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We develop a framework for joint constraints on the CO luminosity functionbased on power spectra (PS) and voxel intensity distributions (VID), and applythis to simulations of COMAP, a CO intensity mapping experiment. This Bayesianframework is based on a Markov chain Monte Carlo (MCMC) sampler coupled to aGaussian likelihood with a joint PS + VID covariance matrix computed from alarge number of fiducial simulations, and re-calibrated with a small number ofsimulations per MCMC step. The simulations are based on dark matter halos fromfast peak patch simulations combined with the $L_\text{CO}(M_\text{halo})$model of Li et al. (2016). We find that the relative power to constrain the COluminosity function depends on the luminosity range of interest. In particular,the VID is more sensitive at both small and large luminosities, while the PS ismore sensitive at intermediate luminosities. The joint analysis is superior tousing either observable separately. When averaging over CO luminosities rangingbetween $L_\text{CO} = 10^4-10^7L_\odot$, and over 10 cosmological realizationsof COMAP Phase 2, the uncertainties (in dex) are larger by 58 % and 30 % forthe PS and VID, respectively, when compared to the joint analysis (PS + VID).This method is generally applicable to any other random field, with acomplicated likelihood, as long a fast simulation procedure is available.

Joint power spectrum and voxel intensity distribution forecast on the CO luminosity function with COMAP