The PDF perspective on the tracer-matter connection: Lagrangian bias and
  non-Poissonian shot noise
  We study the connection of matter density and its tracers from the PDF
perspective. One aspect of this connection is the conditional expectation value
$\langle \delta_{\mathrm{tracer}}|\delta_m\rangle$ when averaging both tracer
and matter density over some scale. We present a new way to incorporate a
Lagrangian bias expansion of this expectation value into standard frameworks
for modelling the PDF of density fluctuations and counts-in-cells statistics.
Using N-body simulations and mock galaxy catalogs we confirm the accuracy of
this expansion and compare it to the more commonly used Eulerian
parametrization. For halos hosting typical luminous red galaxies, the
Lagrangian model provides a significantly better description of $\langle
\delta_{\mathrm{tracer}}|\delta_m\rangle$ at second order in perturbations. A
second aspect of the matter-tracer connection is shot-noise, \ie the scatter of
tracer density around $\langle \delta_{\mathrm{tracer}}|\delta_m\rangle$. It is
well known that this noise can be significantly non-Poissonian and we validate
the performance of a more general, two-parameter shot-noise model for different
tracers and simulations. Both parts of our analysis are meant to pave the way
for forthcoming applications to survey data.
