We constructed a Bayesian hyper-parameter statistical method to quantify the difference between predicted velocities derived from the observed galaxy distribution in the 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 { h ^ { -1 } { Mpc } } because of the inadequate sampling by 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 , \leq 70 { h ^ { -1 } { Mpc } } , 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 } ^ { gal } = 0.42 \pm 0.03 , we obtain an estimate of the growth rate of density fluctuations f \sigma _ { 8 } ( z \sim 0 ) = 0.42 \pm 0.033 , which is in excellent agreement with independent estimates based on different techniques .

Key words : methods : data analysis – methods : statistical – Galaxies : kinematic and dynamics – Cosmology : observations – large-scale structure of Universe