86 lines
3.1 KiB
C++
86 lines
3.1 KiB
C++
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// Copyright 2022 Jay Gohil, Hans Dembinski
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//
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// Distributed under the Boost Software License, version 1.0.
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// (See accompanying file LICENSE_1_0.txt
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// or copy at http://www.boost.org/LICENSE_1_0.txt)
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#ifndef BOOST_HISTOGRAM_UTILITY_WILSON_INTERVAL_HPP
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#define BOOST_HISTOGRAM_UTILITY_WILSON_INTERVAL_HPP
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#include <boost/histogram/fwd.hpp>
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#include <boost/histogram/utility/binomial_proportion_interval.hpp>
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#include <cmath>
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#include <utility>
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namespace boost {
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namespace histogram {
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namespace utility {
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/**
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Wilson interval.
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The Wilson score interval is simple to compute, has good coverage. Intervals are
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automatically bounded between 0 and 1 and never empty. The interval is asymmetric.
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Wilson, E. B. (1927). "Probable inference, the law of succession, and statistical
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inference". Journal of the American Statistical Association. 22 (158): 209-212.
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doi:10.1080/01621459.1927.10502953. JSTOR 2276774.
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The coverage probability for a random ensemble of fractions is close to the nominal
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value. Unlike the Clopper-Pearson interval, the Wilson score interval is not
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conservative. For some values of the fractions, the interval undercovers and overcovers
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for neighboring values. This is a shared property of all alternatives to the
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Clopper-Pearson interval.
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The Wilson score intervals is widely recommended for general use in the literature. For
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a review of the literature, see R. D. Cousins, K. E. Hymes, J. Tucker, Nucl. Instrum.
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Meth. A 612 (2010) 388-398.
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*/
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template <class ValueType>
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class wilson_interval : public binomial_proportion_interval<ValueType> {
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public:
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using value_type = typename wilson_interval::value_type;
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using interval_type = typename wilson_interval::interval_type;
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/** Construct Wilson interval computer.
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@param d Number of standard deviations for the interval. The default value 1
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corresponds to a confidence level of 68 %. Both `deviation` and `confidence_level`
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objects can be used to initialize the interval.
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*/
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explicit wilson_interval(deviation d = deviation{1.0}) noexcept
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: z_{static_cast<value_type>(d)} {}
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using binomial_proportion_interval<ValueType>::operator();
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/** Compute interval for given number of successes and failures.
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@param successes Number of successful trials.
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@param failures Number of failed trials.
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*/
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interval_type operator()(value_type successes, value_type failures) const noexcept {
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// See https://en.wikipedia.org/wiki/
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// Binomial_proportion_confidence_interval
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// #Wilson_score_interval
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// We make sure calculation is done in single precision if value_type is float
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// by converting all literals to value_type. Double literals in the equation
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// would turn intermediate values to double.
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const value_type half{0.5}, quarter{0.25}, zsq{z_ * z_};
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const value_type total = successes + failures;
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const value_type minv = 1 / (total + zsq);
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const value_type t1 = (successes + half * zsq) * minv;
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const value_type t2 =
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z_ * minv * std::sqrt(successes * failures / total + quarter * zsq);
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return {t1 - t2, t1 + t2};
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}
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private:
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value_type z_;
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};
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} // namespace utility
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} // namespace histogram
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} // namespace boost
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#endif
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