  Currently, we have only limited means to probe the presence of planets at
large orbital separations. Foreman-Mackey et al. searched for long-period
transiting planets in the Kepler light curves using an automated pipeline.
Here, we apply their pipeline, with minor modifications, to a larger sample and
use updated stellar parameters from Gaia DR2. The latter boosts the stellar
radii for most of the planet candidates found by FM16, invalidating a number of
them as false positives. We identify 15 candidates, including two new ones. All
have sizes from 0.3 to 1 $R_{\rm J}$, and all but two have periods from 2 to 10
yr. We report two main findings based on this sample. First, the planet
occurrence rate for the above size and period ranges is $0.70^{+0.40}_{-0.20}$
planets per Sun-like star, with the frequency of cold Jupiters agreeing with
that from radial velocity surveys. Planet occurrence rises with decreasing
planet size, roughly describable as $dN/d\log R \propto R^{\alpha}$ with
$\alpha = -1.6^{+1.0}_{-0.9}$, i.e., Neptune-sized planets are some four times
more common than Jupiter-sized ones. Second, five out of our 15 candidates
orbit stars with known transiting planets at shorter periods, including one
with five inner planets. We interpret this high incidence rate to mean: (1)
almost all our candidates should be genuine; (2) across a large orbital range
(from $\sim 0.05$ to a few astronomical units), mutual inclinations in these
systems are at most a few degrees; and (3) large outer planets exist almost
exclusively in systems with small inner planets.
