Bayesian inference for network Poisson models

TL;DR

This paper introduces a Bayesian inference approach for network Poisson models, leveraging variational approximations and Monte Carlo sampling to improve ecological network analysis.

Contribution

It develops a Bayesian inference method using a Laplace approximation of variational estimates and sequential Monte Carlo sampling for network Poisson models.

Findings

Efficient posterior sampling is achieved with improved accuracy.

The method effectively assesses covariate influence on ecological networks.

The approach extends to other latent variable models.

Abstract

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.