  Understanding native point defects is fundamental in order to comprehend the
properties of TiO$_2$ anatase in technological applications. Several
first-principles studies have been performed in order to investigate the defect
chemistry of this material. The reported values are, however, scattered over a
wide range. In this manuscript we perform a comparative study employing
different approaches based on semilocal, DFT+$U$ and screened hybrid
functionals in order to investigate the dependence of defect properties, such
as formation energies and charge transition levels, on the employed
computational method. While the defects in anatase, like in most
transition-metal oxides, generally induce the localization of electrons or
holes on atomic sites, we notice that, provided an alignment of the valence
bands has been performed, the calculated defect formation energies and
transition levels using semi-local functionals are in a fair agreement with
those obtained using hybrid functionals. A similar conclusion can be reached
for the thermochemistry of the Ti-O system and the limit values of the
elemental chemical potentials. We interpret this as a cancellation of error
between the self-interaction error and the overbinding of the O$_2$ molecule in
semi-local functionals. Inclusion of a $U$ term in the electron Hamiltonian
offers a convenient way for obtaining more precise geometric and electronic
configurations of the defective systems.
