Do dark matter halos explain lensing peaks?

We have investigated a recently proposed halo-based model, Camelus, for predicting weak-lensing peak counts, and compared its results over a collection of 162 cosmologies with those from N-body simulations. While counts from both models agree for peaks with S/N>1 (where S/N is the ratio of the peak height to the r.m.s. shape noise), we find ≈50% fewer counts for peaks near S/N=0 and significantly higher counts in the negative S/N tail. Adding shape noise reduces the differences to within 20% for all cosmologies. We also found larger covariances that are more sensitive to cosmological parameters. As a result, credibility regions in the {Ωm,σ8} are ≈30% larger. Even though the credible contours are commensurate, each model draws its predictive power from different types of peaks. Low peaks, especially those with 2<S/N<3, convey important cosmological information in N-body data, as shown in \cite{DietrichHartlap, Kratochvil2010}, but \textsc{Camelus} constrains cosmology almost exclusively from high significance peaks (S/N>3). Our results confirm the importance of using a cosmology-dependent covariance with at least a 14\% improvement in parameter constraints. We identified the covariance estimation as the main driver behind differences in inference, and suggest possible ways to make Camelus even more useful as a highly accurate peak count emulator.