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Traktor/myenv/Lib/site-packages/scipy/stats/tests/test_resampling.py

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losowanie zdjec
2024-05-26 05:12:46 +02:00
import numpy as np
import pytest
from scipy.stats import bootstrap, monte_carlo_test, permutation_test
from numpy.testing import assert_allclose, assert_equal, suppress_warnings
from scipy import stats
from scipy import special
from .. import _resampling as _resampling
from scipy._lib._util import rng_integers
from scipy.optimize import root
def test_bootstrap_iv():
message = "`data` must be a sequence of samples."
with pytest.raises(ValueError, match=message):
bootstrap(1, np.mean)
message = "`data` must contain at least one sample."
with pytest.raises(ValueError, match=message):
bootstrap(tuple(), np.mean)
message = "each sample in `data` must contain two or more observations..."
with pytest.raises(ValueError, match=message):
bootstrap(([1, 2, 3], [1]), np.mean)
message = ("When `paired is True`, all samples must have the same length ")
with pytest.raises(ValueError, match=message):
bootstrap(([1, 2, 3], [1, 2, 3, 4]), np.mean, paired=True)
message = "`vectorized` must be `True`, `False`, or `None`."
with pytest.raises(ValueError, match=message):
bootstrap(1, np.mean, vectorized='ekki')
message = "`axis` must be an integer."
with pytest.raises(ValueError, match=message):
bootstrap(([1, 2, 3],), np.mean, axis=1.5)
message = "could not convert string to float"
with pytest.raises(ValueError, match=message):
bootstrap(([1, 2, 3],), np.mean, confidence_level='ni')
message = "`n_resamples` must be a non-negative integer."
with pytest.raises(ValueError, match=message):
bootstrap(([1, 2, 3],), np.mean, n_resamples=-1000)
message = "`n_resamples` must be a non-negative integer."
with pytest.raises(ValueError, match=message):
bootstrap(([1, 2, 3],), np.mean, n_resamples=1000.5)
message = "`batch` must be a positive integer or None."
with pytest.raises(ValueError, match=message):
bootstrap(([1, 2, 3],), np.mean, batch=-1000)
message = "`batch` must be a positive integer or None."
with pytest.raises(ValueError, match=message):
bootstrap(([1, 2, 3],), np.mean, batch=1000.5)
message = "`method` must be in"
with pytest.raises(ValueError, match=message):
bootstrap(([1, 2, 3],), np.mean, method='ekki')
message = "`bootstrap_result` must have attribute `bootstrap_distribution'"
with pytest.raises(ValueError, match=message):
bootstrap(([1, 2, 3],), np.mean, bootstrap_result=10)
message = "Either `bootstrap_result.bootstrap_distribution.size`"
with pytest.raises(ValueError, match=message):
bootstrap(([1, 2, 3],), np.mean, n_resamples=0)
message = "'herring' cannot be used to seed a"
with pytest.raises(ValueError, match=message):
bootstrap(([1, 2, 3],), np.mean, random_state='herring')
@pytest.mark.parametrize("method", ['basic', 'percentile', 'BCa'])
@pytest.mark.parametrize("axis", [0, 1, 2])
def test_bootstrap_batch(method, axis):
# for one-sample statistics, batch size shouldn't affect the result
np.random.seed(0)
x = np.random.rand(10, 11, 12)
res1 = bootstrap((x,), np.mean, batch=None, method=method,
random_state=0, axis=axis, n_resamples=100)
res2 = bootstrap((x,), np.mean, batch=10, method=method,
random_state=0, axis=axis, n_resamples=100)
assert_equal(res2.confidence_interval.low, res1.confidence_interval.low)
assert_equal(res2.confidence_interval.high, res1.confidence_interval.high)
assert_equal(res2.standard_error, res1.standard_error)
@pytest.mark.parametrize("method", ['basic', 'percentile', 'BCa'])
def test_bootstrap_paired(method):
# test that `paired` works as expected
np.random.seed(0)
n = 100
x = np.random.rand(n)
y = np.random.rand(n)
def my_statistic(x, y, axis=-1):
return ((x-y)**2).mean(axis=axis)
def my_paired_statistic(i, axis=-1):
a = x[i]
b = y[i]
res = my_statistic(a, b)
return res
i = np.arange(len(x))
res1 = bootstrap((i,), my_paired_statistic, random_state=0)
res2 = bootstrap((x, y), my_statistic, paired=True, random_state=0)
assert_allclose(res1.confidence_interval, res2.confidence_interval)
assert_allclose(res1.standard_error, res2.standard_error)
@pytest.mark.parametrize("method", ['basic', 'percentile', 'BCa'])
@pytest.mark.parametrize("axis", [0, 1, 2])
@pytest.mark.parametrize("paired", [True, False])
def test_bootstrap_vectorized(method, axis, paired):
# test that paired is vectorized as expected: when samples are tiled,
# CI and standard_error of each axis-slice is the same as those of the
# original 1d sample
np.random.seed(0)
def my_statistic(x, y, z, axis=-1):
return x.mean(axis=axis) + y.mean(axis=axis) + z.mean(axis=axis)
shape = 10, 11, 12
n_samples = shape[axis]
x = np.random.rand(n_samples)
y = np.random.rand(n_samples)
z = np.random.rand(n_samples)
res1 = bootstrap((x, y, z), my_statistic, paired=paired, method=method,
random_state=0, axis=0, n_resamples=100)
assert (res1.bootstrap_distribution.shape
== res1.standard_error.shape + (100,))
reshape = [1, 1, 1]
reshape[axis] = n_samples
x = np.broadcast_to(x.reshape(reshape), shape)
y = np.broadcast_to(y.reshape(reshape), shape)
z = np.broadcast_to(z.reshape(reshape), shape)
res2 = bootstrap((x, y, z), my_statistic, paired=paired, method=method,
random_state=0, axis=axis, n_resamples=100)
assert_allclose(res2.confidence_interval.low,
res1.confidence_interval.low)
assert_allclose(res2.confidence_interval.high,
res1.confidence_interval.high)
assert_allclose(res2.standard_error, res1.standard_error)
result_shape = list(shape)
result_shape.pop(axis)
assert_equal(res2.confidence_interval.low.shape, result_shape)
assert_equal(res2.confidence_interval.high.shape, result_shape)
assert_equal(res2.standard_error.shape, result_shape)
@pytest.mark.xfail_on_32bit("MemoryError with BCa observed in CI")
@pytest.mark.parametrize("method", ['basic', 'percentile', 'BCa'])
def test_bootstrap_against_theory(method):
# based on https://www.statology.org/confidence-intervals-python/
rng = np.random.default_rng(2442101192988600726)
data = stats.norm.rvs(loc=5, scale=2, size=5000, random_state=rng)
alpha = 0.95
dist = stats.t(df=len(data)-1, loc=np.mean(data), scale=stats.sem(data))
expected_interval = dist.interval(confidence=alpha)
expected_se = dist.std()
config = dict(data=(data,), statistic=np.mean, n_resamples=5000,
method=method, random_state=rng)
res = bootstrap(**config, confidence_level=alpha)
assert_allclose(res.confidence_interval, expected_interval, rtol=5e-4)
assert_allclose(res.standard_error, expected_se, atol=3e-4)
config.update(dict(n_resamples=0, bootstrap_result=res))
res = bootstrap(**config, confidence_level=alpha, alternative='less')
assert_allclose(res.confidence_interval.high, dist.ppf(alpha), rtol=5e-4)
config.update(dict(n_resamples=0, bootstrap_result=res))
res = bootstrap(**config, confidence_level=alpha, alternative='greater')
assert_allclose(res.confidence_interval.low, dist.ppf(1-alpha), rtol=5e-4)
tests_R = {"basic": (23.77, 79.12),
"percentile": (28.86, 84.21),
"BCa": (32.31, 91.43)}
@pytest.mark.parametrize("method, expected", tests_R.items())
def test_bootstrap_against_R(method, expected):
# Compare against R's "boot" library
# library(boot)
# stat <- function (x, a) {
# mean(x[a])
# }
# x <- c(10, 12, 12.5, 12.5, 13.9, 15, 21, 22,
# 23, 34, 50, 81, 89, 121, 134, 213)
# # Use a large value so we get a few significant digits for the CI.
# n = 1000000
# bootresult = boot(x, stat, n)
# result <- boot.ci(bootresult)
# print(result)
x = np.array([10, 12, 12.5, 12.5, 13.9, 15, 21, 22,
23, 34, 50, 81, 89, 121, 134, 213])
res = bootstrap((x,), np.mean, n_resamples=1000000, method=method,
random_state=0)
assert_allclose(res.confidence_interval, expected, rtol=0.005)
tests_against_itself_1samp = {"basic": 1780,
"percentile": 1784,
"BCa": 1784}
def test_multisample_BCa_against_R():
# Because bootstrap is stochastic, it's tricky to test against reference
# behavior. Here, we show that SciPy's BCa CI matches R wboot's BCa CI
# much more closely than the other SciPy CIs do.
# arbitrary skewed data
x = [0.75859206, 0.5910282, -0.4419409, -0.36654601,
0.34955357, -1.38835871, 0.76735821]
y = [1.41186073, 0.49775975, 0.08275588, 0.24086388,
0.03567057, 0.52024419, 0.31966611, 1.32067634]
# a multi-sample statistic for which the BCa CI tends to be different
# from the other CIs
def statistic(x, y, axis):
s1 = stats.skew(x, axis=axis)
s2 = stats.skew(y, axis=axis)
return s1 - s2
# compute confidence intervals using each method
rng = np.random.default_rng(468865032284792692)
res_basic = stats.bootstrap((x, y), statistic, method='basic',
batch=100, random_state=rng)
res_percent = stats.bootstrap((x, y), statistic, method='percentile',
batch=100, random_state=rng)
res_bca = stats.bootstrap((x, y), statistic, method='bca',
batch=100, random_state=rng)
# compute midpoints so we can compare just one number for each
mid_basic = np.mean(res_basic.confidence_interval)
mid_percent = np.mean(res_percent.confidence_interval)
mid_bca = np.mean(res_bca.confidence_interval)
# reference for BCA CI computed using R wboot package:
# library(wBoot)
# library(moments)
# x = c(0.75859206, 0.5910282, -0.4419409, -0.36654601,
# 0.34955357, -1.38835871, 0.76735821)
# y = c(1.41186073, 0.49775975, 0.08275588, 0.24086388,
# 0.03567057, 0.52024419, 0.31966611, 1.32067634)
# twoskew <- function(x1, y1) {skewness(x1) - skewness(y1)}
# boot.two.bca(x, y, skewness, conf.level = 0.95,
# R = 9999, stacked = FALSE)
mid_wboot = -1.5519
# compute percent difference relative to wboot BCA method
diff_basic = (mid_basic - mid_wboot)/abs(mid_wboot)
diff_percent = (mid_percent - mid_wboot)/abs(mid_wboot)
diff_bca = (mid_bca - mid_wboot)/abs(mid_wboot)
# SciPy's BCa CI midpoint is much closer than that of the other methods
assert diff_basic < -0.15
assert diff_percent > 0.15
assert abs(diff_bca) < 0.03
def test_BCa_acceleration_against_reference():
# Compare the (deterministic) acceleration parameter for a multi-sample
# problem against a reference value. The example is from [1], but Efron's
# value seems inaccurate. Straightorward code for computing the
# reference acceleration (0.011008228344026734) is available at:
# https://github.com/scipy/scipy/pull/16455#issuecomment-1193400981
y = np.array([10, 27, 31, 40, 46, 50, 52, 104, 146])
z = np.array([16, 23, 38, 94, 99, 141, 197])
def statistic(z, y, axis=0):
return np.mean(z, axis=axis) - np.mean(y, axis=axis)
data = [z, y]
res = stats.bootstrap(data, statistic)
axis = -1
alpha = 0.95
theta_hat_b = res.bootstrap_distribution
batch = 100
_, _, a_hat = _resampling._bca_interval(data, statistic, axis, alpha,
theta_hat_b, batch)
assert_allclose(a_hat, 0.011008228344026734)
@pytest.mark.parametrize("method, expected",
tests_against_itself_1samp.items())
def test_bootstrap_against_itself_1samp(method, expected):
# The expected values in this test were generated using bootstrap
# to check for unintended changes in behavior. The test also makes sure
# that bootstrap works with multi-sample statistics and that the
# `axis` argument works as expected / function is vectorized.
np.random.seed(0)
n = 100 # size of sample
n_resamples = 999 # number of bootstrap resamples used to form each CI
confidence_level = 0.9
# The true mean is 5
dist = stats.norm(loc=5, scale=1)
stat_true = dist.mean()
# Do the same thing 2000 times. (The code is fully vectorized.)
n_replications = 2000
data = dist.rvs(size=(n_replications, n))
res = bootstrap((data,),
statistic=np.mean,
confidence_level=confidence_level,
n_resamples=n_resamples,
batch=50,
method=method,
axis=-1)
ci = res.confidence_interval
# ci contains vectors of lower and upper confidence interval bounds
ci_contains_true = np.sum((ci[0] < stat_true) & (stat_true < ci[1]))
assert ci_contains_true == expected
# ci_contains_true is not inconsistent with confidence_level
pvalue = stats.binomtest(ci_contains_true, n_replications,
confidence_level).pvalue
assert pvalue > 0.1
tests_against_itself_2samp = {"basic": 892,
"percentile": 890}
@pytest.mark.parametrize("method, expected",
tests_against_itself_2samp.items())
def test_bootstrap_against_itself_2samp(method, expected):
# The expected values in this test were generated using bootstrap
# to check for unintended changes in behavior. The test also makes sure
# that bootstrap works with multi-sample statistics and that the
# `axis` argument works as expected / function is vectorized.
np.random.seed(0)
n1 = 100 # size of sample 1
n2 = 120 # size of sample 2
n_resamples = 999 # number of bootstrap resamples used to form each CI
confidence_level = 0.9
# The statistic we're interested in is the difference in means
def my_stat(data1, data2, axis=-1):
mean1 = np.mean(data1, axis=axis)
mean2 = np.mean(data2, axis=axis)
return mean1 - mean2
# The true difference in the means is -0.1
dist1 = stats.norm(loc=0, scale=1)
dist2 = stats.norm(loc=0.1, scale=1)
stat_true = dist1.mean() - dist2.mean()
# Do the same thing 1000 times. (The code is fully vectorized.)
n_replications = 1000
data1 = dist1.rvs(size=(n_replications, n1))
data2 = dist2.rvs(size=(n_replications, n2))
res = bootstrap((data1, data2),
statistic=my_stat,
confidence_level=confidence_level,
n_resamples=n_resamples,
batch=50,
method=method,
axis=-1)
ci = res.confidence_interval
# ci contains vectors of lower and upper confidence interval bounds
ci_contains_true = np.sum((ci[0] < stat_true) & (stat_true < ci[1]))
assert ci_contains_true == expected
# ci_contains_true is not inconsistent with confidence_level
pvalue = stats.binomtest(ci_contains_true, n_replications,
confidence_level).pvalue
assert pvalue > 0.1
@pytest.mark.parametrize("method", ["basic", "percentile"])
@pytest.mark.parametrize("axis", [0, 1])
def test_bootstrap_vectorized_3samp(method, axis):
def statistic(*data, axis=0):
# an arbitrary, vectorized statistic
return sum(sample.mean(axis) for sample in data)
def statistic_1d(*data):
# the same statistic, not vectorized
for sample in data:
assert sample.ndim == 1
return statistic(*data, axis=0)
np.random.seed(0)
x = np.random.rand(4, 5)
y = np.random.rand(4, 5)
z = np.random.rand(4, 5)
res1 = bootstrap((x, y, z), statistic, vectorized=True,
axis=axis, n_resamples=100, method=method, random_state=0)
res2 = bootstrap((x, y, z), statistic_1d, vectorized=False,
axis=axis, n_resamples=100, method=method, random_state=0)
assert_allclose(res1.confidence_interval, res2.confidence_interval)
assert_allclose(res1.standard_error, res2.standard_error)
@pytest.mark.xfail_on_32bit("Failure is not concerning; see gh-14107")
@pytest.mark.parametrize("method", ["basic", "percentile", "BCa"])
@pytest.mark.parametrize("axis", [0, 1])
def test_bootstrap_vectorized_1samp(method, axis):
def statistic(x, axis=0):
# an arbitrary, vectorized statistic
return x.mean(axis=axis)
def statistic_1d(x):
# the same statistic, not vectorized
assert x.ndim == 1
return statistic(x, axis=0)
np.random.seed(0)
x = np.random.rand(4, 5)
res1 = bootstrap((x,), statistic, vectorized=True, axis=axis,
n_resamples=100, batch=None, method=method,
random_state=0)
res2 = bootstrap((x,), statistic_1d, vectorized=False, axis=axis,
n_resamples=100, batch=10, method=method,
random_state=0)
assert_allclose(res1.confidence_interval, res2.confidence_interval)
assert_allclose(res1.standard_error, res2.standard_error)
@pytest.mark.parametrize("method", ["basic", "percentile", "BCa"])
def test_bootstrap_degenerate(method):
data = 35 * [10000.]
if method == "BCa":
with np.errstate(invalid='ignore'):
msg = "The BCa confidence interval cannot be calculated"
with pytest.warns(stats.DegenerateDataWarning, match=msg):
res = bootstrap([data, ], np.mean, method=method)
assert_equal(res.confidence_interval, (np.nan, np.nan))
else:
res = bootstrap([data, ], np.mean, method=method)
assert_equal(res.confidence_interval, (10000., 10000.))
assert_equal(res.standard_error, 0)
@pytest.mark.parametrize("method", ["basic", "percentile", "BCa"])
def test_bootstrap_gh15678(method):
# Check that gh-15678 is fixed: when statistic function returned a Python
# float, method="BCa" failed when trying to add a dimension to the float
rng = np.random.default_rng(354645618886684)
dist = stats.norm(loc=2, scale=4)
data = dist.rvs(size=100, random_state=rng)
data = (data,)
res = bootstrap(data, stats.skew, method=method, n_resamples=100,
random_state=np.random.default_rng(9563))
# this always worked because np.apply_along_axis returns NumPy data type
ref = bootstrap(data, stats.skew, method=method, n_resamples=100,
random_state=np.random.default_rng(9563), vectorized=False)
assert_allclose(res.confidence_interval, ref.confidence_interval)
assert_allclose(res.standard_error, ref.standard_error)
assert isinstance(res.standard_error, np.float64)
def test_bootstrap_min():
# Check that gh-15883 is fixed: percentileofscore should
# behave according to the 'mean' behavior and not trigger nan for BCa
rng = np.random.default_rng(1891289180021102)
dist = stats.norm(loc=2, scale=4)
data = dist.rvs(size=100, random_state=rng)
true_min = np.min(data)
data = (data,)
res = bootstrap(data, np.min, method="BCa", n_resamples=100,
random_state=np.random.default_rng(3942))
assert true_min == res.confidence_interval.low
res2 = bootstrap(-np.array(data), np.max, method="BCa", n_resamples=100,
random_state=np.random.default_rng(3942))
assert_allclose(-res.confidence_interval.low,
res2.confidence_interval.high)
assert_allclose(-res.confidence_interval.high,
res2.confidence_interval.low)
@pytest.mark.parametrize("additional_resamples", [0, 1000])
def test_re_bootstrap(additional_resamples):
# Test behavior of parameter `bootstrap_result`
rng = np.random.default_rng(8958153316228384)
x = rng.random(size=100)
n1 = 1000
n2 = additional_resamples
n3 = n1 + additional_resamples
rng = np.random.default_rng(296689032789913033)
res = stats.bootstrap((x,), np.mean, n_resamples=n1, random_state=rng,
confidence_level=0.95, method='percentile')
res = stats.bootstrap((x,), np.mean, n_resamples=n2, random_state=rng,
confidence_level=0.90, method='BCa',
bootstrap_result=res)
rng = np.random.default_rng(296689032789913033)
ref = stats.bootstrap((x,), np.mean, n_resamples=n3, random_state=rng,
confidence_level=0.90, method='BCa')
assert_allclose(res.standard_error, ref.standard_error, rtol=1e-14)
assert_allclose(res.confidence_interval, ref.confidence_interval,
rtol=1e-14)
@pytest.mark.xfail_on_32bit("Sensible to machine precision")
@pytest.mark.parametrize("method", ['basic', 'percentile', 'BCa'])
def test_bootstrap_alternative(method):
rng = np.random.default_rng(5894822712842015040)
dist = stats.norm(loc=2, scale=4)
data = (dist.rvs(size=(100), random_state=rng),)
config = dict(data=data, statistic=np.std, random_state=rng, axis=-1)
t = stats.bootstrap(**config, confidence_level=0.9)
config.update(dict(n_resamples=0, bootstrap_result=t))
l = stats.bootstrap(**config, confidence_level=0.95, alternative='less')
g = stats.bootstrap(**config, confidence_level=0.95, alternative='greater')
assert_allclose(l.confidence_interval.high, t.confidence_interval.high,
rtol=1e-14)
assert_allclose(g.confidence_interval.low, t.confidence_interval.low,
rtol=1e-14)
assert np.isneginf(l.confidence_interval.low)
assert np.isposinf(g.confidence_interval.high)
with pytest.raises(ValueError, match='`alternative` must be one of'):
stats.bootstrap(**config, alternative='ekki-ekki')
def test_jackknife_resample():
shape = 3, 4, 5, 6
np.random.seed(0)
x = np.random.rand(*shape)
y = next(_resampling._jackknife_resample(x))
for i in range(shape[-1]):
# each resample is indexed along second to last axis
# (last axis is the one the statistic will be taken over / consumed)
slc = y[..., i, :]
expected = np.delete(x, i, axis=-1)
assert np.array_equal(slc, expected)
y2 = np.concatenate(list(_resampling._jackknife_resample(x, batch=2)),
axis=-2)
assert np.array_equal(y2, y)
@pytest.mark.parametrize("rng_name", ["RandomState", "default_rng"])
def test_bootstrap_resample(rng_name):
rng = getattr(np.random, rng_name, None)
if rng is None:
pytest.skip(f"{rng_name} not available.")
rng1 = rng(0)
rng2 = rng(0)
n_resamples = 10
shape = 3, 4, 5, 6
np.random.seed(0)
x = np.random.rand(*shape)
y = _resampling._bootstrap_resample(x, n_resamples, random_state=rng1)
for i in range(n_resamples):
# each resample is indexed along second to last axis
# (last axis is the one the statistic will be taken over / consumed)
slc = y[..., i, :]
js = rng_integers(rng2, 0, shape[-1], shape[-1])
expected = x[..., js]
assert np.array_equal(slc, expected)
@pytest.mark.parametrize("score", [0, 0.5, 1])
@pytest.mark.parametrize("axis", [0, 1, 2])
def test_percentile_of_score(score, axis):
shape = 10, 20, 30
np.random.seed(0)
x = np.random.rand(*shape)
p = _resampling._percentile_of_score(x, score, axis=-1)
def vectorized_pos(a, score, axis):
return np.apply_along_axis(stats.percentileofscore, axis, a, score)
p2 = vectorized_pos(x, score, axis=-1)/100
assert_allclose(p, p2, 1e-15)
def test_percentile_along_axis():
# the difference between _percentile_along_axis and np.percentile is that
# np.percentile gets _all_ the qs for each axis slice, whereas
# _percentile_along_axis gets the q corresponding with each axis slice
shape = 10, 20
np.random.seed(0)
x = np.random.rand(*shape)
q = np.random.rand(*shape[:-1]) * 100
y = _resampling._percentile_along_axis(x, q)
for i in range(shape[0]):
res = y[i]
expected = np.percentile(x[i], q[i], axis=-1)
assert_allclose(res, expected, 1e-15)
@pytest.mark.parametrize("axis", [0, 1, 2])
def test_vectorize_statistic(axis):
# test that _vectorize_statistic vectorizes a statistic along `axis`
def statistic(*data, axis):
# an arbitrary, vectorized statistic
return sum(sample.mean(axis) for sample in data)
def statistic_1d(*data):
# the same statistic, not vectorized
for sample in data:
assert sample.ndim == 1
return statistic(*data, axis=0)
# vectorize the non-vectorized statistic
statistic2 = _resampling._vectorize_statistic(statistic_1d)
np.random.seed(0)
x = np.random.rand(4, 5, 6)
y = np.random.rand(4, 1, 6)
z = np.random.rand(1, 5, 6)
res1 = statistic(x, y, z, axis=axis)
res2 = statistic2(x, y, z, axis=axis)
assert_allclose(res1, res2)
@pytest.mark.parametrize("method", ["basic", "percentile", "BCa"])
def test_vector_valued_statistic(method):
# Generate 95% confidence interval around MLE of normal distribution
# parameters. Repeat 100 times, each time on sample of size 100.
# Check that confidence interval contains true parameters ~95 times.
# Confidence intervals are estimated and stochastic; a test failure
# does not necessarily indicate that something is wrong. More important
# than values of `counts` below is that the shapes of the outputs are
# correct.
rng = np.random.default_rng(2196847219)
params = 1, 0.5
sample = stats.norm.rvs(*params, size=(100, 100), random_state=rng)
def statistic(data, axis):
return np.asarray([np.mean(data, axis),
np.std(data, axis, ddof=1)])
res = bootstrap((sample,), statistic, method=method, axis=-1,
n_resamples=9999, batch=200)
counts = np.sum((res.confidence_interval.low.T < params)
& (res.confidence_interval.high.T > params),
axis=0)
assert np.all(counts >= 90)
assert np.all(counts <= 100)
assert res.confidence_interval.low.shape == (2, 100)
assert res.confidence_interval.high.shape == (2, 100)
assert res.standard_error.shape == (2, 100)
assert res.bootstrap_distribution.shape == (2, 100, 9999)
@pytest.mark.slow
@pytest.mark.filterwarnings('ignore::RuntimeWarning')
def test_vector_valued_statistic_gh17715():
# gh-17715 reported a mistake introduced in the extension of BCa to
# multi-sample statistics; a `len` should have been `.shape[-1]`. Check
# that this is resolved.
rng = np.random.default_rng(141921000979291141)
def concordance(x, y, axis):
xm = x.mean(axis)
ym = y.mean(axis)
cov = ((x - xm[..., None]) * (y - ym[..., None])).mean(axis)
return (2 * cov) / (x.var(axis) + y.var(axis) + (xm - ym) ** 2)
def statistic(tp, tn, fp, fn, axis):
actual = tp + fp
expected = tp + fn
return np.nan_to_num(concordance(actual, expected, axis))
def statistic_extradim(*args, axis):
return statistic(*args, axis)[np.newaxis, ...]
data = [[4, 0, 0, 2], # (tp, tn, fp, fn)
[2, 1, 2, 1],
[0, 6, 0, 0],
[0, 6, 3, 0],
[0, 8, 1, 0]]
data = np.array(data).T
res = bootstrap(data, statistic_extradim, random_state=rng, paired=True)
ref = bootstrap(data, statistic, random_state=rng, paired=True)
assert_allclose(res.confidence_interval.low[0],
ref.confidence_interval.low, atol=1e-15)
assert_allclose(res.confidence_interval.high[0],
ref.confidence_interval.high, atol=1e-15)
# --- Test Monte Carlo Hypothesis Test --- #
class TestMonteCarloHypothesisTest:
atol = 2.5e-2 # for comparing p-value
def rvs(self, rvs_in, rs):
return lambda *args, **kwds: rvs_in(*args, random_state=rs, **kwds)
def test_input_validation(self):
# test that the appropriate error messages are raised for invalid input
def stat(x):
return stats.skewnorm(x).statistic
message = "Array shapes are incompatible for broadcasting."
data = (np.zeros((2, 5)), np.zeros((3, 5)))
rvs = (stats.norm.rvs, stats.norm.rvs)
with pytest.raises(ValueError, match=message):
monte_carlo_test(data, rvs, lambda x, y: 1, axis=-1)
message = "`axis` must be an integer."
with pytest.raises(ValueError, match=message):
monte_carlo_test([1, 2, 3], stats.norm.rvs, stat, axis=1.5)
message = "`vectorized` must be `True`, `False`, or `None`."
with pytest.raises(ValueError, match=message):
monte_carlo_test([1, 2, 3], stats.norm.rvs, stat, vectorized=1.5)
message = "`rvs` must be callable or sequence of callables."
with pytest.raises(TypeError, match=message):
monte_carlo_test([1, 2, 3], None, stat)
with pytest.raises(TypeError, match=message):
monte_carlo_test([[1, 2], [3, 4]], [lambda x: x, None], stat)
message = "If `rvs` is a sequence..."
with pytest.raises(ValueError, match=message):
monte_carlo_test([[1, 2, 3]], [lambda x: x, lambda x: x], stat)
message = "`statistic` must be callable."
with pytest.raises(TypeError, match=message):
monte_carlo_test([1, 2, 3], stats.norm.rvs, None)
message = "`n_resamples` must be a positive integer."
with pytest.raises(ValueError, match=message):
monte_carlo_test([1, 2, 3], stats.norm.rvs, stat,
n_resamples=-1000)
message = "`n_resamples` must be a positive integer."
with pytest.raises(ValueError, match=message):
monte_carlo_test([1, 2, 3], stats.norm.rvs, stat,
n_resamples=1000.5)
message = "`batch` must be a positive integer or None."
with pytest.raises(ValueError, match=message):
monte_carlo_test([1, 2, 3], stats.norm.rvs, stat, batch=-1000)
message = "`batch` must be a positive integer or None."
with pytest.raises(ValueError, match=message):
monte_carlo_test([1, 2, 3], stats.norm.rvs, stat, batch=1000.5)
message = "`alternative` must be in..."
with pytest.raises(ValueError, match=message):
monte_carlo_test([1, 2, 3], stats.norm.rvs, stat,
alternative='ekki')
def test_batch(self):
# make sure that the `batch` parameter is respected by checking the
# maximum batch size provided in calls to `statistic`
rng = np.random.default_rng(23492340193)
x = rng.random(10)
def statistic(x, axis):
batch_size = 1 if x.ndim == 1 else len(x)
statistic.batch_size = max(batch_size, statistic.batch_size)
statistic.counter += 1
return stats.skewtest(x, axis=axis).statistic
statistic.counter = 0
statistic.batch_size = 0
kwds = {'sample': x, 'statistic': statistic,
'n_resamples': 1000, 'vectorized': True}
kwds['rvs'] = self.rvs(stats.norm.rvs, np.random.default_rng(32842398))
res1 = monte_carlo_test(batch=1, **kwds)
assert_equal(statistic.counter, 1001)
assert_equal(statistic.batch_size, 1)
kwds['rvs'] = self.rvs(stats.norm.rvs, np.random.default_rng(32842398))
statistic.counter = 0
res2 = monte_carlo_test(batch=50, **kwds)
assert_equal(statistic.counter, 21)
assert_equal(statistic.batch_size, 50)
kwds['rvs'] = self.rvs(stats.norm.rvs, np.random.default_rng(32842398))
statistic.counter = 0
res3 = monte_carlo_test(**kwds)
assert_equal(statistic.counter, 2)
assert_equal(statistic.batch_size, 1000)
assert_equal(res1.pvalue, res3.pvalue)
assert_equal(res2.pvalue, res3.pvalue)
@pytest.mark.parametrize('axis', range(-3, 3))
def test_axis(self, axis):
# test that Nd-array samples are handled correctly for valid values
# of the `axis` parameter
rng = np.random.default_rng(2389234)
norm_rvs = self.rvs(stats.norm.rvs, rng)
size = [2, 3, 4]
size[axis] = 100
x = norm_rvs(size=size)
expected = stats.skewtest(x, axis=axis)
def statistic(x, axis):
return stats.skewtest(x, axis=axis).statistic
res = monte_carlo_test(x, norm_rvs, statistic, vectorized=True,
n_resamples=20000, axis=axis)
assert_allclose(res.statistic, expected.statistic)
assert_allclose(res.pvalue, expected.pvalue, atol=self.atol)
@pytest.mark.parametrize('alternative', ("less", "greater"))
@pytest.mark.parametrize('a', np.linspace(-0.5, 0.5, 5)) # skewness
def test_against_ks_1samp(self, alternative, a):
# test that monte_carlo_test can reproduce pvalue of ks_1samp
rng = np.random.default_rng(65723433)
x = stats.skewnorm.rvs(a=a, size=30, random_state=rng)
expected = stats.ks_1samp(x, stats.norm.cdf, alternative=alternative)
def statistic1d(x):
return stats.ks_1samp(x, stats.norm.cdf, mode='asymp',
alternative=alternative).statistic
norm_rvs = self.rvs(stats.norm.rvs, rng)
res = monte_carlo_test(x, norm_rvs, statistic1d,
n_resamples=1000, vectorized=False,
alternative=alternative)
assert_allclose(res.statistic, expected.statistic)
if alternative == 'greater':
assert_allclose(res.pvalue, expected.pvalue, atol=self.atol)
elif alternative == 'less':
assert_allclose(1-res.pvalue, expected.pvalue, atol=self.atol)
@pytest.mark.parametrize('hypotest', (stats.skewtest, stats.kurtosistest))
@pytest.mark.parametrize('alternative', ("less", "greater", "two-sided"))
@pytest.mark.parametrize('a', np.linspace(-2, 2, 5)) # skewness
def test_against_normality_tests(self, hypotest, alternative, a):
# test that monte_carlo_test can reproduce pvalue of normality tests
rng = np.random.default_rng(85723405)
x = stats.skewnorm.rvs(a=a, size=150, random_state=rng)
expected = hypotest(x, alternative=alternative)
def statistic(x, axis):
return hypotest(x, axis=axis).statistic
norm_rvs = self.rvs(stats.norm.rvs, rng)
res = monte_carlo_test(x, norm_rvs, statistic, vectorized=True,
alternative=alternative)
assert_allclose(res.statistic, expected.statistic)
assert_allclose(res.pvalue, expected.pvalue, atol=self.atol)
@pytest.mark.parametrize('a', np.arange(-2, 3)) # skewness parameter
def test_against_normaltest(self, a):
# test that monte_carlo_test can reproduce pvalue of normaltest
rng = np.random.default_rng(12340513)
x = stats.skewnorm.rvs(a=a, size=150, random_state=rng)
expected = stats.normaltest(x)
def statistic(x, axis):
return stats.normaltest(x, axis=axis).statistic
norm_rvs = self.rvs(stats.norm.rvs, rng)
res = monte_carlo_test(x, norm_rvs, statistic, vectorized=True,
alternative='greater')
assert_allclose(res.statistic, expected.statistic)
assert_allclose(res.pvalue, expected.pvalue, atol=self.atol)
@pytest.mark.parametrize('a', np.linspace(-0.5, 0.5, 5)) # skewness
def test_against_cramervonmises(self, a):
# test that monte_carlo_test can reproduce pvalue of cramervonmises
rng = np.random.default_rng(234874135)
x = stats.skewnorm.rvs(a=a, size=30, random_state=rng)
expected = stats.cramervonmises(x, stats.norm.cdf)
def statistic1d(x):
return stats.cramervonmises(x, stats.norm.cdf).statistic
norm_rvs = self.rvs(stats.norm.rvs, rng)
res = monte_carlo_test(x, norm_rvs, statistic1d,
n_resamples=1000, vectorized=False,
alternative='greater')
assert_allclose(res.statistic, expected.statistic)
assert_allclose(res.pvalue, expected.pvalue, atol=self.atol)
@pytest.mark.parametrize('dist_name', ('norm', 'logistic'))
@pytest.mark.parametrize('i', range(5))
def test_against_anderson(self, dist_name, i):
# test that monte_carlo_test can reproduce results of `anderson`. Note:
# `anderson` does not provide a p-value; it provides a list of
# significance levels and the associated critical value of the test
# statistic. `i` used to index this list.
# find the skewness for which the sample statistic matches one of the
# critical values provided by `stats.anderson`
def fun(a):
rng = np.random.default_rng(394295467)
x = stats.tukeylambda.rvs(a, size=100, random_state=rng)
expected = stats.anderson(x, dist_name)
return expected.statistic - expected.critical_values[i]
with suppress_warnings() as sup:
sup.filter(RuntimeWarning)
sol = root(fun, x0=0)
assert sol.success
# get the significance level (p-value) associated with that critical
# value
a = sol.x[0]
rng = np.random.default_rng(394295467)
x = stats.tukeylambda.rvs(a, size=100, random_state=rng)
expected = stats.anderson(x, dist_name)
expected_stat = expected.statistic
expected_p = expected.significance_level[i]/100
# perform equivalent Monte Carlo test and compare results
def statistic1d(x):
return stats.anderson(x, dist_name).statistic
dist_rvs = self.rvs(getattr(stats, dist_name).rvs, rng)
with suppress_warnings() as sup:
sup.filter(RuntimeWarning)
res = monte_carlo_test(x, dist_rvs,
statistic1d, n_resamples=1000,
vectorized=False, alternative='greater')
assert_allclose(res.statistic, expected_stat)
assert_allclose(res.pvalue, expected_p, atol=2*self.atol)
def test_p_never_zero(self):
# Use biased estimate of p-value to ensure that p-value is never zero
# per monte_carlo_test reference [1]
rng = np.random.default_rng(2190176673029737545)
x = np.zeros(100)
res = monte_carlo_test(x, rng.random, np.mean,
vectorized=True, alternative='less')
assert res.pvalue == 0.0001
def test_against_ttest_ind(self):
# test that `monte_carlo_test` can reproduce results of `ttest_ind`.
rng = np.random.default_rng(219017667302737545)
data = rng.random(size=(2, 5)), rng.random(size=7) # broadcastable
rvs = rng.normal, rng.normal
def statistic(x, y, axis):
return stats.ttest_ind(x, y, axis).statistic
res = stats.monte_carlo_test(data, rvs, statistic, axis=-1)
ref = stats.ttest_ind(data[0], [data[1]], axis=-1)
assert_allclose(res.statistic, ref.statistic)
assert_allclose(res.pvalue, ref.pvalue, rtol=2e-2)
def test_against_f_oneway(self):
# test that `monte_carlo_test` can reproduce results of `f_oneway`.
rng = np.random.default_rng(219017667302737545)
data = (rng.random(size=(2, 100)), rng.random(size=(2, 101)),
rng.random(size=(2, 102)), rng.random(size=(2, 103)))
rvs = rng.normal, rng.normal, rng.normal, rng.normal
def statistic(*args, axis):
return stats.f_oneway(*args, axis=axis).statistic
res = stats.monte_carlo_test(data, rvs, statistic, axis=-1,
alternative='greater')
ref = stats.f_oneway(*data, axis=-1)
assert_allclose(res.statistic, ref.statistic)
assert_allclose(res.pvalue, ref.pvalue, atol=1e-2)
@pytest.mark.xfail_on_32bit("Statistic may not depend on sample order on 32-bit")
def test_finite_precision_statistic(self):
# Some statistics return numerically distinct values when the values
# should be equal in theory. Test that `monte_carlo_test` accounts
# for this in some way.
rng = np.random.default_rng(2549824598234528)
n_resamples = 9999
def rvs(size):
return 1. * stats.bernoulli(p=0.333).rvs(size=size, random_state=rng)
x = rvs(100)
res = stats.monte_carlo_test(x, rvs, np.var, alternative='less',
n_resamples=n_resamples)
# show that having a tolerance matters
c0 = np.sum(res.null_distribution <= res.statistic)
c1 = np.sum(res.null_distribution <= res.statistic*(1+1e-15))
assert c0 != c1
assert res.pvalue == (c1 + 1)/(n_resamples + 1)
class TestPermutationTest:
rtol = 1e-14
def setup_method(self):
self.rng = np.random.default_rng(7170559330470561044)
# -- Input validation -- #
def test_permutation_test_iv(self):
def stat(x, y, axis):
return stats.ttest_ind((x, y), axis).statistic
message = "each sample in `data` must contain two or more ..."
with pytest.raises(ValueError, match=message):
permutation_test(([1, 2, 3], [1]), stat)
message = "`data` must be a tuple containing at least two samples"
with pytest.raises(ValueError, match=message):
permutation_test((1,), stat)
with pytest.raises(TypeError, match=message):
permutation_test(1, stat)
message = "`axis` must be an integer."
with pytest.raises(ValueError, match=message):
permutation_test(([1, 2, 3], [1, 2, 3]), stat, axis=1.5)
message = "`permutation_type` must be in..."
with pytest.raises(ValueError, match=message):
permutation_test(([1, 2, 3], [1, 2, 3]), stat,
permutation_type="ekki")
message = "`vectorized` must be `True`, `False`, or `None`."
with pytest.raises(ValueError, match=message):
permutation_test(([1, 2, 3], [1, 2, 3]), stat, vectorized=1.5)
message = "`n_resamples` must be a positive integer."
with pytest.raises(ValueError, match=message):
permutation_test(([1, 2, 3], [1, 2, 3]), stat, n_resamples=-1000)
message = "`n_resamples` must be a positive integer."
with pytest.raises(ValueError, match=message):
permutation_test(([1, 2, 3], [1, 2, 3]), stat, n_resamples=1000.5)
message = "`batch` must be a positive integer or None."
with pytest.raises(ValueError, match=message):
permutation_test(([1, 2, 3], [1, 2, 3]), stat, batch=-1000)
message = "`batch` must be a positive integer or None."
with pytest.raises(ValueError, match=message):
permutation_test(([1, 2, 3], [1, 2, 3]), stat, batch=1000.5)
message = "`alternative` must be in..."
with pytest.raises(ValueError, match=message):
permutation_test(([1, 2, 3], [1, 2, 3]), stat, alternative='ekki')
message = "'herring' cannot be used to seed a"
with pytest.raises(ValueError, match=message):
permutation_test(([1, 2, 3], [1, 2, 3]), stat,
random_state='herring')
# -- Test Parameters -- #
@pytest.mark.parametrize('random_state', [np.random.RandomState,
np.random.default_rng])
@pytest.mark.parametrize('permutation_type',
['pairings', 'samples', 'independent'])
def test_batch(self, permutation_type, random_state):
# make sure that the `batch` parameter is respected by checking the
# maximum batch size provided in calls to `statistic`
x = self.rng.random(10)
y = self.rng.random(10)
def statistic(x, y, axis):
batch_size = 1 if x.ndim == 1 else len(x)
statistic.batch_size = max(batch_size, statistic.batch_size)
statistic.counter += 1
return np.mean(x, axis=axis) - np.mean(y, axis=axis)
statistic.counter = 0
statistic.batch_size = 0
kwds = {'n_resamples': 1000, 'permutation_type': permutation_type,
'vectorized': True}
res1 = stats.permutation_test((x, y), statistic, batch=1,
random_state=random_state(0), **kwds)
assert_equal(statistic.counter, 1001)
assert_equal(statistic.batch_size, 1)
statistic.counter = 0
res2 = stats.permutation_test((x, y), statistic, batch=50,
random_state=random_state(0), **kwds)
assert_equal(statistic.counter, 21)
assert_equal(statistic.batch_size, 50)
statistic.counter = 0
res3 = stats.permutation_test((x, y), statistic, batch=1000,
random_state=random_state(0), **kwds)
assert_equal(statistic.counter, 2)
assert_equal(statistic.batch_size, 1000)
assert_equal(res1.pvalue, res3.pvalue)
assert_equal(res2.pvalue, res3.pvalue)
@pytest.mark.parametrize('random_state', [np.random.RandomState,
np.random.default_rng])
@pytest.mark.parametrize('permutation_type, exact_size',
[('pairings', special.factorial(3)**2),
('samples', 2**3),
('independent', special.binom(6, 3))])
def test_permutations(self, permutation_type, exact_size, random_state):
# make sure that the `permutations` parameter is respected by checking
# the size of the null distribution
x = self.rng.random(3)
y = self.rng.random(3)
def statistic(x, y, axis):
return np.mean(x, axis=axis) - np.mean(y, axis=axis)
kwds = {'permutation_type': permutation_type,
'vectorized': True}
res = stats.permutation_test((x, y), statistic, n_resamples=3,
random_state=random_state(0), **kwds)
assert_equal(res.null_distribution.size, 3)
res = stats.permutation_test((x, y), statistic, **kwds)
assert_equal(res.null_distribution.size, exact_size)
# -- Randomized Permutation Tests -- #
# To get reasonable accuracy, these next three tests are somewhat slow.
# Originally, I had them passing for all combinations of permutation type,
# alternative, and RNG, but that takes too long for CI. Instead, split
# into three tests, each testing a particular combination of the three
# parameters.
def test_randomized_test_against_exact_both(self):
# check that the randomized and exact tests agree to reasonable
# precision for permutation_type='both
alternative, rng = 'less', 0
nx, ny, permutations = 8, 9, 24000
assert special.binom(nx + ny, nx) > permutations
x = stats.norm.rvs(size=nx)
y = stats.norm.rvs(size=ny)
data = x, y
def statistic(x, y, axis):
return np.mean(x, axis=axis) - np.mean(y, axis=axis)
kwds = {'vectorized': True, 'permutation_type': 'independent',
'batch': 100, 'alternative': alternative, 'random_state': rng}
res = permutation_test(data, statistic, n_resamples=permutations,
**kwds)
res2 = permutation_test(data, statistic, n_resamples=np.inf, **kwds)
assert res.statistic == res2.statistic
assert_allclose(res.pvalue, res2.pvalue, atol=1e-2)
@pytest.mark.slow()
def test_randomized_test_against_exact_samples(self):
# check that the randomized and exact tests agree to reasonable
# precision for permutation_type='samples'
alternative, rng = 'greater', None
nx, ny, permutations = 15, 15, 32000
assert 2**nx > permutations
x = stats.norm.rvs(size=nx)
y = stats.norm.rvs(size=ny)
data = x, y
def statistic(x, y, axis):
return np.mean(x - y, axis=axis)
kwds = {'vectorized': True, 'permutation_type': 'samples',
'batch': 100, 'alternative': alternative, 'random_state': rng}
res = permutation_test(data, statistic, n_resamples=permutations,
**kwds)
res2 = permutation_test(data, statistic, n_resamples=np.inf, **kwds)
assert res.statistic == res2.statistic
assert_allclose(res.pvalue, res2.pvalue, atol=1e-2)
def test_randomized_test_against_exact_pairings(self):
# check that the randomized and exact tests agree to reasonable
# precision for permutation_type='pairings'
alternative, rng = 'two-sided', self.rng
nx, ny, permutations = 8, 8, 40000
assert special.factorial(nx) > permutations
x = stats.norm.rvs(size=nx)
y = stats.norm.rvs(size=ny)
data = [x]
def statistic1d(x):
return stats.pearsonr(x, y)[0]
statistic = _resampling._vectorize_statistic(statistic1d)
kwds = {'vectorized': True, 'permutation_type': 'samples',
'batch': 100, 'alternative': alternative, 'random_state': rng}
res = permutation_test(data, statistic, n_resamples=permutations,
**kwds)
res2 = permutation_test(data, statistic, n_resamples=np.inf, **kwds)
assert res.statistic == res2.statistic
assert_allclose(res.pvalue, res2.pvalue, atol=1e-2)
@pytest.mark.parametrize('alternative', ('less', 'greater'))
# Different conventions for two-sided p-value here VS ttest_ind.
# Eventually, we can add multiple options for the two-sided alternative
# here in permutation_test.
@pytest.mark.parametrize('permutations', (30, 1e9))
@pytest.mark.parametrize('axis', (0, 1, 2))
def test_against_permutation_ttest(self, alternative, permutations, axis):
# check that this function and ttest_ind with permutations give
# essentially identical results.
x = np.arange(3*4*5).reshape(3, 4, 5)
y = np.moveaxis(np.arange(4)[:, None, None], 0, axis)
rng1 = np.random.default_rng(4337234444626115331)
res1 = stats.ttest_ind(x, y, permutations=permutations, axis=axis,
random_state=rng1, alternative=alternative)
def statistic(x, y, axis):
return stats.ttest_ind(x, y, axis=axis).statistic
rng2 = np.random.default_rng(4337234444626115331)
res2 = permutation_test((x, y), statistic, vectorized=True,
n_resamples=permutations,
alternative=alternative, axis=axis,
random_state=rng2)
assert_allclose(res1.statistic, res2.statistic, rtol=self.rtol)
assert_allclose(res1.pvalue, res2.pvalue, rtol=self.rtol)
# -- Independent (Unpaired) Sample Tests -- #
@pytest.mark.parametrize('alternative', ("less", "greater", "two-sided"))
def test_against_ks_2samp(self, alternative):
x = self.rng.normal(size=4, scale=1)
y = self.rng.normal(size=5, loc=3, scale=3)
expected = stats.ks_2samp(x, y, alternative=alternative, mode='exact')
def statistic1d(x, y):
return stats.ks_2samp(x, y, mode='asymp',
alternative=alternative).statistic
# ks_2samp is always a one-tailed 'greater' test
# it's the statistic that changes (D+ vs D- vs max(D+, D-))
res = permutation_test((x, y), statistic1d, n_resamples=np.inf,
alternative='greater', random_state=self.rng)
assert_allclose(res.statistic, expected.statistic, rtol=self.rtol)
assert_allclose(res.pvalue, expected.pvalue, rtol=self.rtol)
@pytest.mark.parametrize('alternative', ("less", "greater", "two-sided"))
def test_against_ansari(self, alternative):
x = self.rng.normal(size=4, scale=1)
y = self.rng.normal(size=5, scale=3)
# ansari has a different convention for 'alternative'
alternative_correspondence = {"less": "greater",
"greater": "less",
"two-sided": "two-sided"}
alternative_scipy = alternative_correspondence[alternative]
expected = stats.ansari(x, y, alternative=alternative_scipy)
def statistic1d(x, y):
return stats.ansari(x, y).statistic
res = permutation_test((x, y), statistic1d, n_resamples=np.inf,
alternative=alternative, random_state=self.rng)
assert_allclose(res.statistic, expected.statistic, rtol=self.rtol)
assert_allclose(res.pvalue, expected.pvalue, rtol=self.rtol)
@pytest.mark.parametrize('alternative', ("less", "greater", "two-sided"))
def test_against_mannwhitneyu(self, alternative):
x = stats.uniform.rvs(size=(3, 5, 2), loc=0, random_state=self.rng)
y = stats.uniform.rvs(size=(3, 5, 2), loc=0.05, random_state=self.rng)
expected = stats.mannwhitneyu(x, y, axis=1, alternative=alternative)
def statistic(x, y, axis):
return stats.mannwhitneyu(x, y, axis=axis).statistic
res = permutation_test((x, y), statistic, vectorized=True,
n_resamples=np.inf, alternative=alternative,
axis=1, random_state=self.rng)
assert_allclose(res.statistic, expected.statistic, rtol=self.rtol)
assert_allclose(res.pvalue, expected.pvalue, rtol=self.rtol)
def test_against_cvm(self):
x = stats.norm.rvs(size=4, scale=1, random_state=self.rng)
y = stats.norm.rvs(size=5, loc=3, scale=3, random_state=self.rng)
expected = stats.cramervonmises_2samp(x, y, method='exact')
def statistic1d(x, y):
return stats.cramervonmises_2samp(x, y,
method='asymptotic').statistic
# cramervonmises_2samp has only one alternative, greater
res = permutation_test((x, y), statistic1d, n_resamples=np.inf,
alternative='greater', random_state=self.rng)
assert_allclose(res.statistic, expected.statistic, rtol=self.rtol)
assert_allclose(res.pvalue, expected.pvalue, rtol=self.rtol)
@pytest.mark.xslow()
@pytest.mark.parametrize('axis', (-1, 2))
def test_vectorized_nsamp_ptype_both(self, axis):
# Test that permutation_test with permutation_type='independent' works
# properly for a 3-sample statistic with nd array samples of different
# (but compatible) shapes and ndims. Show that exact permutation test
# and random permutation tests approximate SciPy's asymptotic pvalues
# and that exact and random permutation test results are even closer
# to one another (than they are to the asymptotic results).
# Three samples, different (but compatible) shapes with different ndims
rng = np.random.default_rng(6709265303529651545)
x = rng.random(size=(3))
y = rng.random(size=(1, 3, 2))
z = rng.random(size=(2, 1, 4))
data = (x, y, z)
# Define the statistic (and pvalue for comparison)
def statistic1d(*data):
return stats.kruskal(*data).statistic
def pvalue1d(*data):
return stats.kruskal(*data).pvalue
statistic = _resampling._vectorize_statistic(statistic1d)
pvalue = _resampling._vectorize_statistic(pvalue1d)
# Calculate the expected results
x2 = np.broadcast_to(x, (2, 3, 3)) # broadcast manually because
y2 = np.broadcast_to(y, (2, 3, 2)) # _vectorize_statistic doesn't
z2 = np.broadcast_to(z, (2, 3, 4))
expected_statistic = statistic(x2, y2, z2, axis=axis)
expected_pvalue = pvalue(x2, y2, z2, axis=axis)
# Calculate exact and randomized permutation results
kwds = {'vectorized': False, 'axis': axis, 'alternative': 'greater',
'permutation_type': 'independent', 'random_state': self.rng}
res = permutation_test(data, statistic1d, n_resamples=np.inf, **kwds)
res2 = permutation_test(data, statistic1d, n_resamples=1000, **kwds)
# Check results
assert_allclose(res.statistic, expected_statistic, rtol=self.rtol)
assert_allclose(res.statistic, res2.statistic, rtol=self.rtol)
assert_allclose(res.pvalue, expected_pvalue, atol=6e-2)
assert_allclose(res.pvalue, res2.pvalue, atol=3e-2)
# -- Paired-Sample Tests -- #
@pytest.mark.parametrize('alternative', ("less", "greater", "two-sided"))
def test_against_wilcoxon(self, alternative):
x = stats.uniform.rvs(size=(3, 6, 2), loc=0, random_state=self.rng)
y = stats.uniform.rvs(size=(3, 6, 2), loc=0.05, random_state=self.rng)
# We'll check both 1- and 2-sample versions of the same test;
# we expect identical results to wilcoxon in all cases.
def statistic_1samp_1d(z):
# 'less' ensures we get the same of two statistics every time
return stats.wilcoxon(z, alternative='less').statistic
def statistic_2samp_1d(x, y):
return stats.wilcoxon(x, y, alternative='less').statistic
def test_1d(x, y):
return stats.wilcoxon(x, y, alternative=alternative)
test = _resampling._vectorize_statistic(test_1d)
expected = test(x, y, axis=1)
expected_stat = expected[0]
expected_p = expected[1]
kwds = {'vectorized': False, 'axis': 1, 'alternative': alternative,
'permutation_type': 'samples', 'random_state': self.rng,
'n_resamples': np.inf}
res1 = permutation_test((x-y,), statistic_1samp_1d, **kwds)
res2 = permutation_test((x, y), statistic_2samp_1d, **kwds)
# `wilcoxon` returns a different statistic with 'two-sided'
assert_allclose(res1.statistic, res2.statistic, rtol=self.rtol)
if alternative != 'two-sided':
assert_allclose(res2.statistic, expected_stat, rtol=self.rtol)
assert_allclose(res2.pvalue, expected_p, rtol=self.rtol)
assert_allclose(res1.pvalue, res2.pvalue, rtol=self.rtol)
@pytest.mark.parametrize('alternative', ("less", "greater", "two-sided"))
def test_against_binomtest(self, alternative):
x = self.rng.integers(0, 2, size=10)
x[x == 0] = -1
# More naturally, the test would flip elements between 0 and one.
# However, permutation_test will flip the _signs_ of the elements.
# So we have to work with +1/-1 instead of 1/0.
def statistic(x, axis=0):
return np.sum(x > 0, axis=axis)
k, n, p = statistic(x), 10, 0.5
expected = stats.binomtest(k, n, p, alternative=alternative)
res = stats.permutation_test((x,), statistic, vectorized=True,
permutation_type='samples',
n_resamples=np.inf, random_state=self.rng,
alternative=alternative)
assert_allclose(res.pvalue, expected.pvalue, rtol=self.rtol)
# -- Exact Association Tests -- #
def test_against_kendalltau(self):
x = self.rng.normal(size=6)
y = x + self.rng.normal(size=6)
expected = stats.kendalltau(x, y, method='exact')
def statistic1d(x):
return stats.kendalltau(x, y, method='asymptotic').statistic
# kendalltau currently has only one alternative, two-sided
res = permutation_test((x,), statistic1d, permutation_type='pairings',
n_resamples=np.inf, random_state=self.rng)
assert_allclose(res.statistic, expected.statistic, rtol=self.rtol)
assert_allclose(res.pvalue, expected.pvalue, rtol=self.rtol)
@pytest.mark.parametrize('alternative', ('less', 'greater', 'two-sided'))
def test_against_fisher_exact(self, alternative):
def statistic(x,):
return np.sum((x == 1) & (y == 1))
# x and y are binary random variables with some dependence
rng = np.random.default_rng(6235696159000529929)
x = (rng.random(7) > 0.6).astype(float)
y = (rng.random(7) + 0.25*x > 0.6).astype(float)
tab = stats.contingency.crosstab(x, y)[1]
res = permutation_test((x,), statistic, permutation_type='pairings',
n_resamples=np.inf, alternative=alternative,
random_state=rng)
res2 = stats.fisher_exact(tab, alternative=alternative)
assert_allclose(res.pvalue, res2[1])
@pytest.mark.xslow()
@pytest.mark.parametrize('axis', (-2, 1))
def test_vectorized_nsamp_ptype_samples(self, axis):
# Test that permutation_test with permutation_type='samples' works
# properly for a 3-sample statistic with nd array samples of different
# (but compatible) shapes and ndims. Show that exact permutation test
# reproduces SciPy's exact pvalue and that random permutation test
# approximates it.
x = self.rng.random(size=(2, 4, 3))
y = self.rng.random(size=(1, 4, 3))
z = self.rng.random(size=(2, 4, 1))
x = stats.rankdata(x, axis=axis)
y = stats.rankdata(y, axis=axis)
z = stats.rankdata(z, axis=axis)
y = y[0] # to check broadcast with different ndim
data = (x, y, z)
def statistic1d(*data):
return stats.page_trend_test(data, ranked=True,
method='asymptotic').statistic
def pvalue1d(*data):
return stats.page_trend_test(data, ranked=True,
method='exact').pvalue
statistic = _resampling._vectorize_statistic(statistic1d)
pvalue = _resampling._vectorize_statistic(pvalue1d)
expected_statistic = statistic(*np.broadcast_arrays(*data), axis=axis)
expected_pvalue = pvalue(*np.broadcast_arrays(*data), axis=axis)
# Let's forgive this use of an integer seed, please.
kwds = {'vectorized': False, 'axis': axis, 'alternative': 'greater',
'permutation_type': 'pairings', 'random_state': 0}
res = permutation_test(data, statistic1d, n_resamples=np.inf, **kwds)
res2 = permutation_test(data, statistic1d, n_resamples=5000, **kwds)
assert_allclose(res.statistic, expected_statistic, rtol=self.rtol)
assert_allclose(res.statistic, res2.statistic, rtol=self.rtol)
assert_allclose(res.pvalue, expected_pvalue, rtol=self.rtol)
assert_allclose(res.pvalue, res2.pvalue, atol=3e-2)
# -- Test Against External References -- #
tie_case_1 = {'x': [1, 2, 3, 4], 'y': [1.5, 2, 2.5],
'expected_less': 0.2000000000,
'expected_2sided': 0.4, # 2*expected_less
'expected_Pr_gte_S_mean': 0.3428571429, # see note below
'expected_statistic': 7.5,
'expected_avg': 9.142857, 'expected_std': 1.40698}
tie_case_2 = {'x': [111, 107, 100, 99, 102, 106, 109, 108],
'y': [107, 108, 106, 98, 105, 103, 110, 105, 104],
'expected_less': 0.1555738379,
'expected_2sided': 0.3111476758,
'expected_Pr_gte_S_mean': 0.2969971205, # see note below
'expected_statistic': 32.5,
'expected_avg': 38.117647, 'expected_std': 5.172124}
@pytest.mark.xslow() # only the second case is slow, really
@pytest.mark.parametrize('case', (tie_case_1, tie_case_2))
def test_with_ties(self, case):
"""
Results above from SAS PROC NPAR1WAY, e.g.
DATA myData;
INPUT X Y;
CARDS;
1 1
1 2
1 3
1 4
2 1.5
2 2
2 2.5
ods graphics on;
proc npar1way AB data=myData;
class X;
EXACT;
run;
ods graphics off;
Note: SAS provides Pr >= |S-Mean|, which is different from our
definition of a two-sided p-value.
"""
x = case['x']
y = case['y']
expected_statistic = case['expected_statistic']
expected_less = case['expected_less']
expected_2sided = case['expected_2sided']
expected_Pr_gte_S_mean = case['expected_Pr_gte_S_mean']
expected_avg = case['expected_avg']
expected_std = case['expected_std']
def statistic1d(x, y):
return stats.ansari(x, y).statistic
with np.testing.suppress_warnings() as sup:
sup.filter(UserWarning, "Ties preclude use of exact statistic")
res = permutation_test((x, y), statistic1d, n_resamples=np.inf,
alternative='less')
res2 = permutation_test((x, y), statistic1d, n_resamples=np.inf,
alternative='two-sided')
assert_allclose(res.statistic, expected_statistic, rtol=self.rtol)
assert_allclose(res.pvalue, expected_less, atol=1e-10)
assert_allclose(res2.pvalue, expected_2sided, atol=1e-10)
assert_allclose(res2.null_distribution.mean(), expected_avg, rtol=1e-6)
assert_allclose(res2.null_distribution.std(), expected_std, rtol=1e-6)
# SAS provides Pr >= |S-Mean|; might as well check against that, too
S = res.statistic
mean = res.null_distribution.mean()
n = len(res.null_distribution)
Pr_gte_S_mean = np.sum(np.abs(res.null_distribution-mean)
>= np.abs(S-mean))/n
assert_allclose(expected_Pr_gte_S_mean, Pr_gte_S_mean)
@pytest.mark.parametrize('alternative, expected_pvalue',
(('less', 0.9708333333333),
('greater', 0.05138888888889),
('two-sided', 0.1027777777778)))
def test_against_spearmanr_in_R(self, alternative, expected_pvalue):
"""
Results above from R cor.test, e.g.
options(digits=16)
x <- c(1.76405235, 0.40015721, 0.97873798,
2.2408932, 1.86755799, -0.97727788)
y <- c(2.71414076, 0.2488, 0.87551913,
2.6514917, 2.01160156, 0.47699563)
cor.test(x, y, method = "spearm", alternative = "t")
"""
# data comes from
# np.random.seed(0)
# x = stats.norm.rvs(size=6)
# y = x + stats.norm.rvs(size=6)
x = [1.76405235, 0.40015721, 0.97873798,
2.2408932, 1.86755799, -0.97727788]
y = [2.71414076, 0.2488, 0.87551913,
2.6514917, 2.01160156, 0.47699563]
expected_statistic = 0.7714285714285715
def statistic1d(x):
return stats.spearmanr(x, y).statistic
res = permutation_test((x,), statistic1d, permutation_type='pairings',
n_resamples=np.inf, alternative=alternative)
assert_allclose(res.statistic, expected_statistic, rtol=self.rtol)
assert_allclose(res.pvalue, expected_pvalue, atol=1e-13)
@pytest.mark.parametrize("batch", (-1, 0))
def test_batch_generator_iv(self, batch):
with pytest.raises(ValueError, match="`batch` must be positive."):
list(_resampling._batch_generator([1, 2, 3], batch))
batch_generator_cases = [(range(0), 3, []),
(range(6), 3, [[0, 1, 2], [3, 4, 5]]),
(range(8), 3, [[0, 1, 2], [3, 4, 5], [6, 7]])]
@pytest.mark.parametrize("iterable, batch, expected",
batch_generator_cases)
def test_batch_generator(self, iterable, batch, expected):
got = list(_resampling._batch_generator(iterable, batch))
assert got == expected
def test_finite_precision_statistic(self):
# Some statistics return numerically distinct values when the values
# should be equal in theory. Test that `permutation_test` accounts
# for this in some way.
x = [1, 2, 4, 3]
y = [2, 4, 6, 8]
def statistic(x, y):
return stats.pearsonr(x, y)[0]
res = stats.permutation_test((x, y), statistic, vectorized=False,
permutation_type='pairings')
r, pvalue, null = res.statistic, res.pvalue, res.null_distribution
correct_p = 2 * np.sum(null >= r - 1e-14) / len(null)
assert pvalue == correct_p == 1/3
# Compare against other exact correlation tests using R corr.test
# options(digits=16)
# x = c(1, 2, 4, 3)
# y = c(2, 4, 6, 8)
# cor.test(x, y, alternative = "t", method = "spearman") # 0.333333333
# cor.test(x, y, alternative = "t", method = "kendall") # 0.333333333
def test_all_partitions_concatenated():
# make sure that _all_paritions_concatenated produces the correct number
# of partitions of the data into samples of the given sizes and that
# all are unique
n = np.array([3, 2, 4], dtype=int)
nc = np.cumsum(n)
all_partitions = set()
counter = 0
for partition_concatenated in _resampling._all_partitions_concatenated(n):
counter += 1
partitioning = np.split(partition_concatenated, nc[:-1])
all_partitions.add(tuple([frozenset(i) for i in partitioning]))
expected = np.prod([special.binom(sum(n[i:]), sum(n[i+1:]))
for i in range(len(n)-1)])
assert_equal(counter, expected)
assert_equal(len(all_partitions), expected)
@pytest.mark.parametrize('fun_name',
['bootstrap', 'permutation_test', 'monte_carlo_test'])
def test_parameter_vectorized(fun_name):
# Check that parameter `vectorized` is working as desired for all
# resampling functions. Results don't matter; just don't fail asserts.
rng = np.random.default_rng(75245098234592)
sample = rng.random(size=10)
def rvs(size): # needed by `monte_carlo_test`
return stats.norm.rvs(size=size, random_state=rng)
fun_options = {'bootstrap': {'data': (sample,), 'random_state': rng,
'method': 'percentile'},
'permutation_test': {'data': (sample,), 'random_state': rng,
'permutation_type': 'samples'},
'monte_carlo_test': {'sample': sample, 'rvs': rvs}}
common_options = {'n_resamples': 100}
fun = getattr(stats, fun_name)
options = fun_options[fun_name]
options.update(common_options)
def statistic(x, axis):
assert x.ndim > 1 or np.array_equal(x, sample)
return np.mean(x, axis=axis)
fun(statistic=statistic, vectorized=None, **options)
fun(statistic=statistic, vectorized=True, **options)
def statistic(x):
assert x.ndim == 1
return np.mean(x)
fun(statistic=statistic, vectorized=None, **options)
fun(statistic=statistic, vectorized=False, **options)
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