  We use analytic computations to predict the power spectrum as well as the
bispectrum of Cosmic Infrared Background (CIB) anisotropies. Our approach is
based on the halo model and takes into account the mean luminosity-mass
relation. The model is used to forecast the possibility to simultaneously
constrain cosmological, CIB and halo occupation distribution (HOD) parameters
in the presence of foregrounds. For the analysis we use wavelengths in eight
frequency channels between 200 and 900$\;\mathrm{GHz}$ with survey
specifications given by Planck and LiteBird. We explore the sensitivity to the
model parameters up to multipoles of $\ell =1000$ using auto- and
cross-correlations between the different frequency bands. With this setting,
cosmological, HOD and CIB parameters can be constrained to a few percent.
Galactic dust is modeled by a power law and the shot noise contribution as a
frequency dependent amplitude which are marginalized over. We find that dust
residuals in the CIB maps only marginally influence constraints on standard
cosmological parameters. Furthermore, the bispectrum yields tighter constraints
(by a factor four in $1\sigma$ errors) on almost all model parameters while the
degeneracy directions are very similar to the ones of the power spectrum. The
increase in sensitivity is most pronounced for the sum of the neutrino masses.
Due to the similarity of degeneracies a combination of both analysis is not
needed for most parameters. This, however, might be due to the simplified bias
description generally adopted in such halo model approaches.
