  We present a framework for quantifying the uncertainty that results from the
choice of exchange-correlation (XC) functional in predictions of phonon
properties and thermal conductivity that use density functional theory (DFT) to
calculate the atomic force constants. The energy ensemble capabilities of the
BEEF-vdW XC functional are first applied to determine an ensemble of
interatomic force constants, which are then used as inputs to lattice dynamics
calculations and a solution of the Boltzmann transport equation. The framework
is applied to isotopically-pure silicon. We find that the uncertainty estimates
bound property predictions (e.g., phonon dispersions, specific heat, thermal
conductivity) from other XC functionals and experiments. We distinguish between
properties that are correlated with the predicted thermal conductivity [e.g.,
the transverse acoustic branch sound speed ($R^2=0.89$) and average Gr\"uneisen
parameter ($R^2=0.85$)] and those that are not [e.g., longitudinal acoustic
branch sound speed ($R^2=0.23$) and specific heat ($R^2=0.00$)]. We find that
differences in ensemble predictions of thermal conductivity are correlated with
the behavior of phonons with mean free paths between $100$ and $300$ nm. The
framework systematically accounts for XC uncertainty in phonon calculations and
should be used whenever it is suspected that the choice of XC functional is
influencing physical interpretations.
