mad statistic

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In the motivating toy example to our ABC model choice paper, we compare summary statistics, mean, median, variance, and… median absolute deviation (mad). The latest is the only one able to discriminate between our normal and Laplace models (as now discussed on Cross Validated!). When rerunning simulations to produce nicer graphical outcomes (for the revision), I noticed a much longer run time associated with the computation of the mad statistic. Here is a comparison for the computation of the mean, median, and mad on identical simulations:

> system.time(mmean(10^5))
   user  system elapsed
  4.040   0.056   4.350
> system.time(mmedian(10^5))
user  system elapsed
12.509   0.012  15.353
> system.time(mmad(10^5))
   user  system elapsed
 23.345   0.036  23.458

Now, this is not particularly surprising: computing a median takes longer than computing a mean, even using quicksort!, hence computing two medians… Still, having to wait about six times longer for the delivery of a mad statistics is somehow…mad!

Filed under: R, Statistics, University life Tagged: ABC, mad, median, quicksort, R, revision

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