Dr. YUAN Zunli and Prof. WANG Jiancheng from Yunnan Observatories (YNAO) of the Chinese Academy of Sciences, and their collaborator from Oxford University, recently proposed a precise method for estimating luminosity functions (LFs) based on kernel density estimation (KDE). This study was published in The Astrophysical Journal Supplement Series.

The LF is a very fundamental statistic, which provides one of the most important tools to probe the distribution and evolution of galaxies and active galactic nuclei over cosmic time. Accurately measuring the LF of extragalactic objects has long been an important pursuit in modern astronomy. However, the existing methods all have insurmountable disadvantages. For example, some of them are model dependent, while some are poor in stability and accuracy.

To overcome these disadvantages, YUAN's group proposed a new method for estimating LFs based on KDE. One challenge in applying KDE to LFs is how to treat the boundary bias problem. The group invented novel statistical techniques. This method does not assume a particular parametric form for the LF, and does not require dividing the data into arbitrary bins, thereby reducing information loss and preventing potential biases caused by evolution within the bins.

Besides, different from the old binning method, this method produces smooth and continuous estimates and utilizes the Bayesian method to maximize the exploitation of data information, which gives it the flexibility to deal with various LF estimating problems in the future surveys.

"Monte Carlo simulations suggest that it has good stability and reliability in performance, and is around an order of magnitude more accurate than using the old binning method," YUAN said.

YUAN's group is planning to apply their new method to the MIGHTEE survey led by Prof. JARVIS Matt of Oxford University, to accurately estimate the LF of radio source and reveal the physics processes that govern their cosmic evolution.