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Accelerating Bayesian estimation for network Poisson models using frequentist variational estimates

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  • Sophie Donnet
  • Stéphane Robin

Abstract

This work is motivated by the analysis of ecological interaction networks. Poisson stochastic block models 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 the 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 several ecological networks, as well as the existence of a residual interaction structure.

Suggested Citation

  • Sophie Donnet & Stéphane Robin, 2021. "Accelerating Bayesian estimation for network Poisson models using frequentist variational estimates," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(4), pages 858-885, August.
  • Handle: RePEc:bla:jorssc:v:70:y:2021:i:4:p:858-885
    DOI: 10.1111/rssc.12489
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    References listed on IDEAS

    as
    1. Pierre Del Moral & Arnaud Doucet & Ajay Jasra, 2006. "Sequential Monte Carlo samplers," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 411-436, June.
    2. David M. Blei & Alp Kucukelbir & Jon D. McAuliffe, 2017. "Variational Inference: A Review for Statisticians," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 859-877, April.
    3. repec:dau:papers:123456789/5671 is not listed on IDEAS
    4. Ajay Jasra & David A. Stephens & Arnaud Doucet & Theodoros Tsagaris, 2011. "Inference for Lévy‐Driven Stochastic Volatility Models via Adaptive Sequential Monte Carlo," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 38(1), pages 1-22, March.
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