Statistical detection of clumps and gaps in a random sample by continuous wavelet transforms: the 2D case

Abstract

We present a self-consistent framework to perform the wavelet analysis of two-dimensional statistical distributions. The analysis targets the 2D probability density function (p.d.f.) of an input sample, in which each object is characterized by two peer parameters. The method performs a probabilistic detection of various `patterns', or `structures' related to the behaviour of the p.d.f. Laplacian. These patterns may include regions of local convexity or local concavity of the p.d.f., in particular peaks (groups of objects) or gaps. In the end, the p.d.f. itself is reconstructed based on the least noisy (most economic) superposition of such patterns. Among other things, our method also involves optimal minimum-noise wavelets and minimum-noise reconstruction of the distribution density function. The new 2D algorithm is now implemented and released along with an improved and optimized 1D version. The code relies on the C++11 language standard, and is fully parallelized. The algorithm has a rich range of applications in astronomy: Milky Way stellar population analysis, investigations of the exoplanets diversity, Solar System minor bodies statistics, etc.

arXiv comment27 pages, 4 figures, submitted to Astronomy & Computing; see the accompanying paper at arXiv:1711.07820; the C++ code can be downloaded at https://sourceforge.net/projects/waveletstat/

References in corpus (7)

• Gaia Data Release 2. Summary of the contents and survey properties
• A high-significance detection of non-Gaussianity in the WMAP 1-year data using directional spherical wavelets
• Radial Velocity Data Analysis with Compressed Sensing Techniques
• Detecting non-sinusoidal periodicities in observational data: the von Mises periodogram for variable stars and exoplanetary transits
• N-body simulations with two-orders-of-magnitude higher performance using wavelets
• Wavelet-Bayesian inference of cosmic strings embedded in the cosmic microwave background
• Statistical detection of patterns in unidimensional distributions by continuous wavelet transforms