def ff(self, x, mu, sigma):
r"""
Failure (CDF or unreliability) function for the LogNormal Distribution:
.. math::
F(x) = \Phi \left( \frac{\ln(x) - \mu}{\sigma} \right )
Parameters
----------
x : numpy array or scalar
The values at which the function will be calculated
mu : numpy array or scalar
The location parameter for the LogNormal distribution
sigma : numpy array or scalar
The scale parameter for the LogNormal distribution
Returns
-------
ff : scalar or numpy array
The value(s) of the failure function at x.
Examples
--------
>>> import numpy as np
>>> from surpyval import LogNormal
>>> x = np.array([1, 2, 3, 4, 5])
>>> LogNormal.ff(x, 3, 4)
array([0.22662735, 0.28206661, 0.31726986, 0.34331728, 0.36405509])
"""
return norm.cdf(np.log(x), mu, sigma)
def ff(self, x, mu, sigma):
r"""
CDF (or unreliability or failure) function for the Normal Distribution:
.. math::
F(x) = \Phi \left( \frac{x - \mu}{\sigma} \right )
Parameters
----------
x : numpy array or scalar
The values at which the function will be calculated
mu : numpy array or scalar
The location parameter for the Normal distribution
sigma : numpy array or scalar
The scale parameter for the Normal distribution
Returns
-------
ff : scalar or numpy array
The value(s) of the failure function at x.
Examples
--------
>>> import numpy as np
>>> from surpyval import Normal
>>> x = np.array([1, 2, 3, 4, 5])
>>> Normal.ff(x, 3, 4)
array([0.30853754, 0.40129367, 0.5 , 0.59870633, 0.69146246])
"""
return norm.cdf(x, mu, sigma)
def reparameterize(x, prior=None):
if prior == None:
return x
elif prior == 'horseshoe':
eta = np.tan(.5 * np.pi * norm.cdf(x))
return eta**2 * x
elif prior == 'exp':
return -np.log(x)
elif prior == 'laplace':
return -np.sign(x) * np.log(1 - 2 * x)
elif prior == 'lognorm':
return np.exp(x)
elif prior == 'IG':
return 1 / x
elif prior == 'dropout':
return npr.binomial(1, .8, size=x.shape) * x
def expected_new_max(mean, std, max_so_far):
return max_so_far - \
(mean - max_so_far) * norm.cdf(mean, max_so_far, std) \
+ std * norm.pdf(mean, max_so_far, std)
def probability_of_improvement(mean, std, max_so_far):
return norm.cdf(max_so_far, mean, std)
import autograd.numpy as np
import pylab as plt
from autograd.scipy.stats import norm, t, multivariate_normal as mvn
import GPy
from util import plot_with_uncertainty
import ep_unimodality_2d as ep
from importlib import reload
reload(ep)
# auxilary functions
phi = lambda x: norm.cdf(x)
npdf = lambda x, m, v: 1. / np.sqrt(2 * np.pi * v) * np.exp(-(x - m)**2 /
(2 * v))
####################################################################################################################################################3
# Parameters
####################################################################################################################################################3
# set seed
np.random.seed(1000)
# dimension
D = 4
####################################################################################################################################################3
# Define test objective function
####################################################################################################################################################3
def objective(p):
return norm.cdf(p)
def _cumulative_hazard(self, params, times):
mu_, sigma_ = params
Z = (np.log(times) - mu_) / sigma_
cdf = norm.cdf(Z, loc=0, scale=1)
cdf = np.clip(cdf, 0.0, 1 - 1e-14)
return -np.log1p(-cdf)