  We present occurrence rates for rocky planets in the habitable zones (HZ) of
main-sequence dwarf stars based on the Kepler DR25 planet candidate catalog and
Gaia-based stellar properties. We provide the first analysis in terms of
star-dependent instellation flux, which allows us to track HZ planets. We
define $\eta_\oplus$ as the HZ occurrence of planets with radius between 0.5
and 1.5 $R_\oplus$ orbiting stars with effective temperatures between 4800 K
and 6300 K. We find that $\eta_\oplus$ for the conservative HZ is between
$0.37^{+0.48}_{-0.21}$ (errors reflect 68\% credible intervals) and
$0.60^{+0.90}_{-0.36}$ planets per star, while the optimistic HZ occurrence is
between $0.58^{+0.73}_{-0.33}$ and $0.88^{+1.28}_{-0.51}$ planets per star.
These bounds reflect two extreme assumptions about the extrapolation of
completeness beyond orbital periods where DR25 completeness data are available.
The large uncertainties are due to the small number of detected small HZ
planets. We find similar occurrence rates using both a Poisson likelihood
Bayesian analysis and Approximate Bayesian Computation. Our results are
corrected for catalog completeness and reliability. Both completeness and the
planet occurrence rate are dependent on stellar effective temperature. We also
present occurrence rates for various stellar populations and planet size
ranges. We estimate with $95\%$ confidence that, on average, the nearest HZ
planet around G and K dwarfs is about 6 pc away, and there are about 4 HZ rocky
planets around G and K dwarfs within 10 pc of the Sun.
