  Using a maximum entropy technique within a finite band Eliashberg formalism
we extract from recent high accuracy nodal direction angular resolved
photo-emission spectroscopy (ARPES) data in optimally doped
Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi2212) a quasiparticle electron-boson
spectral density. Both normal and superconducting state with d-wave gap
symmetry are treated. Finite and infinite band results are considered and
contrasted. We compare with results obtained for the related transport spectral
density which follows from a similar inversion of optical data. We discuss the
implication of our results for quasiparticle renormalizations in the antinodal
direction.
