  Radio jet and core data for a complete sample of 98 FRII sources with z < 1
are analysed with a Markov-Chain Monte Carlo (MCMC) model fitting method to
obtain constraints on bulk-flow speeds in the beam. The Bayesian
parameter-inference method is described and demonstrated to be capable of
providing meaningful constraints on the Lorentz factor at both kiloparsec and
parsec scales. For both jets and cores we show that models in which some
intrinsic dispersion is present in the features' intrinsic prominence,
bulk-flow speeds or both provide the best fit to the data. The constraints on
the Lorentz factor on parsec scales are found to be consistent with the
expected values given VLBI observations and other evidence, with mean gamma ~
10-14. On kiloparsec scales, the Lorentz factor is found to be ~ 1.18 - 1.49,
in agreement with the results of previous analyses of radio jet data. These
values are clearly not consistent with the gamma ~ 10 speeds required by beamed
inverse-Compton models of X-ray emission from quasar jets; our results
therefore support models that require velocity structure in powerful jets.
