def test_laplace_posterior_cdf():
# Test the LaplacePosterior cdf vs pdf
np.random.seed(1)
y = np.random.randn(15).tolist()
c = statistics.LaplacePosterior(y)
num_cdf = lambda t: integrate.quad(c.pdf, -np.inf, t, limit=1000)[0]
with warnings.catch_warnings():
warnings.simplefilter("ignore", category=integrate.IntegrationWarning)
for t in np.linspace(-5, 5, 70):
x = c.cdf(t)
assert abs(x - num_cdf(t)) < 1e-5
assert abs(c.ppf(x) - t) < 1e-5
def test_laplace_posterior_basic():
# Test the LaplacePosterior mle/cdf/ppf
# even
y = [1, 2, 3, 4, 5, 6][::-1]
c = statistics.LaplacePosterior(y)
assert abs(c.mle - 3.5) < 1e-8
# odd
y = [1, 2, 3, 4, 5][::-1]
c = statistics.LaplacePosterior(y)
assert abs(c.mle - 3) < 1e-8
# check pdf vs cdf
sx = 200
dx = 1.0 / sx
cdf = 0
for jx in range(-10 * sx, 10 * sx):
cdf += c.pdf(dx * jx) * dx
got = c.cdf(dx * jx)
assert abs(cdf - got) < 3e-3
assert abs(cdf - 1.0) < 1e-3
# large input (must not cause overflows)
y = list(range(500))
c = statistics.LaplacePosterior(y)
assert abs(c.mle - 249.5) < 1e-8
assert abs(c.cdf(249.5) - 0.5) < 1e-8
# check cdf sanity
assert c.cdf(float('inf')) == 1.0
assert c.cdf(-float('inf')) == 0.0
assert abs(c.cdf(-1e9) - 0) < 1e-6
assert abs(c.cdf(1e9) - 1) < 1e-6
# check ppf
for p in [0.0, 1e-3, 0.01, 0.1, 0.5, 0.9, 0.99, 0.999, 1.0]:
assert abs(c.cdf(c.ppf(p)) - p) < 1e-3
t = c.ppf(1.1)
assert t != t
# check zero variance
y = [1, 1, 1, 1, 1]
c = statistics.LaplacePosterior(y)
assert c.mle == 1
assert c.pdf(1 - 1e-5) == 0
assert c.pdf(1 + 1e-5) == 0
assert c.cdf(1 - 1e-5) == 0
assert c.cdf(1 + 1e-5) == 1.0
assert c.ppf(1.0) == 1.0
# one item
y = [1]
c = statistics.LaplacePosterior(y)
assert c.cdf(1 - 1e-5) == 0
assert c.cdf(1 + 1e-5) == 1.0
# zero items
with pytest.raises(ValueError):
statistics.LaplacePosterior([])
def estimator(z, alpha):
c = statistics.LaplacePosterior(z.tolist())
a, b = c.ppf(alpha / 2), c.ppf(1 - alpha / 2)
a = min(c.mle, a) # force MLE inside CI
b = max(c.mle, b)
return c.mle, (a, b)
