Bayesian inference of cosmic density fields from nonlinear, scaledependent, and stochastic biased tracers
Abstract
We present a Bayesian reconstruction algorithm to generate unbiased samples of the underlying dark matter field from halo catalogues. Our new contribution consists of implementing a nonPoisson likelihood including a deterministic nonlinear and scaledependent bias. In particular we present the Hamiltonian equations of motions for the negative binomial (NB) probability distribution function. This permits us to efficiently sample the posterior distribution function of density fields given a sample of galaxies using the Hamiltonian Monte Carlo technique implemented in the ARGO code. We have tested our algorithm with the Bolshoi Nbody simulation at redshift z = 0, inferring the underlying dark matter density field from subsamples of the halo catalogue with biases smaller and larger than one. Our method shows that we can draw closely unbiased samples (compatible within 1σ) from the posterior distribution up to scales of about k ∼ 1 h Mpc^{1} in terms of powerspectra and celltocell correlations. We find that a Poisson likelihood including a scaledependent nonlinear deterministic bias can yield reconstructions with power spectra deviating more than 10 per cent at k = 0.2 h Mpc^{1}. Our reconstruction algorithm is especially suited for emission line galaxy data for which a complex nonlinear stochastic biasing treatment beyond Poissonity becomes indispensable.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 February 2015
 DOI:
 10.1093/mnras/stu2347
 arXiv:
 arXiv:1408.2566
 Bibcode:
 2015MNRAS.446.4250A
 Keywords:

 catalogues;
 galaxies: statistics;
 cosmology: theory;
 largescale structure of Universe;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 Mathematics  Statistics Theory
 EPrint:
 10 pages, 7 figures