posterior distribution. This is a reasonable assumption since they are the dominant contribution to the joint constraints. They are thus useful auxiliary distributions and are biased distributions of the target distributions. To obtain the two unbiased joint distributions (WMAP+CFHTLS and WMAP+BAO+SNe+CFHTLS), we scale the chains by multiplying the weight of each chain element by its likelihood with respect to the cosmic shear data.

This method allows us to accelerate the computation compared to sampling directly the joint posterior with a grid or a Markov chain, since it requires only the computation of the cosmic shear likelihood for each model of the chains. Each model of the chains has a constant ${N_\mathrm{eff}}=3.04$, hence in the joint analysis, we consider only 7+1 physically independent parameters, i.e., the remaining 7 cosmological parameters used in the cosmic shear analysis and the lensing sources redshift.

Results {#sec3}
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CFHTLS-T0003 alone {#sec3a}
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We now discuss the analysis of cosmic-shear data alone. Figure \[fig:nufu\] shows the marginalized confidence contours in the $(\sigma_8,\Omega_{\mathrm{m}})$ plane. The degeneracy direction in the case of massless neutrinos is fitted by $$\sigma_8\,({\Omega_{\mathrm{m}}}/0.25)^{0.72}=0.744 \pm 0.052.$$ This value was found by marginalizing over $h$ but for fixed $\omega_{\mathrm{b}}$ and ${n_\mathrm{s}}$ to be more directly 