  We constructed a Bayesian hyper-parameter statistical method to quantify the
difference between predicted velocities derived from the observed galaxy
distribution in the \textit{IRAS}-PSC$z$ redshift survey and peculiar
velocities measured using different distance indicators. In our analysis we
find that the model--data comparison becomes unreliable beyond $70 \hmpc$
because of the inadequate sampling by \textit{IRAS} survey of prominent,
distant superclusters, like the Shapley Concentration. On the other hand, the
analysis of the velocity residuals show that the PSC$z$ gravity field provides
an adequate model to the local, $\le 70 \hmpc$, peculiar velocity field. The
hyper-parameter combination of ENEAR, SN, A1SN and SFI++ catalogues in the
Bayesian framework constrains the amplitude of the linear flow to be
$\beta=0.53 \pm 0.014$. For an rms density fluctuations in the PSC$z$ galaxy
number density $\sigma_8^{\rm gal}=0.42\pm0.03$, we obtain an estimate of the
growth rate of density fluctuations $f\sigma_{8}(z\sim0) = 0.42 \pm 0.033$,
which is in excellent agreement with independent estimates based on different
techniques.
