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

The PDF perspective on the tracer-matter connection: Lagrangian bias and non-Poissonian shot noise