SOMBI: Bayesian identification of parameter relations in unstructured cosmological data

TL;DR

This paper introduces SOMBI, a Bayesian method combining Self Organizing Maps and Bayesian inference to identify and analyze parameter relations in unstructured high-dimensional cosmological data, validated with mock and real datasets.

Contribution

SOMBI is a novel approach that automatically detects data clusters and infers polynomial relations between parameters using Bayesian inference and model selection.

Findings

Identified correlations between galaxy properties and cosmic density fields.

Revealed different clustering structures in galaxy and LSS data.

Detected both positive and inverted correlations in cosmological datasets.

Abstract

This work describes the implementation and application of a correlation determination method based on Self Organizing Maps and Bayesian Inference (SOMBI). SOMBI aims to automatically identify relations between different observed parameters in unstructured cosmological or astrophysical surveys by automatically identifying data clusters in high-dimensional datasets via the Self Organizing Map neural network algorithm. Parameter relations are then revealed by means of a Bayesian inference within respective identified data clusters. Specifically such relations are assumed to be parametrized as a polynomial of unknown order. The Bayesian approach results in a posterior probability distribution function for respective polynomial coefficients. To decide which polynomial order suffices to describe correlation structures in data, we include a method for model selection, the Bayesian Information Criterion, to the analysis. The performance of the SOMBI algorithm is tested with mock data. As illustration we also provide applications of our method to cosmological data. In particular, we present results of a correlation analysis between galaxy and AGN properties provided by the SDSS catalog with the cosmic large-scale-structure (LSS). The results indicate that the combined galaxy and LSS dataset indeed is clustered into several sub-samples of data with different average properties (for example different stellar masses or web-type classifications). The majority of data clusters appear to have a similar correlation structure between galaxy properties and the LSS. In particular we revealed a positive and linear dependency between the stellar mass, the absolute magnitude and the color of a galaxy with the corresponding cosmic density field. A remaining subset of data shows inverted correlations, which might be an artifact of non-linear redshift distortions.