Commit 91b44bd9 authored by Theophile GENTILHOMME's avatar Theophile GENTILHOMME

Fix doc and add guide description

parent 880d989b
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in 20 minutes and 43 seconds
......@@ -9,24 +9,20 @@ def confidence_for_indicator_variable(x, n, alpha=0.05):
The Clopper-Pearson interval method is used for estimating the confidence
intervals.
More info on confidence intervals
---------------------------------
https://en.wikipedia.org/wiki/Confidence_interval
https://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval#Clopper-Pearson_interval
Parameters
----------
x : int
The number of successes.
n : int
The number of trials.
alpha : float, optional
alpha : :obj:`float`, optional
The 1-confidence value that you want. For example, alpha should be 0.05
to obtain 95% confidence intervals.
Returns
-------
(float, float) Returns a tuple of (lower_bound, upper_bound) which
(:obj:`float`, :obj:`float`)
a tuple of (lower_bound, upper_bound) which
shows the limit of your success rate: lower_bound < x/n < upper_bound
'''
lower_bound = scipy.stats.beta.ppf(alpha / 2.0, x, n - x + 1)
......
......@@ -205,6 +205,25 @@ Both functions require that at least one probe item exists, which has no accordi
>>> dir = bob.measure.detection_identification_rate(rr_scores, threshold = 0, rank=1)
>>> far = bob.measure.false_alarm_rate(rr_scores, threshold = 0)
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
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`.
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%.
Plotting
--------
......@@ -436,4 +455,4 @@ that best suits you.
.. _`The Expected Performance Curve`: http://publications.idiap.ch/downloads/reports/2005/bengio_2005_icml.pdf
.. _`The DET curve in assessment of detection task performance`: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.117.4489&rep=rep1&type=pdf
.. _openbr: http://openbiometrics.org
.. _`The Clopper-Pearson interval`: https://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval#Clopper-Pearson_interval
......@@ -64,6 +64,13 @@ Generic
bob.measure.rmse
bob.measure.get_config
Confidence interval
-------------------
.. autosummary::
bob.measure.utils.confidence_for_indicator_variable
Calibration
-----------
......
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