KiDS-450: Cosmological Constraints from Weak Lensing Peak Statistics-I:
  Inference from Analytical Prediction of High Signal-to-Noise Ratio
  Convergence Peaks
  This paper is the first of a series of papers constraining cosmological
parameters with weak lensing peak statistics using $\sim 450~\rm deg^2$ of
imaging data from the Kilo Degree Survey (KiDS-450). We measure high
signal-to-noise ratio (SNR: $\nu$) weak lensing convergence peaks in the range
of $3<\nu<5$, and employ theoretical models to derive expected values. These
models are validated using a suite of simulations. We take into account two
major systematic effects, the boost factor and the effect of baryons on the
mass-concentration relation of dark matter haloes. In addition, we investigate
the impacts of other potential astrophysical systematics including the
projection effects of large scale structures, intrinsic galaxy alignments, as
well as residual measurement uncertainties in the shear and redshift
calibration. Assuming a flat $\Lambda$CDM model, we find constraints for
$S_{\rm 8}=\sigma_{\rm 8}(\Omega_{\rm m}/0.3)^{0.5}=0.746^{+0.046}_{-0.107}$
according to the degeneracy direction of the cosmic shear analysis and
$\Sigma_{\rm 8}=\sigma_{\rm 8}(\Omega_{\rm
m}/0.3)^{0.38}=0.696^{+0.048}_{-0.050}$ based on the derived degeneracy
direction of our high-SNR peak statistics. The difference between the power
index of $S_{\rm 8}$ and in $\Sigma_{\rm 8}$ indicates that combining the two
probes has the potential to break the degeneracy in $\sigma_{\rm 8}$ and
$\Omega_{\rm m}$. Our results are consistent with the cosmic shear tomographic
correlation analysis of the same dataset and $\sim 2\sigma$ lower than the
Planck 2016 results.
