Astronomical Applications of Survival Analysis.
Abstract
Astronomers often observe a sample of objects in search of statistical results such as luminosity functions and correlations. I discuss statistical techniques applicable to a sample in which a portion of the variables are not detected, e.g., when upper limits are present in the variables. An extensive field of statistics called "survival analysis" addresses this problem. I present several survival analysis techniques most useful to astronomical data analysis. Using Monte Carlo simulations, I test the performance and accuracy of survival analysis in astronomical situations. The simulations show that survival analysis is reliable in the search for correlations between luminosities at different bands. As an application of univariate survival analysis, I present a study of infrared luminosity functions of normal galaxies. I construct a volume limited sample (v <=q 1400 km s^{-1} ) of 443 nearby galaxies from the Zwicky catalog. The infrared data were obtained from the IRAS Point Source Catalog and ADDSCAN processing. Comparison with infrared spectra of galactic interstellar matter confirms that the major part of 60mum emission from the normal galaxies is due to reradiation from dust heated by the interstellar radiation field. I also find that, on average, all spiral galaxies have similar far infrared luminosity functions when normalized to a standard surface area. As an application of bivariate survival analysis, I present a study of continuum radiation from active galactic nuclei (AGNs). I have constructed a data base for 469 objects which include radio selected quasars, optically selected quasars, X-ray selected AGNs, BL Lac objects and optically unidentified compact radio sources. Each object has measurements of its radio, optical, and X-ray core continuum luminosities, though some of them are not detected. I confirm several previous studies with correct statistical methods and large databases: Radio selected quasars have two different emission mechanisms in the X -ray band; BL Lac objects appear to be special cases of the radio selected quasars; some compact radio sources show the possibility of Synchritron-Self-Conpton in the optical band. I encourage astronomers to adopt these methods in studies involving censored data.
- Publication:
-
Ph.D. Thesis
- Pub Date:
- April 1989
- Bibcode:
- 1989PhDT.........1I
- Keywords:
-
- Physics: Astronomy and Astrophysics;
- Active Galactic Nuclei;
- Continuous Spectra;
- Infrared Spectra;
- Monte Carlo Method;
- Statistical Analysis;
- Astronomy;
- Bl Lacertae Objects;
- Data Bases;
- Interstellar Matter;
- Quasars;
- Simulation;
- Stellar Luminosity;
- X Rays;
- Astronomy