def test_probability_model_mcmc():
np.random.seed(100)
mu, sigma = 10, 1 # true mean and standard deviation
np.random.seed(1)
data = np.random.normal(mu, sigma, 100).reshape((-1, 1))
p0 = Uniform(loc=0., scale=15)
p1 = Lognormal(s=1., loc=0., scale=1.)
prior = JointIndependent(marginals=[p0, p1])
# create an instance of class Model
candidate_model = DistributionModel(distributions=Normal(loc=None,
scale=None),
n_parameters=2,
prior=prior)
sampling = MetropolisHastings(jump=10,
burn_length=10,
seed=[1.0, 0.2],
random_state=1)
bayes_estimator = BayesParameterEstimation(sampling_class=sampling,
inference_model=candidate_model,
data=data,
nsamples=5)
s = bayes_estimator.sampler.samples
assert s[0, 1] == 3.5196936384257835
assert s[1, 0] == 11.143811671048994
assert s[2, 0] == 10.162512455643435
assert s[3, 1] == 0.8541521389437781
assert s[4, 1] == 1.0095454025762525
def test_probability_model_importance_sampling():
# Generate data from a probability model, here a Gaussian pdf, then learn its parameters,
# mean and covariance, from this data
np.random.seed(100)
mu, sigma = 10, 1 # true mean and standard deviation
np.random.seed(1)
data = np.random.normal(mu, sigma, 100).reshape((-1, 1))
p0 = Uniform(loc=0., scale=15)
p1 = Lognormal(s=1., loc=0., scale=1.)
prior = JointIndependent(marginals=[p0, p1])
# create an instance of class Model
candidate_model = DistributionModel(distributions=Normal(loc=None,
scale=None),
n_parameters=2,
prior=prior)
sampling = ImportanceSampling(random_state=1)
bayes_estimator = BayesParameterEstimation(sampling_class=sampling,
inference_model=candidate_model,
data=data,
nsamples=10000)
bayes_estimator.sampler.resample()
s_posterior = bayes_estimator.sampler.unweighted_samples
assert s_posterior[0, 1] == 0.8616126410951304
assert s_posterior[9999, 0] == 10.02449120238032
def test_bic():
data = Gamma(a=2, loc=0, scale=2).rvs(nsamples=500, random_state=12)
m0 = DistributionModel(distributions=Gamma(a=None, loc=None, scale=None), n_parameters=3, name='gamma')
m1 = DistributionModel(distributions=Exponential(loc=None, scale=None), n_parameters=2, name='exponential')
m2 = DistributionModel(distributions=ChiSquare(df=None, loc=None, scale=None),
n_parameters=3, name='chi-square')
candidate_models = [m0, m1, m2]
mle1 = MLE(inference_model=m0, random_state=0, data=data)
mle2 = MLE(inference_model=m1, random_state=0, data=data)
mle3 = MLE(inference_model=m2, random_state=0, data=data)
selector = InformationModelSelection(parameter_estimators=[mle1, mle2, mle3], criterion=BIC(),
n_optimizations=[5]*3)
selector.sort_models()
assert 0.5000000575021204 == selector.probabilities[0]
assert 0.4999999424978796 == selector.probabilities[1]
assert 3.939737591540338e-18 == selector.probabilities[2]
def test_aic():
data = Gamma(a=2, loc=0, scale=2).rvs(nsamples=500, random_state=12)
m0 = DistributionModel(distributions=Gamma(a=None, loc=None, scale=None), n_parameters=3, name='gamma')
m1 = DistributionModel(distributions=Exponential(loc=None, scale=None), n_parameters=2, name='exponential')
m2 = DistributionModel(distributions=ChiSquare(df=None, loc=None, scale=None),
n_parameters=3, name='chi-square')
candidate_models = [m0, m1, m2]
mle1 = MLE(inference_model=m0, random_state=0, data=data)
mle2 = MLE(inference_model=m1, random_state=0, data=data)
mle3 = MLE(inference_model=m2, random_state=0, data=data)
selector = InformationModelSelection(parameter_estimators=[mle1, mle2, mle3], criterion=AIC(),
n_optimizations=[5]*3)
selector.sort_models()
assert 2285.9685816790425 == selector.criterion_values[0]
assert 2285.9685821390594 == selector.criterion_values[1]
assert 2368.9477307542193 == selector.criterion_values[2]
def test_simple_probability_model():
np.random.seed(1)
mu, sigma = 0, 0.1 # true mean and standard deviation
data_1 = np.random.normal(mu, sigma, 1000).reshape((-1, 1))
# set parameters to be learnt as None
dist = Normal(loc=None, scale=None)
candidate_model = DistributionModel(distributions=dist, n_parameters=2)
ml_estimator = MLE(inference_model=candidate_model,
data=data_1,
n_optimizations=3,
random_state=1)
assert ml_estimator.mle[0] == 0.003881247615960185
assert ml_estimator.mle[1] == 0.09810041339322118
import numpy as np
from UQpy.inference import *
from UQpy.distributions import *
from UQpy.inference.inference_models.DistributionModel import DistributionModel
# data used throughout
from UQpy.inference.information_criteria import BIC, AICc
from UQpy.sampling.mcmc import MetropolisHastings
data = [0., 1., -1.5, -0.2]
# first candidate model, 1-dimensional
prior = Lognormal(s=1., loc=0., scale=1.)
dist = Normal(loc=0., scale=None)
candidate_model = DistributionModel(n_parameters=1,
distributions=dist,
prior=prior)
candidate_model_no_prior = DistributionModel(n_parameters=1,
distributions=dist)
# second candidate model, 2-dimensional
prior2 = JointIndependent(
[Uniform(loc=0., scale=0.5),
Lognormal(s=1., loc=0., scale=1.)])
dist2 = Uniform(loc=None, scale=None)
candidate_model2 = DistributionModel(n_parameters=2,
distributions=dist2,
prior=prior2)
def test_mle():
ml_estimator = MLE(inference_model=candidate_model,
data=data,