  Transiting hot Jupiters occupy a wedge-shaped region in the mass
ratio-orbital separation diagram. Its upper boundary is eroded by tidal
spiral-in of massive, close-in planets and is sensitive to the stellar tidal
dissipation parameter $Q_s'$. We develop a simple generative model of the
orbital separation distribution of the known population of transiting hot
Jupiters, subject to tidal orbital decay, XUV-driven evaporation and
observational selection bias. From the joint likelihood of the observed orbital
separations of hot Jupiters discovered in ground-based wide-field transit
surveys, measured with respect to the hyperparameters of the underlying
population model, we recover narrow posterior probability distributions for
$Q_s'$ in two different tidal forcing frequency regimes. We validate the method
using mock samples of transiting planets with known tidal parameters. We find
that $Q_s'$ and its temperature dependence are retrieved reliably over five
orders of magnitude in $Q_s'$. A large sample of hot Jupiters from
small-aperture ground-based surveys yields $\log_{10} Q_s'=(8.26\pm 0.14)$ for
223 systems in the equilibrium-tide regime. We detect no significant dependence
of $Q_s'$ on stellar effective temperature. A further 19 systems in the
dynamical-tide regime yield $\log_{10} Q_s'=7.3\pm 0.4$, indicating stronger
coupling. Detection probabilities for transiting planets at a given orbital
separation scale inversely with the increase in their tidal migration rates
since birth. The resulting bias towards younger systems explains why the
surface gravities of hot Jupiters correlate with their host stars'
chromospheric emission fluxes. We predict departures from a linear
transit-timing ephemeris of less than 4 seconds for WASP-18 over a 20-year
baseline.

Earth and Planetary Astrophysics