Several methods of combining P-values
Project description
MultiTest -- Global Tests for Multiple Hypothesis
MultiTest includes several techniques for multiple hypothesis testing:
MultiTest.hc
Higher CriticismMultiTest.hcstar
Higher Criticism with limited range proposed in [1]MultiTest.hc_jin
Higher Criticism with limited range proposed as proposed in [3]MultiTest.berk_jones
Berk-Jones statisticMultiTest.fdr
False-discovery rate with optimized rate parameterMultiTest.minp
Minimal P-values as in Bonferroni style inferenceMultiTest.fisher
Fisher's method to combine P-values In all cases, one should reject the null for large values of the test statistic.
Example:
import numpy as np
from scipy.stats import norm
from multitest import MultiTest
p = 100
z = np.random.randn(p)
pvals = 2*norm.cdf(-np.abs(z)/2)
mtest = MultiTest(pvals)
hc, p_hct = mtest.hc(gamma = 0.3)
bj = mtest.berk_jones()
ii = np.arange(len(pvals))
print(f"HC = {hc}, Indices of P-values below HCT: {ii[pvals <= p_hct]}")
print(f"Berk-Jones = {bj}")
Use cases:
This package was used to obtain evaluations reported in [5] and [6].
References:
[1] Donoho, David. L. and Jin, Jiashun. "Higher criticism for detecting sparse hetrogenous mixtures." The Annals of Statistics 32, no. 3 (2004): 962-994. [2] Donoho, David L. and Jin, Jiashun. "Higher critcism thresholding: Optimal feature selection when useful features are rare and weak." proceedings of the national academy of sciences, 2008. [3] Jin, Jiashun, and Wanjie Wang. "Influential features PCA for high dimensional clustering." The Annals of Statistics 44, no. 6 (2016): 2323-2359. [4] Amit Moscovich, Boaz Nadler, and Clifford Spiegelman. "On the exact Berk-Jones statistics and their p-value calculation." Electronic Journal of Statistics. 10 (2016): 2329-2354. [5] Donoho, David L., and Alon Kipnis. "Higher criticism to compare two large frequency tables, with sensitivity to possible rare and weak differences." The Annals of Statistics 50, no. 3 (2022): 1447-1472. [6] Kipnis, Alon. "Unification of rare/weak detection models using moderate deviations analysis and log-chisquared p-values." Statistica Scinica 2025.
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