to more reliable results when applying GP to reconstructions using distance measurements [@Yang15]. Using this covariance function, values of data points at other redshifts which have not be observed can also be obtained, which could effectively bridges the redshift gap between current data. Following @Seikel12a in which the detailed technical description of GP can be found, we use the Gaussian processes in Python (GaPP) [^2] to execute the model-independent method and derive our GP results. The reconstructed function $\mathcal{D}_{\rm obs}(\langle z_l\rangle,
z_s)$, as well as the estimation of the $1\sigma$ confidence region with the 390 simulated strong lensing systems is shown in Fig. 3.

In order to demonstrate how the reconstructed function $\mathcal{D}_{\rm obs}(\langle z_l\rangle, z_s)$ works, we have constrained two simple cosmological models: the $\Lambda$CDM and DGP models under assumption of spatially flat Universe. On the other hand, in the face of different competing cosmological scenarios, it is important to find an effective way to decide which one is most favored by the data. Following the analysis of @Yennapureddy, a new type of model comparison statistics, Area Minimization Statistics, will be used for this purpose.

Competing cosmological models and statistical analysis
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Flatness of the Friedmann-Robertso-Walker (FRW) metric is 