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preprint · arXiv (Cornell University) · 2023

Asymptotics of approximate Bayesian computation when summary statistics converge at heterogeneous rates

Caroline Lawless, Christian P. Robert, Judith Rousseau, Robin Ryder

Cited by 1Open access

Abstract

We consider the asymptotic properties of Approximate Bayesian Computation (ABC) for the realistic case of summary statistics with heterogeneous rates of convergence. We allow some statistics to converge faster than the ABC tolerance, other statistics to converge slower, and cover the case where some statistics do not converge at all. We give conditions for the ABC posterior to converge, and provide an explicit representation of the shape of the ABC posterior distribution in our general setting; in particular, we show how the shape of the posterior depends on the number of slow statistics. We then quantify the gain brought by the local linear post-processing step.

Cite this paper

APA 7

Lawless, C., Robert, C. P., Rousseau, J., & Ryder, R. (2023). Asymptotics of approximate Bayesian computation when summary statistics converge at heterogeneous rates. arXiv (Cornell University). https://doi.org/10.48550/arxiv.2311.10080

MLA 9

Lawless, Caroline, et al. “Asymptotics of approximate Bayesian computation when summary statistics converge at heterogeneous rates.” arXiv (Cornell University), 2023, https://doi.org/10.48550/arxiv.2311.10080.

Chicago

Lawless, Caroline, Christian P. Robert, Judith Rousseau, and Robin Ryder. 2023. “Asymptotics of approximate Bayesian computation when summary statistics converge at heterogeneous rates.” arXiv (Cornell University). https://doi.org/10.48550/arxiv.2311.10080.

Harvard

Lawless, C. et al. (2023) ‘Asymptotics of approximate Bayesian computation when summary statistics converge at heterogeneous rates’, arXiv (Cornell University). Available at: https://doi.org/10.48550/arxiv.2311.10080.

BibTeX
@misc{lawless2023asymptotics,
  title = {{Asymptotics of approximate Bayesian computation when summary statistics converge at heterogeneous rates}},
  author = {Lawless, Caroline and Robert, Christian P. and Rousseau, Judith and Ryder, Robin},
  journal = {arXiv (Cornell University)},
  year = {2023},
  doi = {10.48550/arxiv.2311.10080}
}

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