Non-Gaussianities of dynamical origin are disentangled from primordial ones using the formalism of large deviation statistics with spherical collapse dynamics .
This is achieved by relying on accurate analytical predictions for the one-point probability distribution function ( PDF ) and the two-point clustering of spherically-averaged cosmic densities ( sphere bias ) .
Sphere bias extends the idea of halo bias to intermediate density environments and voids as underdense regions .
In the presence of primordial non-Gaussianity , sphere bias displays a strong scale dependence relevant for both high and low density regions , which is predicted analytically .
The statistics of densities in spheres are built to model primordial non-Gaussianity via an initial skewness with a scale-dependence that depends on the bispectrum of the underlying model .
The analytical formulas with the measured nonlinear dark matter variance as input are successfully tested against numerical simulations .
For local non-Gaussianity with a range from f _ { NL } = -100 to +100 they are found to agree within 2 % or better for densities \rho \in [ 0.5 , 3 ] in spheres of radius 15 Mpc / h down to z = 0.35 .
The validity of the large deviation statistics formalism is thereby established for all observationally relevant local-type departures from perfectly Gaussian initial conditions .
The corresponding estimators for the amplitude of the nonlinear variance \sigma _ { 8 } and primordial skewness f _ { NL } are validated using a fiducial joint maximum likelihood experiment .
The influence of observational effects and the prospects for a future detection of primordial non-Gaussianity from joint one- and two-point densities-in-spheres statistics are discussed .