78 lines
3.0 KiB
C++
78 lines
3.0 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_JEFFREYS_INTERVAL_HPP
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#define BOOST_HISTOGRAM_UTILITY_JEFFREYS_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 <boost/math/distributions/beta.hpp>
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#include <cmath>
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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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Jeffreys interval.
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This is the Bayesian credible interval with a Jeffreys prior. Although it has a
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Bayesian derivation, it has good coverage. The interval boundaries are close to the
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Wilson interval. A special property of this interval is that it is equal-tailed; the
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probability of the true value to be above or below the interval is approximately equal.
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To avoid coverage probability tending to zero when the fraction approaches 0 or 1,
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this implementation uses a modification described in section 4.1.2 of the
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paper by L.D. Brown, T.T. Cai, A. DasGupta, Statistical Science 16 (2001) 101-133,
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doi:10.1214/ss/1009213286.
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*/
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template <class ValueType>
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class jeffreys_interval : public binomial_proportion_interval<ValueType> {
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public:
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using value_type = typename jeffreys_interval::value_type;
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using interval_type = typename jeffreys_interval::interval_type;
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/** Construct Jeffreys interval computer.
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@param cl Confidence level for the interval. The default value produces a
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confidence level of 68 % equivalent to one standard deviation. Both `deviation` and
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`confidence_level` objects can be used to initialize the interval.
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*/
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explicit jeffreys_interval(confidence_level cl = deviation{1}) noexcept
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: alpha_half_{static_cast<value_type>(0.5 - 0.5 * static_cast<double>(cl))} {}
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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 L.D. Brown, T.T. Cai, A. DasGupta, Statistical Science 16 (2001) 101-133,
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// doi:10.1214/ss/1009213286, section 4.1.2.
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const value_type half{0.5};
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const value_type total = successes + failures;
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// if successes or failures are 0, modified interval is equal to Clopper-Pearson
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if (successes == 0) return {0, 1 - std::pow(alpha_half_, 1 / total)};
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if (failures == 0) return {std::pow(alpha_half_, 1 / total), 1};
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math::beta_distribution<value_type> beta(successes + half, failures + half);
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const value_type a = successes == 1 ? 0 : math::quantile(beta, alpha_half_);
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const value_type b = failures == 1 ? 1 : math::quantile(beta, 1 - alpha_half_);
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return {a, b};
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}
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private:
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value_type alpha_half_;
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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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