  We provide new constraints on the dark matter halo density profile of Milky
Way (MW) dwarf spheroidal galaxies (dSphs) using the phase-space distribution
function (DF) method. After assessing the systematics of the approach against
mock data from the Gaia Challenge project, we apply the DF analysis to the
entire kinematic sample of well-measured MW dwarf satellites for the first
time. Contrary to previous findings for some of these objects, we find that the
DF analysis yields results consistent with the standard Jeans analysis. In
particular, in the present study we rediscover: i) a large diversity in the
inner halo densities of dSphs (bracketed by Draco and Fornax), and ii) an
anti-correlation between inner halo density and pericenter distance of the
bright MW satellites. Regardless of the strength of the anti-correlation, we
find that the distribution of these satellites in density vs. pericenter space
is inconsistent with the results of the high-res N-body simulations that
include a disk potential. Our analysis motivates further studies on the role of
internal feedback and dark matter microphysics in these dSphs.
