  We study the voltage noise properties including the switching rates and
statistics of phase-slips in moderately damped Josephson junctions using a
novel efficient numerical approach combining the matrix continued-fraction
method with the full counting statistics. By analyzing the noise results
obtained for the RCSJ model we identify different dominating components, namely
the thermal noise close to equilibrium (small current-bias regime), the shot
noise of (multiple) phase-slips in the intermediate range of biases and the
switching noise for yet higher bias currents. We extract thus far inaccessible
characteristic rates of phase-slips in the shot noise regime as well as the
escape and retrapping rates in the switching regime as functions of various
junction's parameters. The method can be extended and applied to other
experimentally relevant Josephson junction circuits.
