  We study the impact of baryonic physics on cosmological parameter estimation
with weak lensing surveys. We run a set of cosmological hydrodynamics
simulations with different galaxy formation models. We then perform ray-tracing
simulations through the total matter density field to generate 100 independent
convergence maps of 25 ${\rm deg}^2$ field-of-view, and use them to examine the
ability of the following three lensing statistics as cosmological probes; power
spectrum, peak counts, and Minkowski functionals. For the upcoming wide-field
observations such as Subaru Hyper Suprime-Cam (HSC) survey with a sky coverage
of 1400 ${\rm deg}^2$, these three statistics provide tight constraints on the
matter density, density fluctuation amplitude, and dark energy equation of
state, but parameter bias is induced by the baryonic processes such as gas
cooling and stellar feedback. The bias can be significant when the statistical
errors become small in future observations with a much larger survey area. We
find the bias is induced in different directions in the parameter space
depending on the statistics employed. While the two-point statistic, i.e. power
spectrum, yields robust results against baryonic effects, the overall
constraining power is weak compared with peak counts and Minkowski functionals.
On the other hand, using one of peak counts or Minkowski functionals, or
combined analysis with multiple statistics, results in biased parameter
estimate. The bias can be as large as $1\sigma$ for HSC survey, and will be
more significant for upcoming wider area surveys. We suggest to use an
optimized combination so that the baryonic effects on parameter estimation are
mitigated. Such `calibrated' combination can place stringent and robust
constraints on cosmological parameters.
