define the “edge” of the distribution $t(z)$ to be where $\ln P(z,t)$ drops by $0.5$ from its maximum (i.e. $\Delta \ln P=0.5$. We associate an error to this determination $\delta_{t(z)}$ given by $t_{2}(z)-t(z)$ where $t_{2}(z)$ corresponds to where $\ln P(z,t)$ drops by $2$ from its maximum (i.e. $\Delta \ln
P=2$, this approximately corresponds to the 68% confidence level). This procedure makes the determination of the “edge” less sensitive to the outliers (see also @RBBG97). Figure 6 presents the resultant $t(z)$ relation.

For $z<z_{\rm max}$, we fit $t(z)$ with a straight line whose slope $dt/dz$ is related to the Hubble constant at an effective redshift by $H(z_{\rm eff})= - \frac{1}{1+z_{\rm eff}} (\frac{dt}{dz})^{-1}$. This fit is performed by standard $\chi^2$ minimization. We also compute $P_{\ge \chi^2}$, the probability of obtaining equal or greater value of the reduced $\chi^2$ if the $t(z)$ points were truly lying on a straight line. Values of $P_{\ge \chi^2}<0.1$ means that a straight line is not a good fit to the points.

For $w = -1$, we obtain $H_0=H(z_{\rm eff})\left[\Omega_m(1+z_{\rm
eff})^3+\Omega_{\Lambda}\right]^{-\frac{1}{2}}$ where $\Omega_m=0.27$, $\Omega_\Lambda=0.7$. Figure 7 shows how the $H_0$ measurement depends on $z_{\rm max}$. For $z_{\rm max} > 0.17$ not only the value for $H_0$ drifts but 