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Naive estimates of the statistics of large scale structure and weak lensingpower spectrum measurements that include only Gaussian errors exaggerate theirscientific impact. Non-linear evolution and finite volume effects are bothsignificant sources of non-Gaussian covariance that reduce the ability of powerspectrum measurements to constrain cosmological parameters. Using a halo modelformalism, we derive an intuitive understanding of the various contributions tothe covariance and show that our analytical treatment agrees with simulations.This approach enables an approximate derivation of a joint likelihood for thecluster number counts, the weak lensing power spectrum and the bispectrum. Weshow that this likelihood is a good description of the ray-tracing simulation.Since all of these observables are sensitive to the same finite volume effectsand contain information about the non-linear evolution, a combined analysisrecovers much of the "lost" information and obviates the non-Gaussiancovariance. For upcoming weak lensing surveys, we estimate that a jointanalysis of power spectrum, number counts and bispectrum will produce animprovement of about $30-40\%$ in determinations of the matter density and thescalar amplitude. This improvement is equivalent to doubling the survey area.

Joint likelihood function of cluster counts and $n$-point correlation functions: Improving their power through including halo sample variance