  This work is motivated by the analysis of ecological interaction networks.
Poisson stochastic blockmodels are widely used in this field to decipher the
structure that underlies a weighted network, while accounting for covariate
effects. Efficient algorithms based on variational approximations exist for
frequentist inference, but without statistical guaranties as for the resulting
estimates. In absence of variational Bayes estimates, we show that a good proxy
of the posterior distribution can be straightforwardly derived from the
frequentist variational estimation procedure, using a Laplace approximation. We
use this proxy to sample from the true posterior distribution via a sequential
Monte-Carlo algorithm. As shown in the simulation study, the efficiency of the
posterior sampling is greatly improved by the accuracy of the approximate
posterior distribution. The proposed procedure can be easily extended to other
latent variable models. We use this methodology to assess the influence of
available covariates on the organization of two ecological networks, as well as
the existence of a residual interaction structure.
