Often we have datasets in which quantities are not detected. Those upper limits contain information — the flux was definitely below X. It turns out, there’s a rich statistical literature on how to consider both detections and upper limits. Yet often astronomers don’t properly incorporate those upper limits in their analysis.
Fortunately, several authors have explained those techniques for astronomers, shown examples using astrophysical datasets, and written a package that does the analysis for you. Interested?
The first paper is Feigelson & Nelson 1985, which deals with univariate distributions (luminosity functions, line ratios, mean values, etc.)
The second paper is Isobe, Feigelson, and Nelson 1986, which deals with correlation and regression.
The package ASURV implements these techniques. The included manual is very helpful.
It took me 2 hrs to figure out the funky syntax required for the data files (stupid fortran), and after that, bingo, I generated reconstructed distribution functions and the probability that my samples were drawn from the same parent. Exactly what I needed to solve my, “So, is this result significant, or what?” problem.
Wow, I was JUST dealing with that problem today in IDL. I might come by and bug you a bit, but great links! thx