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 $\mathcal{S}\mathcal{/}\mathcal{N}>1$ (where $\mathcal{S}\mathcal{/}\mathcal{N}$ is the ratio of the peak height to the r.m.s. shape noise), we find $\approx 50\mathrm{\%}$ fewer counts for peaks near $\mathcal{S}\mathcal{/}\mathcal{N}=0$ and significantly higher counts in the negative $\mathcal{S}\mathcal{/}\mathcal{N}$ tail. Adding shape noise reduces the differences to within $20\mathrm{\%}$ for all cosmologies. We also found larger covariances that are more sensitive to cosmological parameters. As a result, credibility regions in the $\{{\mathrm{\Omega }}_m,{\sigma }_8\}$ are $\approx 30\mathrm{\%}$ larger. Even though the credible contours are commensurate, each model draws its predictive power from different types of peaks. Low peaks, especially those with $2<\mathcal{S}\mathcal{/}\mathcal{N}<3$, convey important cosmological information in N-body data, as shown in \cite{DietrichHartlap, Kratochvil2010}, but $\text{textsc}Camelus$ constrains cosmology almost exclusively from high significance peaks $(\mathcal{S}\mathcal{/}\mathcal{N}>3)$. 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.