Halo bias in Lagrangian Space: Estimators and theoretical predictions
  We present several methods to accurately estimate Lagrangian bias parameters
and substantiate them using simulations. In particular, we focus on the
quadratic terms, both the local and the non local ones, and show the first
clear evidence for the latter in the simulations. Using Fourier space
correlations, we also show for the first time, the scale dependence of the
quadratic and non-local bias coefficients. For the linear bias, we fit for the
scale dependence and demonstrate the validity of a consistency relation between
linear bias parameters. Furthermore we employ real space estimators, using both
cross-correlations and the Peak-Background Split argument. This is the first
time the latter is used to measure anisotropic bias coefficients. We find good
agreement for all the parameters among these different methods, and also good
agreement for local bias with ESP$\tau$ theory predictions. We also try to
exploit possible relations among the different bias parameters. Finally, we
show how including higher order bias reduces the magnitude and scale dependence
of stochasticity of the halo field.
