Asymptotic properties of approximate Bayesian computation
By David T. Frazier, Gael M. Martin, Christian P. Robert, Judith Rousseau. Biometrika, 2016
112 citations recorded by the source corpus.
Summary Approximate Bayesian computation allows for statistical analysis using models with intractable likelihoods. In this paper we consider the asymptotic behaviour of the posterior distribution obtained by this method. We give general results on the rate at which the posterior distribution concentrates on sets containing the true parameter, the limiting shape of the posterior distribution, and the asymptotic distribution of the posterior mean. These results hold under given rates for the tolerance used within the method, mild regularity conditions on the summary statistics, and a condition linked to identification of the true parameters. Implications for practitioners are discussed.
Subfields: Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/5edd496b404468c6d112f7dad7a51a6850c5983d
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In Mathematical Physics
In Statistics and Probability
Citations in the corpus
- Learning in Implicit Generative Models (2016, unknown): “But we still lack the tools to make theoretical statements that allow us to assess the correctness of the model learning framework, although theoretical developments in the literature on approximate Bayesian computation may help in this regard, e.g., Frazier et al. (2016).”
- Under Review as a Conference Paper at Iclr 2017 Learning in Implicit Generative Models (2017, background): “Furthermore, we have also not yet gained the tools to make theoretical statements that allow us to assess the correctness of the model learning framework, although theoretical developments in the literature on approximate Bayesian computation may help in this regard, e.g., Frazier et al. (2016).”