))
# covariance from objective._covar should be almost equal to
# the covariance matrix from sampling
covar2 = np.cov(samples.T)
assert_almost_equal(np.sqrt(np.diag(covar2))[:2], uncertainties[:2], 2)
# check covariance of self.objective
# TODO
var_arr = result['x'][:]
var_arr[0], var_arr[1], var_arr[2] = var_arr[2], var_arr[1], var_arr[0]