Primordial Non-Gaussianity from Biased Tracers: Likelihood Analysis of
  Real-Space Power Spectrum and Bispectrum
  Upcoming galaxy redshift surveys promise to significantly improve current
limits on primordial non-Gaussianity (PNG) through measurements of 2- and
3-point correlation functions in Fourier space. However, realizing the full
potential of this dataset is contingent upon having both accurate theoretical
models and optimized analysis methods. Focusing on the local model of PNG,
parameterized by $f_{\rm NL}$, we perform a Monte-Carlo Markov Chain analysis
to confront perturbation theory predictions of the halo power spectrum and
bispectrum in real space against a suite of N-body simulations. We model the
halo bispectrum at tree-level, including all contributions linear and quadratic
in $f_{\rm NL}$, and the halo power spectrum at 1-loop, including tree-level
terms up to quadratic order in $f_{\rm NL}$ and all loops induced by local PNG
linear in $f_{\rm NL}$. Keeping the cosmological parameters fixed, we examine
the effect of informative priors on the linear non-Gaussian bias parameter on
the statistical inference of $f_{\rm NL}$. A conservative analysisof the
combined power spectrum and bispectrum, in which only loose priors are imposed
and all parameters are marginalized over, can improve the constraint on $f_{\rm
NL}$ by more than a factor of 5 relative to the power spectrum-only
measurement. Imposing a strong prior on $b_\phi$, or assuming bias relations
for both $b_\phi$ and $b_{\phi\delta}$ (motivated by a universal mass function
assumption), improves the constraints further by a factor of few. In this case,
however, we find a significant systematic shift in the inferred value of
$f_{\rm NL}$ if the same range of wavenumber is used. Likewise, a Poisson noise
assumption can lead to significant systematics, and it is thus essential to
leave all the stochastic amplitudes free.
