def _logp(self, x):
""" Compute log pdf of model """
dist = Normal(x, self.var)
val = self.prior.logp(x)
for i in range(len(self.data)):
val = val + dist.logp(self.data[i])
return val
def _grad_logp(self, x):
""" Computes gradient of log pdf of model """
dist = Normal(x, self.var)
val = self.prior.grad_logp(x)
for i in range(len(self.data)):
val = val - dist.grad_logp(self.data[i])
return val
def _pdf(self, x):
""" Computes pdf of model """
dist = Normal(x, self.var)
val = self.prior.pdf(x)
for i in range(len(self.data)):
val = val * dist.pdf(self.data[i])
return val
def setUp(self):
""" Sets up unit tests. """
self.size = 1000
self.threshold = 0.01
self.data = np.random.normal(5, 2, 1000)
self.m = 0
self.tau = 4
self.prior = Normal(self.m, self.tau)
self.var = 2
def test_nuts_sampling_normal(self):
""" Tests NUTS sampling from Normal distribution """
self.report('Test NUTS sampling of Normal Distribution.')
mean = 11
variance = 3
dist = Normal(mean, variance)
samples = dist.draw_samples('nuts', self.size, np.array([0.1]), 10)
mean_r = self._compute_mean(samples)
var_r = self._compute_variance(samples)
self._check_sample_sizes(samples)
assert abs(mean - mean_r) <= self.threshold
assert abs(variance - var_r) <= self.threshold
self.report('%s :: test result: mean=%0.3f, variance=%0.3f'\
%(str(dist), mean_r, var_r), 'test_result')
def test_metropolis_normal(self):
""" Tests metropolis sampling from Normal distribution """
self.report('Test metropolis sampling from Normal Distribution.')
mean = 11
var = 3
dist = Normal(mean, var)
samples = dist.draw_samples('metropolis', self.size, np.array([11]))
mean_r = self._compute_mean(samples)
var_r = self._compute_variance(samples)
self._check_sample_sizes(samples)
assert abs(mean - mean_r) <= self.threshold
assert abs(var - var_r) <= self.threshold
self.report('%s :: test result: mean=%0.3f, variance=%0.3f'\
%(str(dist), mean_r, var_r), 'test_result')
def test_rand_sampling_normal(self):
""" Tests random sampling from Normal distribution """
self.report('Test random sampling of Normal Distribution.')
mean = 0
variance = 1
dist = Normal(mean, variance)
samples = dist.draw_samples('random', self.size)
mean_r = self._compute_mean(samples)
var_r = self._compute_variance(samples)
self._check_sample_sizes(samples)
assert abs(mean - mean_r) <= self.threshold
assert abs(variance - var_r) <= self.threshold
self.report('%s :: test result: mean=%0.3f, variance=%0.3f'%\
(str(dist), mean_r, var_r), 'test_result')
def test_rand_sampling(self):
""" Tests random sampling from Joint distribution """
self.report('Test random sampling of Joint Distribution.')
normal_rv = Normal(0, 1)
exp_rv = Exponential(2)
uniform_rv = ContinuousUniform(-5, 5)
dist = JointDistribution([normal_rv, exp_rv, uniform_rv])
samples = dist.draw_samples('random', self.size)
for i, rv in enumerate(dist.get_rv_s()):
self._check_sample_sizes(samples[i])
assert abs(rv.get_mean() -
self._compute_mean(samples[i])) <= self.threshold
assert abs(rv.get_variance() -
self._compute_variance(samples[i])) <= self.threshold
class PosteriorTestCase(BaseTestClass):
""" Unit test for posterior sampling with Gaussian likelihood and Gaussian prior"""
def setUp(self):
""" Sets up unit tests. """
self.size = 1000
self.threshold = 0.01
self.data = np.random.normal(5, 2, 1000)
self.m = 0
self.tau = 4
self.prior = Normal(self.m, self.tau)
self.var = 2
def _check_sample_sizes(self, samples):
""" Compares the sample sizes with the size parameter"""
assert self.size == len(samples)
def _compute_mean(self, samples):
""" Computes Mean """
return np.mean(samples)
def _compute_variance(self, samples):
""" Computes Variance """
return np.var(samples)
def _pdf(self, x):
""" Computes pdf of model """
dist = Normal(x, self.var)
val = self.prior.pdf(x)
for i in range(len(self.data)):
val = val * dist.pdf(self.data[i])
return val
def _logp(self, x):
""" Compute log pdf of model """
dist = Normal(x, self.var)
val = self.prior.logp(x)
for i in range(len(self.data)):
val = val + dist.logp(self.data[i])
return val
def _grad_logp(self, x):
""" Computes gradient of log pdf of model """
dist = Normal(x, self.var)
val = self.prior.grad_logp(x)
for i in range(len(self.data)):
val = val - dist.grad_logp(self.data[i])
return val
def test_posterior_NUTS(self):
""" Tests posterior estimation using NUTS sampling """
self.report(
'Test posterior estimation with Gaussian likelihood and Gaussian prior '
'using NUTS sampling')
model_a = Model(self._pdf, self._logp, self._grad_logp)
samples = model_a.draw_samples('nuts', self.size, np.array([3]), 10)
avg = 0
for i in range(len(self.data)):
avg = avg + self.data[i]
avg = avg / len(self.data)
# Map estimation
val = self.var / len(self.data)
mean_a = (self.tau * avg) / (self.tau +
val) + self.m * (val / (self.tau + val))
var_a = (val * self.tau) / (self.tau + val)
mean_r = self._compute_mean(samples)
var_r = self._compute_variance(samples)
self._check_sample_sizes(samples)
assert abs(mean_a - mean_r) <= self.threshold
assert abs(var_a - var_r) <= self.threshold
self.report(
'Map Estimation: mean=%0.3f, variance=%0.3f :: test result: mean=%0.3f, '
'variance=%0.3f' % (mean_a, var_a, mean_r, var_r), 'test_result')
def test_posterior_Slice(self):
""" Tests posterior estimation using Slice sampling """
self.report(
'Test posterior estimation with Gaussian likelihood and Gaussian prior '
'using Slice sampling')
model_a = Model(self._pdf, self._logp, self._grad_logp)
samples = model_a.draw_samples('slice', self.size, np.array([4.5]))
avg = 0
for i in range(len(self.data)):
avg = avg + self.data[i]
avg = avg / len(self.data)
# Map estimation
val = self.var / len(self.data)
mean_a = (self.tau * avg) / (self.tau +
val) + self.m * (val / (self.tau + val))
var_a = (val * self.tau) / (self.tau + val)
mean_r = self._compute_mean(samples)
var_r = self._compute_variance(samples)
self._check_sample_sizes(samples)
assert abs(mean_a - mean_r) <= self.threshold
assert abs(var_a - var_r) <= self.threshold
self.report(
'Map Estimation: mean=%0.3f, variance=%0.3f :: test result: mean=%0.3f, '
'variance=%0.3f' % (mean_a, var_a, mean_r, var_r), 'test_result')