Cosmological inference from emulator based halo model I: Validation
  tests with HSC and SDSS mock catalogs
  We present validation tests of emulator-based halo model method for
cosmological parameter inference, assuming hypothetical measurements of the
projected correlation function of galaxies, $w_{\rm p}(R)$, and the
galaxy-galaxy weak lensing, $\Delta\!\Sigma(R)$, from the spectroscopic SDSS
galaxies and the Hyper Suprime-Cam Year1 (HSC-Y1) galaxies. To do this, we use
\textsc{Dark Emulator} developed in Nishimichi et al. based on an ensemble of
$N$-body simulations, which is an emulation package enabling a fast, accurate
computation of halo clustering quantities for flat-geometry $w$CDM cosmologies.
Adopting the halo occupation distribution, the emulator allows us to obtain
model predictions of $\Delta\!\Sigma$ and $w_{\rm p}$ for the SDSS-like
galaxies at a few CPU seconds for an input set of parameters. We present
performance and validation of the method by carrying out Markov Chain Monte
Carlo analyses of the mock signals measured from a variety of mock catalogs
that mimic the SDSS and HSC-Y1 galaxies. We show that the halo model method can
recover the underlying true cosmological parameters to within the 68\% credible
interval, except for the mocks including the assembly bias effect (although we
consider the unrealistically-large amplitude of assembly bias effect). Even for
the assembly bias mock, we demonstrate that the cosmological parameters can be
recovered {\it if} the analysis is restricted to scales $R\gtrsim 10~h^{-1}{\rm
Mpc}$. We also show that, by using a single population of source galaxies to
infer the relative strengths of $\Delta\!\Sigma$ for multiple lens samples at
different redshifts, the joint probes method allows for self-calibration of
photometric redshift errors and multiplicative shear bias. Thus we conclude
that the emulator-based halo model method can be safely applied to the HSC-Y1
dataset, achieving a precision of $\sigma(S_8)\simeq 0.04$.
