# MultiTest -- Global Tests for Multiple Hypothesis
MultiTest includes several techniques for multiple hypothesis testing:
- ``MultiTest.hc`` Higher Criticism
- ``MultiTest.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 statistic
- ``MultiTest.fdr`` False-discovery rate with optimized rate parameter
- ``MultiTest.minp`` Minimal P-values as in Bonferroni style inference
- ``MultiTest.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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"description": "# MultiTest -- Global Tests for Multiple Hypothesis\n\nMultiTest includes several techniques for multiple hypothesis testing:\n- ``MultiTest.hc`` Higher Criticism\n- ``MultiTest.hcstar`` Higher Criticism with limited range proposed in [1]\n- ``MultiTest.hc_jin`` Higher Criticism with limited range proposed as proposed in [3]\n- ``MultiTest.berk_jones`` Berk-Jones statistic\n- ``MultiTest.fdr`` False-discovery rate with optimized rate parameter\n- ``MultiTest.minp`` Minimal P-values as in Bonferroni style inference\n- ``MultiTest.fisher`` Fisher's method to combine P-values\nIn all cases, one should reject the null for large values of the test statistic.\n\n## Example:\n```\nimport numpy as np\nfrom scipy.stats import norm\nfrom multitest import MultiTest\n\np = 100\nz = np.random.randn(p)\npvals = 2*norm.cdf(-np.abs(z)/2)\n\nmtest = MultiTest(pvals)\n\nhc, p_hct = mtest.hc(gamma = 0.3)\nbj = mtest.berk_jones()\n\nii = np.arange(len(pvals))\nprint(f\"HC = {hc}, Indices of P-values below HCT: {ii[pvals <= p_hct]}\")\nprint(f\"Berk-Jones = {bj}\")\n```\n\n## Use cases: \nThis package was used to obtain evaluations reported in [5] and [6].\n\n## References:\n[1] Donoho, David. L. and Jin, Jiashun. \"Higher criticism for detecting sparse hetrogenous mixtures.\" The Annals of Statistics 32, no. 3 (2004): 962-994.\n[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.\n[3] Jin, Jiashun, and Wanjie Wang. \"Influential features PCA for high dimensional clustering.\" The Annals of Statistics 44, no. 6 (2016): 2323-2359.\n[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.\n[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.\n[6] Kipnis, Alon. \"Unification of rare/weak detection models using moderate deviations analysis and log-chisquared p-values.\" Statistica Scinica 2025.\n",
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