  We present a statistical analysis that demonstrates that the overwhelming
majority of Kepler candidate multiple transiting systems (multis) indeed
represent true, physically-associated transiting planets. Binary stars provide
the primary source of false positives among Kepler planet candidates, implying
that false positives should be nearly randomly-distributed among Kepler
targets. In contrast, true transiting planets would appear clustered around a
smaller number of Kepler targets if detectable planets tend to come in systems
and/or if the orbital planes of planets encircling the same star are
correlated. There are more than one hundred times as many Kepler planet
candidates in multi-candidate systems as would be predicted from a random
distribution of candidates, implying that the vast majority are true planets.
Most of these multis are multiple planet systems orbiting the Kepler target
star, but there are likely cases where (a) the planetary system orbits a
fainter star, and the planets are thus significantly larger than has been
estimated, or (b) the planets orbit different stars within a binary/multiple
star system. We use the low overall false positive rate among Kepler multis,
together with analysis of Kepler spacecraft and ground-based data, to validate
the closely-packed Kepler-33 planetary system, which orbits a star that has
evolved somewhat off of the main sequence. Kepler-33 hosts five transiting
planets with periods ranging from 5.67 to 41 days.
