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

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Cabass,  Giovanni
Physical Cosmology, MPI for Astrophysics, Max Planck Society;

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Schmidt,  Fabian
Physical Cosmology, MPI for Astrophysics, Max Planck Society;

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Citation

Cabass, G., & Schmidt, F. (2020). The likelihood for LSS: stochasticity of bias coefficients at all orders. Journal of Cosmology and Astroparticle Physics, 2020(7): 051. doi:10.1088/1475-7516/2020/07/051.


Cite as: http://hdl.handle.net/21.11116/0000-0007-1E73-7
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.