  We present an \textit{ab initio} framework to calculate anharmonic phonon
frequency and phonon lifetime that is applicable to severely anharmonic
systems. We employ self-consistent phonon (SCPH) theory with microscopic
anharmonic force constants, which are extracted from density-functional
calculations using the least absolute shrinkage and selection operator
technique. We apply the method to the high-temperature phase of SrTiO$_{3}$ and
obtain well-defined phonon quasiparticles that are free from imaginary
frequencies. Here we show that the anharmonic phonon frequency of the
antiferrodistortive mode depends significantly on the system size near the
critical temperature of the cubic-to-tetragonal phase transition. By applying
perturbation theory to the SCPH result, phonon lifetimes are calculated for
cubic SrTiO$_{3}$, which are then employed to predict lattice thermal
conductivity using the Boltzmann transport equation within the relaxation-time
approximation. The presented methodology is efficient and accurate, paving the
way toward a reliable description of thermodynamic, dynamic, and transport
properties of systems with severe anharmonicity, including thermoelectric,
ferroelectric, and superconducting materials.
