The likelihood for LSS: stochasticity of bias coefficients at all orders

Abstract

In the EFT of biased tracers the noise field ϵg is not exactly uncorrelated with the nonlinear matter field δ. Its correlation with δ is effectively captured by adding stochasticities to each bias coefficient. We show that if these stochastic fields are Gaussian (the impact of their non-Gaussianity being subleading on quasi-linear scales anyway) it is possible to resum exactly their effect on the conditional likelihood P[δg|δ] to observe a galaxy field δg given an underlying δ. This resummation allows to take them into account in EFT-based approaches to Bayesian forward modeling. We stress that the resulting corrections to a purely Gaussian conditional likelihood with white-noise covariance are the most relevant on scales where the EFT is under control: they are more important than any non-Gaussianity of the noise ϵg.