  We propose a methodological framework to perform forward asteroseismic
modeling of stars with a convective core, based on gravity-mode oscillations.
These probe the near-core region in the deep stellar interior. The modeling
relies on a set of observed high-precision oscillation frequencies of
low-degree coherent gravity modes with long lifetimes and their observational
uncertainties. Identification of the mode degree and azimuthal order is assumed
to be achieved from rotational splitting and/or from period spacing patterns.
This paper has two major outcomes. The first is a comprehensive list and
discussion of the major uncertainties of theoretically predicted gravity-mode
oscillation frequencies based on linear pulsation theory, caused by fixing
choices of the input physics for evolutionary models. Guided by a hierarchy
among these uncertainties of theoretical frequencies, we subsequently provide a
global methodological scheme to achieve forward asteroseismic modeling. We
properly take into account correlations amongst the free parameters included in
stellar models. Aside from the stellar mass, metalicity and age, the major
parameters to be estimated are the near-core rotation rate, the amount of
convective core overshooting, and the level of chemical mixing in the radiative
zones. This modeling scheme allows for maximum likelihood estimation of the
stellar parameters for fixed input physics of the equilibrium models, followed
by stellar model selection considering various choices of the input physics.
Our approach uses the Mahalanobis distance instead of the often used $\chi^2$
statistic and includes heteroscedasticity. It provides estimation of the
unknown variance of the theoretically predicted oscillation frequencies.
