Histograms — matplotlib vs. R

When possible, I like to use R for its really, really good statistical visualization capabilities. I’m doing a modeling project in Python right now (R is too slow, bad at large data, bad at structured data, etc.), and in comparison to base R, the matplotlib library is just painful. I wrote a toy Metropolis sampler for a triangle distribution and all I want to see is whether it looks like it’s working. For the same dataset, here are histograms with default settings. (Python: pylab.hist(d), R: hist(d))

I want to know whether my Metropolis sampler is working; those two plots give a very different idea. Of course, you could say this is an unfair comparison, since matplotlib is only using 10 bins, while R is using 18 here — and it’s always important to vary the bin size a few times when looking at histograms. But R’s defaults really are better: it actually uses an adaptive bin size, and the heuristic worked, choosing a reasonable number for the data. The hist() manual says it’s from Sturges (1926). It’s hard to find other computer software that cites 100 year old papers for its design decisions — and where it matters. (Old versions of R used to yell at you when you made a pie chart, citing perceptual studies that humans are really bad at interpreting them (here). This is what originally made me love R.)

Second, R is much smarter about breakpoints. In the following plots, I’ve manually set the number of bins to 10, and then 30 for each.

The second one is now OK for matplotlib — it’s good enough to figure out what’s going on — though still a little lame. Why the gaps?

The problem is that my data are discrete — they’re all integers from 1 through 19 — and I think matplotlib is naively carving up that range into bins, which sometimes lumps together two integers, and sometimes gets zero of them. I understand this is the simple naive implementation, and you could say it’s my fault that I shouldn’t have used the pylab histogram function for this type of data — but it’s really not as good as whatever R is doing, which works rather well here, and I didn’t have to waste time thinking about the internals of the algorithm. For reference, here is the correct visualization of the data (R: plot(table(d))). Note that R’s original Sturges breakpoints did make one error: the first two values got combined into one bin.

Lessons: (1) always vary the bin sizes for histograms, especially if you’re using naive breakpoint selection, and (2) don’t ignore a century’s worth of statistical research on these issues. And since it’s hard to learn a century’s worth of statistics, just use R, where they’re compiled it in for you.