  The most distant Kuiper belt objects appear to be clustered in longitude of
perihelion and in orbital pole position. To date, the only two suggestions for
the cause of these apparent clusterings have been either the effects of
observational bias or the existence of the distant giant planet in an eccentric
inclined orbit known as Planet Nine. To determine if observational bias can be
the cause of these apparent clusterings, we develop a rigorous method of
quantifying the observational biases in the observations of longitude of
perihelion and orbital pole position. From this now more complete understanding
of the biases we calculate that the probability that these distant Kuiper belt
objects would be clustered as strongly as observed in both longitude of
perihelion and in orbital pole position is only 0.2%. While explanations other
than Planet Nine may someday be found, the statistical significance of this
clustering is now difficult to discount.

Earth and Planetary Astrophysics