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test_resampling.py
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test_resampling.py
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import pytest
import numpy as np
from numpy.testing import assert_allclose, assert_equal, suppress_warnings
from scipy.conftest import array_api_compatible
from scipy._lib._util import rng_integers
from scipy._lib._array_api import (is_numpy, xp_assert_close,
xp_assert_equal, array_namespace)
from scipy import stats, special
from scipy.optimize import root
from scipy.stats import bootstrap, monte_carlo_test, permutation_test, power
import scipy.stats._resampling as _resampling
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.slow
@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.slow
@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.slow
@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.slow
@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 get_rvs(self, rvs_in, rs, dtype=None, xp=np):
return lambda *args, **kwds: xp.asarray(rvs_in(*args, random_state=rs, **kwds),
dtype=dtype)
def get_statistic(self, xp):
def statistic(x, axis):
m = xp.mean(x, axis=axis)
v = xp.var(x, axis=axis, correction=1)
n = x.shape[axis]
return m / (v/n)**0.5
# return stats.ttest_1samp(x, popmean=0., axis=axis).statistic)
return statistic
@array_api_compatible
def test_input_validation(self, xp):
# test that the appropriate error messages are raised for invalid input
data = xp.asarray([1., 2., 3.])
def stat(x, axis=None):
return xp.mean(x, axis=axis)
message = "Array shapes are incompatible for broadcasting."
temp = (xp.zeros((2, 5)), xp.zeros((3, 5)))
rvs = (stats.norm.rvs, stats.norm.rvs)
with pytest.raises(ValueError, match=message):
monte_carlo_test(temp, rvs, lambda x, y, axis: 1, axis=-1)
message = "`axis` must be an integer."
with pytest.raises(ValueError, match=message):
monte_carlo_test(data, stats.norm.rvs, stat, axis=1.5)
message = "`vectorized` must be `True`, `False`, or `None`."
with pytest.raises(ValueError, match=message):
monte_carlo_test(data, 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(data, None, stat)
with pytest.raises(TypeError, match=message):
temp = xp.asarray([[1., 2.], [3., 4.]])
monte_carlo_test(temp, [lambda x: x, None], stat)
message = "If `rvs` is a sequence..."
with pytest.raises(ValueError, match=message):
temp = xp.asarray([[1., 2., 3.]])
monte_carlo_test(temp, [lambda x: x, lambda x: x], stat)
message = "`statistic` must be callable."
with pytest.raises(TypeError, match=message):
monte_carlo_test(data, stats.norm.rvs, None)
message = "`n_resamples` must be a positive integer."
with pytest.raises(ValueError, match=message):
monte_carlo_test(data, stats.norm.rvs, stat, n_resamples=-1000)
message = "`n_resamples` must be a positive integer."
with pytest.raises(ValueError, match=message):
monte_carlo_test(data, 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(data, stats.norm.rvs, stat, batch=-1000)
message = "`batch` must be a positive integer or None."
with pytest.raises(ValueError, match=message):
monte_carlo_test(data, stats.norm.rvs, stat, batch=1000.5)
message = "`alternative` must be in..."
with pytest.raises(ValueError, match=message):
monte_carlo_test(data, stats.norm.rvs, stat, alternative='ekki')
# *If* this raises a value error, make sure it has the intended message
message = "Signature inspection of statistic"
def rvs(size):
return xp.asarray(stats.norm.rvs(size=size))
try:
monte_carlo_test(data, rvs, xp.mean)
except ValueError as e:
assert str(e).startswith(message)
@array_api_compatible
def test_input_validation_xp(self, xp):
def non_vectorized_statistic(x):
return xp.mean(x)
message = "`statistic` must be vectorized..."
sample = xp.asarray([1., 2., 3.])
if is_numpy(xp):
monte_carlo_test(sample, stats.norm.rvs, non_vectorized_statistic)
return
with pytest.raises(ValueError, match=message):
monte_carlo_test(sample, stats.norm.rvs, non_vectorized_statistic)
with pytest.raises(ValueError, match=message):
monte_carlo_test(sample, stats.norm.rvs, xp.mean, vectorized=False)
@pytest.mark.xslow
@array_api_compatible
def test_batch(self, xp):
# 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 = xp.asarray(rng.standard_normal(size=10))
xp_test = array_namespace(x) # numpy.std doesn't have `correction`
def statistic(x, axis):
batch_size = 1 if x.ndim == 1 else x.shape[0]
statistic.batch_size = max(batch_size, statistic.batch_size)
statistic.counter += 1
return self.get_statistic(xp_test)(x, axis=axis)
statistic.counter = 0
statistic.batch_size = 0
kwds = {'sample': x, 'statistic': statistic,
'n_resamples': 1000, 'vectorized': True}
kwds['rvs'] = self.get_rvs(stats.norm.rvs, np.random.default_rng(328423), xp=xp)
res1 = monte_carlo_test(batch=1, **kwds)
assert_equal(statistic.counter, 1001)
assert_equal(statistic.batch_size, 1)
kwds['rvs'] = self.get_rvs(stats.norm.rvs, np.random.default_rng(328423), xp=xp)
statistic.counter = 0
res2 = monte_carlo_test(batch=50, **kwds)
assert_equal(statistic.counter, 21)
assert_equal(statistic.batch_size, 50)
kwds['rvs'] = self.get_rvs(stats.norm.rvs, np.random.default_rng(328423), xp=xp)
statistic.counter = 0
res3 = monte_carlo_test(**kwds)
assert_equal(statistic.counter, 2)
assert_equal(statistic.batch_size, 1000)
xp_assert_equal(res1.pvalue, res3.pvalue)
xp_assert_equal(res2.pvalue, res3.pvalue)
@array_api_compatible
@pytest.mark.parametrize('axis', range(-3, 3))
def test_axis_dtype(self, axis, xp):
# test that Nd-array samples are handled correctly for valid values
# of the `axis` parameter; also make sure non-default dtype is maintained
rng = np.random.default_rng(2389234)
size = [2, 3, 4]
size[axis] = 100
# Determine non-default dtype
dtype_default = xp.asarray(1.).dtype
dtype_str = 'float32'if ("64" in str(dtype_default)) else 'float64'
dtype_np = getattr(np, dtype_str)
dtype = getattr(xp, dtype_str)
# ttest_1samp is CPU array-API compatible, but it would be good to
# include CuPy in this test. We'll perform ttest_1samp with a
# NumPy array, but all the rest with be done with fully array-API
# compatible code.
x = rng.standard_normal(size=size, dtype=dtype_np)
expected = stats.ttest_1samp(x, popmean=0., axis=axis)
x = xp.asarray(x, dtype=dtype)
xp_test = array_namespace(x) # numpy.std doesn't have `correction`
statistic = self.get_statistic(xp_test)
rvs = self.get_rvs(stats.norm.rvs, rng, dtype=dtype, xp=xp)
res = monte_carlo_test(x, rvs, statistic, vectorized=True,
n_resamples=20000, axis=axis)
ref_statistic = xp.asarray(expected.statistic, dtype=dtype)
ref_pvalue = xp.asarray(expected.pvalue, dtype=dtype)
xp_assert_close(res.statistic, ref_statistic)
xp_assert_close(res.pvalue, ref_pvalue, atol=self.atol)
@array_api_compatible
@pytest.mark.parametrize('alternative', ("two-sided", "less", "greater"))
def test_alternative(self, alternative, xp):
# test that `alternative` is working as expected
rng = np.random.default_rng(65723433)
x = rng.standard_normal(size=30)
ref = stats.ttest_1samp(x, 0., alternative=alternative)
x = xp.asarray(x)
xp_test = array_namespace(x) # numpy.std doesn't have `correction`
statistic = self.get_statistic(xp_test)
rvs = self.get_rvs(stats.norm.rvs, rng, xp=xp)
res = monte_carlo_test(x, rvs, statistic, alternative=alternative)
xp_assert_close(res.statistic, xp.asarray(ref.statistic))
xp_assert_close(res.pvalue, xp.asarray(ref.pvalue), atol=self.atol)
# Tests below involve statistics that are not yet array-API compatible.
# They can be converted when the statistics are converted.
@pytest.mark.slow
@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.get_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.get_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.get_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.xslow
@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)