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  "Description": "The harmonic mean p-value (HMP) test combines p-values and\ncorrects for multiple testing while controlling the\nstrong-sense family-wise error rate. It is more powerful than\ncommon alternatives including Bonferroni and Simes procedures\nwhen combining large proportions of all the p-values, at the\ncost of slightly lower power when combining small proportions\nof all the p-values. It is more stringent than controlling the\nfalse discovery rate, and possesses theoretical robustness to\npositive correlations between tests and unequal weights. It is\na multi-level test in the sense that a superset of one or more\nsignificant tests is certain to be significant and conversely\nwhen the superset is non-significant, the constituent tests are\ncertain to be non-significant. It is based on MAMML (model\naveraging by mean maximum likelihood), a frequentist analogue\nto Bayesian model averaging, and is theoretically grounded in\ngeneralized central limit theorem. For detailed examples type\nvignette(\"harmonicmeanp\") after installation. Version 3.0\naddresses errors in versions 1.0 and 2.0 that led function\np.hmp to control the familywise error rate only in the weak\nsense, rather than the strong sense as intended.",
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      "title": "Asymptotically Exact Harmonic Mean p-Value",
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      "title": "Compute the Harmonic Mean _p_-Value",
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        "hmp.stat"
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      "title": "Compute the Model-Averaged Mean Maximized Likelihood",
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      "title": "The Harmonic Mean p-Value Asymptotic Distribution",
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        "hmp"
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      "title": "The Landau Distribution",
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        "pLandau",
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        "rLandau"
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      "title": "Model-Averaged Mean Maximized Likelihood Ratio Asymptotic Distribution",
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        "qmamml",
        "rmamml"
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    {
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      "title": "Compute a combined _p_-value via the model-averaged mean maximized likelihood ratio",
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        "Preliminaries",
        "Example 1. Sliding Window Analysis",
        "Example 2. Model-averaging in Regression",
        "Optimizing the Weights in the Comparative Phylogenetics Example",
        "Prior specification",
        "Power specification",
        "Appendix I. Function to enumerate all possible models",
        "References"
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