  We study the position-dependent power spectrum and the integrated bispectrum
statistic for 2D cosmological fields on the sphere (integrated angular
bispectrum). First, we derive a useful, $m$-independent, formula for the
full-sky integrated angular bispectrum, based on the construction of
azimuthally symmetric patches. We then implement a pipeline for integrated
angular bispectrum estimation, including a mean-field correction to account for
spurious isotropy-breaking effects in realistic conditions (e.g., inhomogenous
noise, sky masking). Finally, we show examples of applications of this
estimator to CMB analysis, both using simulations and actual Planck data. Such
examples include $f_\mathrm{NL}$ estimation, analyses of non-Gaussianity from
secondary anisotropies (ISW-lensing and ISW-tSZ-tSZ bispectra) and studies of
non-Gaussian signatures from foreground contamination.
