  We investigate how the occurrence rate of giant planets (minimum mass $>
0.3\, M_\mathrm{Jup}$) around Sun-like stars depends on the age, mass, and
metallicity of their host stars. We develop a hierarchical Bayesian framework
to infer the number of planets per star (NPPS) as a function of both planetary
and stellar parameters. The framework fully takes into account the
uncertainties in the latter by utilizing the posterior samples for the stellar
parameters obtained by fitting stellar isochrone models to the spectroscopic
parameters, Gaia DR3 parallaxes, and 2MASS $K_{\rm s}$-band magnitudes adopting
a certain bookkeeping prior. We apply the framework to 46 Doppler giants found
around a sample of 382 Sun-like stars from the California Legacy Survey catalog
that publishes spectroscopic parameters and search completeness for all the
surveyed stars. We find evidence that the NPPS of hot Jupiters (orbital period
$P=1$-$10\,\mathrm{days}$) decreases roughly in the latter half of the main
sequence over the timescale of $\mathcal{O}(\mathrm{Gyr})$, while that of cold
Jupiters ($P=1$-$10\,\mathrm{yr}$) does not. Assuming that this decrease is
real and caused by tidal orbital decay, the modified stellar tidal quality
factor $Q^\prime_\star$ is implied to be $\mathcal{O}(10^6)$ for a Sun-like
main-sequence star orbited by a Jupiter-mass planet with $P\approx
3\,\mathrm{days}$.
