This against that

What do your data really say?

As we’ve noted, our astronomer is dealing with the report of a referee on a recently submitted paper.  Several of the comments ask for more graphs, plots of this against that, additions to the many that are already there.  He intends to comply with some of them, if only to show that they show nothing.

Plots are of course among the basic ways to communicate science.  But our concern here is using plots to discover science.  If your data are relatively simple, for instance distance and redshift, it’s not hard to come up with a diagram and see at a glance if there’s any pattern.  For distance and redshift you get a reasonably clear, nearly linear trend.  That’s the best kind, because there are all sorts of statistical tools for a straight line fit.  In fact often you’ll convert one or both of your variables in order to get a linear fit; taking the square root, for instance, or maybe the logarithm.  At any rate, plotting two (sometimes three) variables against each other can tell you a great deal, even if there is no pattern.  Our astronomer has found that expected patterns don’t always appear.

If your data are more complicated the task is harder.  Our astronomer struggled for some time with a four-dimensional data set, coming up with many plots of one thing against another, most of which showed nothing.  But that was no guarantee that there was no pattern; a curved surface in four-dimensional space could easily smear out in any two-dimensional look.  He finally fitted a plausible model, and looked for deviations from it.

Consider now the task of analyzing the data from the Gaia mission.  For each of two billion objects, the satellite is producing seven dimensions of data: three of position, three of velocity and one of brightness.  And there’s no expectation of a linear fit: the stars in the Galaxy are rotating around the center in orbits that are anything but simple, with disturbances in the spiral arms and from clumps of gas and dust (and other stars).  Our astronomer does not pretend to be familiar with the details of Gaia-analysis, but he can guess at the sophistication of the programs involved from the abstracts of papers he skims.  Rather wistfully, he thinks that, if he were starting out in astronomy today, he might enjoy the challenge.

For now, though, he is mostly working out how to explain to the referee that most of the suggested plots are actually useless and would waste valuable space and time.  And do it tactfully.