From 4eec2a43c503588dbbbc97614d2a7b70dc689820 Mon Sep 17 00:00:00 2001 From: Heiko Strathmann Date: Fri, 1 Apr 2016 11:34:06 +0100 Subject: [PATCH] more cookbook updates --- .../examples/statistical_testing/linear_time_mmd.rst | 5 +++-- .../examples/statistical_testing/quadratic_time_mmd.rst | 8 ++------ 2 files changed, 5 insertions(+), 8 deletions(-) diff --git a/doc/cookbook/source/examples/statistical_testing/linear_time_mmd.rst b/doc/cookbook/source/examples/statistical_testing/linear_time_mmd.rst index 9b8a07681f2..9fd59ac01ab 100644 --- a/doc/cookbook/source/examples/statistical_testing/linear_time_mmd.rst +++ b/doc/cookbook/source/examples/statistical_testing/linear_time_mmd.rst @@ -2,12 +2,13 @@ Linear Time MMD =============== -The unbiased statistic is given by +The linear time MMD implements a nonparametric statistical hypothesis test to reject the null hypothesis that to distributions :math:`p` and :math:`q`, each only observed via :math:`n` samples, are the same, i.e. :math:`H_0:p=q`. + +The (unbiased) statistic is given by .. math:: \frac{2}{n}\sum_{i=1}^n k(x_{2i},x_{2i}) + k(x_{2i+1}, x_{2i+1}) - 2k(x_{2i},x_{2i+1}). - See :cite:`gretton2012kernel` for a detailed introduction. diff --git a/doc/cookbook/source/examples/statistical_testing/quadratic_time_mmd.rst b/doc/cookbook/source/examples/statistical_testing/quadratic_time_mmd.rst index 9f0b5ee0199..c6dc57a71db 100644 --- a/doc/cookbook/source/examples/statistical_testing/quadratic_time_mmd.rst +++ b/doc/cookbook/source/examples/statistical_testing/quadratic_time_mmd.rst @@ -2,11 +2,7 @@ Quadratic Time MMD ================== -The Quadratic time MMD implements a nonparametric statistical hypothesis test to reject the null hypothesis that to distributions :math:`p` and :math:`q`, only observed via :math:`n` and :math:`m` samples respectively, are the same: - -.. math:: - - H_0:p=q. +The quadratic time MMD implements a nonparametric statistical hypothesis test to reject the null hypothesis that to distributions :math:`p` and :math:`q`, only observed via :math:`n` and :math:`m` samples respectively, are the same, i.e. :math:`H_0:p=q`. The (biased) test statistic is given by @@ -37,7 +33,7 @@ Biased statistic .. sgexample:: quadratic_time_mmd.sg:estimate_mmd_biased -There are multiple ways to perform the actual hypothesis test. The permutation version simulates from :math:`H_0` via repeatedly permuting the samples from :math:`p` and :math:`q`: +There are multiple ways to perform the actual hypothesis test, see :sgclass:`CQuadraticTimeMMD` for details. The permutation version simulates from :math:`H_0` via repeatedly permuting the samples from :math:`p` and :math:`q`: .. sgexample:: quadratic_time_mmd.sg:perform_test_permutation