Beschreibung
Standard analyses of galaxy clustering rely on summary statistics such as the power spectrum and bispectrum, but extending to higher-order n-point functions quickly becomes intractable. Field-level inference (FLI) offers an alternative by forward-modeling the galaxy density field and explicitly employing the full joint posterior of the initial conditions, cosmological parameters, and bias parameters given the data. We consider a simplified scenario in which analytical predictions at the field level are possible, enabling a direct and controlled comparison with n-point statistics. Within the framework of the Effective Field Theory of Large-Scale Structure (EFTofLSS), we describe galaxy clustering with a finite set of effective parameters and construct summary statistics from auto- and cross-correlations of powers of the observed density field, providing an efficient means of incorporating higher-order information. This approach allows us to assess the relative information content and robustness of field-level and n-point analyses. The same framework can be extended to more complex forward model, such as those including primordial non-Gaussianity or additional bias operators, paving the way for testing new physics.