2013/06/07 by Jens Jasche, Benjamin D. Wandelt, B. D. Wandelt
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Artificial intelligence #Astrophysics #Bayesian inference #Bayesian probability #Computer science #Galaxies: Formation, Evolution, Phenomena #Galaxy #Gaussian Processes and Bayesian Inference #Inference #Markov chain Monte Carlo #Mathematics #Physics #Reversible-jump Markov chain Monte Carlo #Spectral density #Statistical Methods and Inference #Statistical physics #Statistics #astro-ph.CO
paper · pdf · doi:10.1088/0004-637x/779/1/15
arxiv created 2013/06/07 · openalex publication_date 2013/11/19 · arxiv updated 2015/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We derive and implement a full Bayesian large scale structure inference method aiming at precision recovery of the cosmological power spectrum from galaxy redshift surveys. Our approach improves upon previous Bayesian methods by performing a joint inference of the three-dimensional density field, the cosmological power spectrum, luminosity dependent galaxy biases, and corresponding normalizations. We account for all joint and correlated uncertainties between all inferred quantities. Classes of galaxies with different biases are treated as separate subsamples. This method therefore also allows the combined analysis of more than one galaxy survey. In particular, it solves the problem of inferring the power spectrum from galaxy surveys with non-trivial survey geometries by exploring the joint posterior distribution with efficient implementations of multiple block Markov chain and Hybrid Monte Carlo methods. Our Markov sampler achieves high statistical efficiency in low signal-to-noise regimes by using a deterministic reversible jump algorithm. This approach reduces the correlation length of the sampler by several orders of magnitude, turning the otherwise numerically unfeasible problem of joint parameter exploration into a numerically manageable task. We test our method on an artificial mock galaxy survey, emulating characteristic features of the Sloan Digital Sky Survey data release 7, such as its survey geometry and luminosity-dependent biases. These tests demonstrate the numerical feasibility of our large scale Bayesian inference frame work when the parameter space has millions of dimensions. This method reveals and correctly treats the anti-correlation between bias amplitudes and power spectrum, which are not taken into account in current approaches to power spectrum estimation, a 20% effect across large ranges in k space. In addition, this method results in constrained realizations of density fields obtained without assuming the power spectrum or bias parameters in advance.