  We present an ab-initio method to simulate the current noise in the presence
of electron-vibration interactions in atomic and molecular junctions at finite
temperature. Using a combination of nonequilibrium Keldysh Green's function
techniques and density functional theory, we study the elastic and inelastic
contributions to electron current and shot noise within a wide range of
transmission values in systems exhibiting multiple electronic levels and
vibrational modes. Within our model we find the upper threshold, at which the
inelastic noise contribution changes sign, at a total transmission between
$\tau\approx 0.90$ and $0.95$ for gold contacts. This is higher than predicted
by the single-level Holstein model but in agreement with earlier experimental
observations. We support our theoretical studies by noise measurements on
single-atom gold contacts which confirm previous experiments but make use of a
new setup with strongly reduced complexity of electronic circuitry.
Furthermore, we identify 1,4-benzenedithiol connected to gold electrodes as a
system to observe the lower sign change, which we predict at around
$\tau\approx 0.2$. Finally, we discuss the influence of vibrational heating on
the current noise.
