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 $\mathcal{S/N}>1$ (where $\mathcal{S/N}$ is the
ratio of the peak height to the r.m.s. shape noise), we find $\approx 50\%$
fewer counts for peaks near $\mathcal{S/N}=0$ and significantly higher counts
in the negative $\mathcal{S/N}$ 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 $\{\Omega_m, \sigma_8\}$ are $\approx 30\%$ larger.
Even though the credible contours are commensurate, each model draws its
predictive power from different types of peaks. Low peaks, especially those
with $2<\mathcal{S/N}<3$, 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
$(\mathcal{S/N}>3)$. 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.
