  Future precision cosmology from large-scale structure experiments including
the Dark Energy Spectroscopic Instrument (DESI) and Euclid will probe wider and
deeper cosmic volumes than those covered by previous surveys. The Cartesian
power spectrum analysis of anisotropic galaxy clustering based on the Fourier
plane wave basis makes a number of assumptions, including the local
plane-parallel approximation, that will no longer be valid on very large scales
and may degrade cosmological constraints. We propose an approach that utilises
a hybrid basis: on the largest scales, clustering statistics are decomposed
into spherical Fourier modes which respect the natural geometry of both survey
observations and physical effects along the line of sight, such as
redshift-space distortions, the Alcock--Paczy\'nsky and light-cone effects; on
smaller scales with far more clustering modes, we retain the computational
benefit of the power spectrum analysis aided by fast Fourier transforms. This
approach is particularly suited to the likelihood analysis of local primordial
non-Gaussianity $f_\textrm{NL}$ through the scale-dependent halo bias, and we
demonstrate its applicability with $N$-body simulations. We also release our
public code Harmonia (https://github.com/MikeSWang/Harmonia) for galaxy
clustering likelihood inference in spherical Fourier or hybrid-basis analyses.
