id	summary	reporter	owner	description	type	status	milestone	component	version	severity	resolution	keywords	cc
12688	Boost..Accumulators test/median.cpp testing method is flawed	A. Sinan Unur <sinan@…>	Eric Niebler	"I am going to stick with Stats terminology, because I get confused. I am going to use the word ''sample'' to mean a collection of data points or draws or observations, not a single one.

1. In the test, you generate a sample of 100,000 observations from N(1,1), and check if the medians computed by the implementations are close enough to the true population median of 1.

That is flawed: The algorithms are for calculating the median of the set of numbers you have. Therefore, the medians they produce should be compared to the actual median of the sample you just generated. The median of that sample can be obtained by storing the draws in a `vector` and getting the exact median from that.

This is not hard to do. I am not, however, submitting a pull request to do that because I am not convinced this approach is the right way to test the algorithms.

2. In the case of P^2^, the original paper contains a worked-out example by the authors using 20 observations. They show exactly what the algorithm should produce at each step. Your implementation does not match those steps.

The following short program demonstrates this:

{{{
#include <algorithm>
#include <iostream>
#include <string>
#include <utility>
#include <vector>
#include <boost/accumulators/accumulators.hpp>
#include <boost/accumulators/statistics/stats.hpp>
#include <boost/accumulators/statistics/median.hpp>

namespace bacc = boost::accumulators;

int main(void)
{
    bacc::accumulator_set<double,
        bacc::stats<bacc::tag::median(bacc::with_p_square_quantile)> > acc;

    // See http://www.cse.wustl.edu/~jain/papers/psqr.htm

    // First five observations
    acc(0.02);
    acc(0.5);
    acc(0.74);
    acc(3.39);
    acc(0.83);

    const std::vector<std::pair<double, double> > jain_chlamtac {
        { 22.37, 0.74 },
        { 10.15, 0.74 },
        { 15.43, 2.18 },
        { 38.62, 4.75 },
        { 15.92, 4.75 },
        { 34.60, 9.28 },
        { 10.28, 9.28 },
        {  1.47, 9.28 },
        {  0.40, 9.28 },
        {  0.05, 6.30 },
        { 11.39, 6.30 },
        {  0.27, 6.30 },
        {  0.42, 6.30 },
        {  0.09, 4.44 },
        { 11.37, 4.44 },
    };

    for (auto p: jain_chlamtac)
    {
        acc(p.first);
        std::cout << ""calculated= "" << bacc::median(acc)
            << ""\texpected= "" << p.second << '\n';
    }

    return 0;
}
}}}

This produces

{{{
calculated= 0.74        expected= 0.74
calculated= 0.74        expected= 0.74
calculated= 2.06167     expected= 2.18
calculated= 4.55176     expected= 4.75
calculated= 4.55176     expected= 4.75
calculated= 9.15196     expected= 9.28
calculated= 9.15196     expected= 9.28
calculated= 9.15196     expected= 9.28
calculated= 9.15196     expected= 9.28
calculated= 6.17976     expected= 6.3
calculated= 6.17976     expected= 6.3
calculated= 6.17976     expected= 6.3
calculated= 6.17976     expected= 6.3
calculated= 4.24624     expected= 4.44
calculated= 4.24624     expected= 4.44
}}}

More a more detailed exposition, see my blog post https://www.nu42.com/2016/12/cpp-boost-median-test.html

This is the first time I am looking at Boost.Accumulators and I haven't figured out everything yet, so I do not have a fix (and I can't promise I am going to have a fix soon), but I thought I would get the ball rolling. Maybe the issue will be more transparent to you.

To summarize:

1. The implementations should be tested against cases where we know what they are supposed to do.

2. It looks like there is a problem in the implementation of the P^2^ algorithm.

HTH,

-- Sinan"	Bugs	new	To Be Determined	accumulator	Boost 1.62.0	Problem		testing, median, algorithm, accumulator