130 lines
4.2 KiB
C++
130 lines
4.2 KiB
C++
/* @file SampleStatistics.hpp */
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#pragma once
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#include <cstdint>
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namespace xo {
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namespace statistics {
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/* accumlate statistics online for a sample */
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class SampleStatistics {
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public:
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SampleStatistics() = default;
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/* given we have a sample S(n) of size n with given mean,
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* compute mean of sample with one event x added
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*
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* n. #of samples *preceding* x
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*/
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static double update_online_mean(double x, uint32_t n, double mean) {
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/* to update mean in a numerically stable way:
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* avoid computing running sample sum, to avoid
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* adding floating point numbers with distant magnitudes;
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* instead compute correction to the mean directly
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*
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* n / x(i) \
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* mean(Sn) := Sum | ----- |
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* i=1 \ n /
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*
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* so
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* n+1 / x(i) \
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* mean(S(n+1)) = Sum | ----- |
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* i=1 \ n+1 /
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*
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* n n+1 / x(i) \
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* = --- Sum | ----- |
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* n+1 i=1 \ n /
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*
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* n / x(n+1) n x(i) \
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* = --- | ------ + Sum ---- |
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* n+1 \ n i=1 n /
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*
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* x(n+1) / n \
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* = ------ + | --- . mean(S(n)) |
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* n+1 \ n+1 /
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*
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* x(n+1) / -1 \
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* = ------ + mean(S(n)) + | --- . mean(S(n)) |
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* n+1 \ n+1 /
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*
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* = mean(S(n)) + (x(n+1) - mean(S(n))) / (n+1)
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*/
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return mean + ((1.0 / (n+1)) * (x - mean));
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} /*update_online_mean*/
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/*
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* with S(n) = Sn = {set of n samples},
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* u(n) = mean(Sn)
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*
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* (with mean, variance meaning "estimate for")
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*
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* 1 n / 2 \ / 1 \ 2
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* variance(Sn) := --- . Sum | (x(i) | - | --- . Sum x(i) |
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* n i=1 \ / \ n i=1 /
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*
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* using Welford's recurrence for 2nd moment:
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*
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* define
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* M2(n+1) := M2(n) + (x(n+1) - mean(S(n)))
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* . (x(n+1) - mean(S(n+1))
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*
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* then unbiased variance estimate for S(n+1) is:
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*
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* M2(n+1)
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* -------
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* n
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*
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* x. new sample value
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* mean_np1. mean estimate for S(n+1)
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* mean_n. mean estimate for S(n)
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* moment2. 2nd moment for S(n)
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*/
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static double update_online_moment2(double x,
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double mean_np1, double mean_n,
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double moment2)
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{
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return moment2 + (x - mean_n) * (x - mean_np1);
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} /*update_online_moment2*/
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uint32_t n_sample() const { return n_sample_; }
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double mean() const { return mean_; }
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double moment2() const { return moment2_; }
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/* 'sample variance' = variance estimate,
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* applying Bessel correction for sample bias
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*
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* require: n_sample >= 2
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*/
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double sample_variance() const { return moment2_ / (n_sample_ - 1); }
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/* biased variance estimate
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* = (1 - 1/(n+1)) * .sample_variance()
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*
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* .variance() -> .sample_variance() as sample size -> +oo
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*
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* require: n_sample >= 1
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*/
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double variance() const { return moment2_ / n_sample_; }
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void include_sample(double x) {
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/* n+1 */
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uint32_t np1 = this->n_sample_ + 1;
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double mean_np1 = update_online_mean(x, this->n_sample_, this->mean_);
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double moment2_np1 = update_online_moment2(x, this->mean_, mean_np1, this->moment2_);
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this->n_sample_ = np1;
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this->mean_ = mean_np1;
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this->moment2_ = moment2_np1;
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} /*include_sample*/
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private:
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uint32_t n_sample_ = 0;
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/* estimated mean */
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double mean_ = 0.0;
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/* estimated 2nd moment E[X^2] */
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double moment2_ = 0.0;
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}; /*SampleStatistics*/
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} /*namespace statistics*/
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} /*namespace xo*/
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/* end SampleStatistics.hpp */
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