From 3798c61efd21a6f396ebe0df6bfa2d50cd9a7898 Mon Sep 17 00:00:00 2001 From: Theophile GENTILHOMME <tgentilhomme@jurasix08.idiap.ch> Date: Thu, 22 Mar 2018 08:07:36 +0100 Subject: [PATCH] Math support for conf inter doc --- doc/guide.rst | 18 +++++++++++------- 1 file changed, 11 insertions(+), 7 deletions(-) diff --git a/doc/guide.rst b/doc/guide.rst index f29a8de..352f23a 100644 --- a/doc/guide.rst +++ b/doc/guide.rst @@ -208,18 +208,22 @@ Both functions require that at least one probe item exists, which has no accordi Confidence interval ------------------- -A confidence interval for parameter `x` consists of a lower -estimate `L`, and an upper estimate `U`, such that the probability of the true value being -within the interval estimate is equal to `\alpha`. For example, -a 95% confidence interval (i.e. `\alpha = 0.95`) for a parameter `x` is given by `[L, U]` such that -`Prob(x∈[L,U]) = 95%`. The smaller the test size, the wider the confidence -interval will be, and the greater `alpha`, the smaller the confidence interval +A confidence interval for parameter :math:`x` consists of a lower +estimate :math:`L`, and an upper estimate :math:`U`, such that the probability +of the true value being within the interval estimate is equal to :math:`\alpha`. +For example, a 95% confidence interval (i.e. :math:`\alpha = 0.95`) for a +parameter :math:`x` is given by :math:`[L, U]` such that + +.. math:: Prob(x∈[L,U]) = 95% + +The smaller the test size, the wider the confidence +interval will be, and the greater :math:`\alpha`, the smaller the confidence interval will be. `The Clopper-Pearson interval`_, a common method for calculating confidence intervals, is function of the number of success, the number of trials and confidence -value `\alpha` is used as :py:func:`bob.measure.utils.confidence_for_indicator_variable`. +value :math:`\alpha` is used as :py:func:`bob.measure.utils.confidence_for_indicator_variable`. It is based on the cumulative probabilities of the binomial distribution. This method is quite conservative, meaning that the true coverage rate of a 95% Clopper–Pearson interval may be well above 95%. -- GitLab