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.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.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) assert_allclose(g.confidence_interval.low, t.confidence_interval.low) 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) 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)