  The covariance matrix of the matter and halo power spectrum and bispectrum
are studied. Using a large suite of simulations, we find that the
non-Gaussianity in the covariance is significant already at mildly nonlinear
scales. We compute the leading disconnected non-Gaussian correction to the
matter bispectrum covariance using perturbation theory, and find that the
corrections result in good agreement in the mildly nonlinear regime. The shot
noise contribution to the halo power spectrum and bispectrum covariance is
computed using the Poisson model, and the model yields decent agreement with
simulation results. However, when the shot noise is estimated from the
individual realization, which is usually done in reality, we find that the halo
covariance is substantially reduced and gets close to the Gaussian covariance.
This is because most of the non-Gaussianity in the covariance arises from the
fluctuations in the Poisson shot noise. We use the measured non-Gaussian
covariance to access the information content of the power spectrum and
bispectrum. The signal-to-noise ratio, S/N, of the matter and halo power
spectrum levels off in the mildly nonlinear regime, $k \sim 0.1 - 0.2
\,\mathrm{Mpc} h^{-1}$. In the nonlinear regime the S/N of the matter and halo
bispectrum increases but much slower than the Gaussian results suggest. We find
that both the S/N for power spectrum and bispectrum are overestimated by the
Gaussian covariances, but the problem being much more serious for the
bispectrum. Because the bispectrum is affected strongly by nonlinearity and
shot noise, inclusion of the bispectrum only adds modest amount of S/N compared
to that of the power spectrum.
