  Recent experimental data on the optical conductivity of niobium doped
SrTiO$_{3}$ are interpreted in terms of a gas of large polarons with effective
coupling constant $\alpha_{eff}\approx2$. The {theoretical approach takes into
account} many-body effects, the electron-phonon interaction with multiple
LO-phonon branches, and the degeneracy and the anisotropy of the Ti t$_{2g}$
conduction band. {Based on the Fr\"{o}hlich interaction, the many-body
large-polaron theory} provides an interpretation for the essential
characteristics, except -- interestingly -- for the unexpectedly large
intensity of a peak at $\sim130$ meV, of the observed optical conductivity
spectra of SrTi$_{1-x}$Nb$_{x}$O$_{3}$ \textit{without} any adjustment of
material parameters.
