The AstroStat Slog

Since I began to subscribe arxiv/astro-ph abstracts, from an astrostatistical point of view, one of the most frequent topics has been photometric redshifts. This photometric redshift has been a popular topic as the catalog of remote photometric object observation multiplies its volume and sky survey projects in multiple bands lead to virtual observatories (VO – will discuss in the later posting). Just searching by photometric redshifts in google scholar and arxiv.org provides more than 2000 articles since 2000.

Quantifying redshifts is one of the key astronomical measures to identify the type of objects as well as to provide their distance. Typically, measuring redshifts requires spectral data, which are quite expensive in many aspects compared to photometric data. Let me explain a little what are spectral data and photometric data to enhance understandings for non astronomers.

Collecting photometric data starts from taking pictures with different filters. Through blue, yellow, red optical filters, or infrared, ultra-violet, X-ray filters, objects look different (or have different light intensity) and various astronomical objects can be identify via investigating pictures of many filter combinations. On the other hand, collecting spectral data starts from dispersing light through a specially designed prism. Because of this light dispersion, it takes longer to collect lights from a object and the smaller number of objects are recorded in a picture plate compared to collecting photometric data. A nice feature of this expensive spectral data is providing the physical condition of the object directly: first, the distance by the relative spectral line shifts of spectral lines; second, abundance (the metallic composition of the object), temperature, type of the object also from spectral lines. Therefore, utilizing photometric data to infer measures normally available from spectral data is a very attractive topic in astronomy.

However, there are many challenges. The massive volume of data and sampling bias*, like Malmquist bias (wiki) and Lutz-Kelker bias, hinder traditional regression techniques, where numerous statistical and machine learning methods have been introduced to make most of these photometric data to infer distances economically and quickly.

*((For a reference regarding these biases and astronomical distances, please check Distance Estimation in Cosmology by
Hendry, M. A. and Simmons, J. F. L., Vistas in Astronomy, vol. 39, Issue 3, pp.297-314.))