Likelihood Estimate (MLE) outlined in §\[sec:mle\]. Tests of the methods using mock catalogues designed to match the SFI++ catalogue are presented in §\[sec:mle\]. Results for the bulk flows from the SFI++ data are given in §\[sec:res\] with the subsection §\[sec:comp\] providing a comparison with the $\Lambda$CDM models. Finally, §\[sec:disc\] discusses the results and some of their cosmological implications.

The All Space Constrained Estimate () {#sec:ace}
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Observations of distance (peculiar velocity) indicators, such as the SFI++ TF survey, are available for only a small fraction of galaxies in the local Universe (out to $\sim 100\hmpc$). The absence of uniformly distributed data prevents a direct application of equation (\[eq:bdef\]). To circumvent this problem, the  method effectively uses (\[eq:bdef\]) to reconstruct the bulk flow from a 3D field $\vv({\vx})$ which satisfies two conditions: a) at sufficiently large distances from the observed galaxies in the TF data, it has a power spectrum that is dictated by a cosmological model such as the $\Lambda$CDM, and b) it has radial peculiar velocities at the positions of the observed galaxies, which are consistent with the TF measurements. The approach is similar to that of constrained realization from noisy data [@hr91; @zh95], but it is more general 