def test_two_gaussian_nest():
np.random.seed(0)
# gaussians centered at (1, 1) and (-1, -1)
mu1 = np.ones(2)
mu2 = -np.ones(2)
# Width of 0.1 in each dimension
sigma = 0.1
ivar = 1.0/(sigma*sigma)
sigma1inv = np.diag([ivar, ivar])
sigma2inv = np.diag([ivar, ivar])
def logl(x):
dx1 = x - mu1
dx2 = x - mu2
return np.logaddexp(-np.dot(dx1, np.dot(sigma1inv, dx1))/2.0,
-np.dot(dx2, np.dot(sigma2inv, dx2))/2.0)
# Use a flat prior, over [-5, 5] in both dimensions
def prior(x):
return 10.0 * x - 5.0
res = nestle.nest(logl, prior, 2, nobj=100)
# (Approximate) analytic evidence for two identical Gaussian blobs,
# over a uniform prior [-5:5][-5:5] with density 1/100 in this domain:
analytic_logz = np.log(2.0 * 2.0*np.pi*sigma*sigma / 100.0)
# Note that this is a terrible test and only works for this
# specific random seed.
assert abs(res.logz - analytic_logz) < res.logzerr
def test_two_gaussian_nest():
# (Approximate) analytic evidence for two identical Gaussian blobs,
# over a uniform prior [-5:5][-5:5] with density 1/100 in this domain:
analytic_evidence = np.log(2.0 * 2.0 * np.pi * sigma * sigma / 100.0)
res = nestle.nest(logl, prior, 2, nobj=100)
print "logz =", res.logz, " +/- ", res.logzerr
print "analytic", analytic_evidence
return -0.5*(np.sum((y-model)**2/yerr**2))
def prior(theta):
return np.array([10.0, 20.0])*theta+np.array([-5.0, -10.0])
def prior1(x):
"""
Uniform prior, this maps x=[0, 1) to m, c in -5, 5
"""
return 10.0*x-5.0
start=time()
#perform sampling
res = nt.nest(lnlike, prior, 2, nobj=1000, maxiter=100000)
#perform sampling for different model
res_poly=nt.nest(lnlike_poly, prior1, 3, nobj=1000, maxiter=100000)
end=time()
#prints output, can compare evidence
print "\nEvidence is:", res.logz
print "Best fit slope value:\t ", np.median(res.samples[:,0]), np.median(res.samples[:,1])
print "\nEvidence for degree 2 polynomial is: \t", res_poly.logz
print "\nTime it took (in seconds) \t:", end-start
#use the fabulous triangle plot machinery to show the samples
a=z*(1-q0)/(np.sqrt(1+2*q0*z)+1+q0*z )
dl=(1+a)*c*z/h0
return dl
except:
return np.inf
def lnlikel(theta):
"""
Define chi_sq likelihood
"""
sn1=sn[2:3]
z=sn1[:,0]; mag=sn1[:,1]; sig=sn1[:,2]
#dl=lum_dist(z, theta[0], theta[1])
#uses cosmocalc distance measurement
#model=dist.mod(z)
model= z**2
return -0.5*np.sum((mag-model)**2/sig**2.)
def prior(u):
"""
define prior on omega_lam and omega_m
"""
return 2.0*u
res=nt.nest(lnlikel, prior, 2)
