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bob
bob.measure
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3798c61e
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3798c61e
authored
Mar 22, 2018
by
Theophile GENTILHOMME
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Math support for conf inter doc
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@@ -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%.
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