Context. Weak-lensing peak counts have been shown to be a powerful tool for cosmology. They provide non-Gaussian information of large scale structures and are complementary to second-order statistics. Aims. We propose a new flexible method for predicting weak-lensing peak counts, which can be adapted to realistic scenarios, such as a real source distribution, intrinsic galaxy alignment, mask effects, and photo-z errors from surveys. The new model is also suitable for applying the tomography technique and nonlinear filters. Methods. A probabilistic approach to modeling peak counts is presented. First, we sample halos from a mass function. Second, we assign them density profiles. Third, we place those halos randomly on the field of view. The creation of these “fast simulations” requires much less computing time than do N-body runs. Then, we perform ray-tracing through these fast simulation boxes and select peaks from weak-lensing maps to predict peak number counts. The computation is achieved by our Camelus algorithm. Results. We compare our results to N-body simulations to validate our model. We find that our approach is in good agreement with full N-body runs. We show that the lensing signal dominates shape noise and Poisson noise for peaks with S/N between 4 and 6. Also, counts from the same S/N range are sensitive to Ωm and σ8. We show how our model can distinguish between various combinations of those two parameters. Conclusions. In this paper, we offer a powerful tool for studying weak-lensing peaks. The potential of our forward model is its high flexibility, which makes the using peak counts under realistic survey conditions feasible.
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