Posted by Vaddi, Sravani at March 03. 2015
Hi,
I am trying to study the relation between two luminosities. Since there is a tight correlation between distance and luminosity, any property that is related to distance will appear as luminosity dependent relation, which is the Malmquist bias.
Can anyone suggest a statistical technique to correct for Malmquist bias and be able to identify if the luminosity relation we see is actually due to the intrinsic property of the sample and not due to the bias?
Thanks,
Sravani
Posted by Feigelson, Eric at November 23. 2015Sravani,
If all objects are detected in both properties, then any relationship you see in the bivariate data is intrinsically present in the dataset. (Of course, if your sample is biased with respect to the underlying population, the conclusions may not be generally applicable … but this is true for any populational study in astronomy.)
Statistical problems arise when some objects are undetected in one or another luminosity … then if you ignore the non detections, a spurious correlation due to distance often appears. This can be alleviate using methods of `survival analysis’, a field of applied statistics developed mostly during the 1960-80s designed to treat `censored’ data (upper limits are left-censored data points). The elements of survival analysis for astronomy are presented in Chpt 10 of our text `Modern Statistical Methods for Astronomy with R Applications’ (MSMA, Feigelson & Babu 2012). Very useful material also appears in the monograph: Statistics for Censored Environmental Data Using Minicab and R’, D.R. Helpless, 2nd ed, Wiley 2012. Helsel authored the R/CRAN package `NADA’ that implements many of these methods in the public domain R statistical software environment … see a tutorial in the MSMA text.
Eric