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 max,P = 0.3 h Mpc-1 for the power spectrum and k max,B = 0.09 h 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 1000h -3 Gpc3. 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 max,B on all triangle sides can lead to a better exploitation of the information contained in the bispectrum.
