  We present a joint likelihood analysis of the halo power spectrum and
bispectrum in real space. We take advantage of a large set of numerical
simulations and of an even larger set of halo mock catalogs to provide a robust
estimate of the covariance properties. We derive constraints on bias and
cosmological parameters assuming a theoretical model from perturbation theory
at one-loop for the power spectrum and tree-level for the bispectrum. By means
of the Deviance Information Criterion, we select a reference bias model
dependent on seven parameters that can describe the data up to $k_{\rm
max,P}=0.3\, h \, {\rm Mpc}^{-1}$ for the power spectrum and $k_{\rm
max,B}=0.09\, h \, {\rm Mpc}^{-1}$ for the bispectrum at redshift $z=1$. This
model is able to accurately recover three selected cosmological parameters even
for the rather extreme total simulation volume of $1000\, h^{-3} \, {\rm
Gpc}^3$. With the same tools, we study how relations among bias parameters can
improve the fit while reducing the parameter space. In addition, we compare
common approximations to the covariance matrix against the full covariance
estimated from the mocks, and quantify the (non-negligible) effect of ignoring
the cross-covariance between the two statistics. Finally, we explore different
selection criteria for the triangular configurations to include in the
analysis, showing that excluding nearly equilateral triangles rather than
simply imposing a fixed maximum $k_{\rm max,B}$ on all triangle sides can lead
to a better exploitation of the information contained in the bispectrum.
