From 3798c61efd21a6f396ebe0df6bfa2d50cd9a7898 Mon Sep 17 00:00:00 2001 From: Theophile GENTILHOMME 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%. -- 2.21.0