On recovering the nonlinear bias function from counts-in-cells measurements

We present a simple and accurate method to constrain galaxy bias based on the distribution of counts in cells. The unique feature of our technique is that it is applicable to nonlinear scales, where both dark matter statistics and the nature of galaxy bias are fairly complex. First, we estimate the underlying continuous distribution function from precise counts-in-cells measurements, assuming local Poisson sampling. Then a robust, nonparametric inversion of the bias function is recovered from the comparison of the cumulative distributions in simulated dark Matter and galaxy catalogs. Obtaining continuous statistics from the discrete counts is the most delicate and novel part of our recipe, which corresponds to a deconvolution of a (Poisson) kernel. For this we present two alternatives: a model-independent algorithm based on Richardson-Lucy iteration, and a solution using a parametric skewed lognormal model. We find that the latter is an excellent approximation for the dark matter distribution, but the model-independent iterative procedure is more suitable for galaxies. Tests based on high-resolution dark matter simulations and corresponding mock galaxy catalogs show that we can reconstruct the nonlinear bias function down to highly nonlinear scales with high precision in the range of -1less than or equal todeltaless than or equal to5. As far as the stochasticity of the bias, we have found a remarkably simple and accurate formula based on Poisson noise, which provides an excellent approximation for the scatter around the mean nonlinear bias function. In addition, we have found that redshift distortions have a negligible effect on our bias reconstruction; therefore, our recipe can be safely applied to redshift surveys.