  We present an efficient approach to set informative physically motivated
priors for EFT-based full-shape analyses of galaxy survey data. We extract
these priors from simulated galaxy catalogs based on halo occupation
distribution (HOD) models. As a first step, we build a joint distribution
between EFT galaxy bias and HOD parameters from a set of 10,500 HOD mock
catalogs. We make use of the field level EFT technique that allows for cosmic
variance cancellation, enabling a precision calibration of EFT parameters from
computationally inexpensive small-volume simulations. As a second step, we use
neural density estimators -- normalizing flows -- to model the marginal
probability density of the EFT parameters, which can be used as a prior
distribution in full shape analyses. As a first application, we use our
HOD-based prior distribution in a new analysis of galaxy power spectra and
bispectra from the BOSS survey in the context of single field primordial
non-Gaussianity. We find that our approach leads to a reduction of the
posterior volume of bias parameters by an order of magnitude. We also find
$f_{\rm NL}^{\rm equil} = 650\pm 310$ and $f_{\rm NL}^{\rm ortho} = 42\pm 130$
(at 68\% CL) in a combined two-template analysis, representing a $\approx 40\%$
improvement in constraints on single field primordial non-Gaussianity,
equivalent to doubling the survey volume.
