Method max_abs_deviation in stan/mcmc/chainset should be *median* not max

[mitzimorris]

Summary:

Naming mistake during implementation - assumed the "M" in "MAD" was "max". Wrong - it's "median".

Description:

The name of this function is inaccurate. The code shows what's going on:

  /**
   * Compute maximum absolute deviation (mad) for specified parameter.
   *
   * Follows R implementation:  constant * median(abs(x - center))
   * where the value of center is median(x) and the constant is 1.4826,
   * a scale factor for asymptotically normal consistency: `1/qnorm(3/4)`.
   * (R stats version 3.6.2)
   *
   * @param index parameter index
   * @return sample mad
   */
  double max_abs_deviation(const int index) const {
    Eigen::MatrixXd draws = samples(index);
    auto center = median(index);
    Eigen::MatrixXd abs_dev = (draws.array() - center).abs();
    Eigen::Map<Eigen::VectorXd> map(abs_dev.data(), abs_dev.size());
    return 1.4826 * stan::math::quantile(map, 0.5);
  }

Current Version:

v2.35.0

[mitzimorris]

fixing this requires changing the function name (everywhere, including CmdStan's stansummary utility) and the docstring.
it won't actually change the code. worth doing before the release?

[bob-carpenter]

If not before the release, then soon after. This kind of thing is super confusing if you leave it around.

[WardBrian]

#3319