  We address key points for an efficient implementation of likelihood codes for
modern weak lensing large-scale structure surveys. Specifically, we focus on
the joint weak lensing convergence power spectrum-bispectrum probe and we
tackle the numerical challenges required by a realistic analysis. Under the
assumption of (multivariate) Gaussian likelihoods, we have developed a high
performance code that allows highly parallelised prediction of the binned
tomographic observables and of their joint non-Gaussian covariance matrix
accounting for terms up to the 6-point correlation function and super-sample
effects. This performance allows us to qualitatively address several
interesting scientific questions. We find that the bispectrum provides an
improvement in terms of signal-to-noise ratio (S/N) of about 10% on top of the
power spectrum, making it a non-negligible source of information for future
surveys. Furthermore, we are capable to test the impact of theoretical
uncertainties in the halo model used to build our observables; with presently
allowed variations we conclude that the impact is negligible on the S/N.
Finally, we consider data compression possibilities to optimise future analyses
of the weak lensing bispectrum. We find that, ignoring systematics, 5
equipopulated redshift bins are enough to recover the information content of a
Euclid-like survey, with negligible improvement when increasing to 10 bins. We
also explore principal component analysis and dependence on the triangle shapes
as ways to reduce the numerical complexity of the problem.
