Diagnostic tools for approximate Bayesian computation using the coverage property

Summary Approximate Bayesian computation (ABC) is an approach to sampling from an approximate posterior distribution in the presence of a computationally intractable likelihood function. A common implementation is based on simulating model, parameter and dataset triples from the prior, and then acce...

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Bibliographic Details
Published in:Australian & New Zealand journal of statistics 2014-12, Vol.56 (4), p.309-329
Main Authors: Prangle, D., Blum, M. G. B., Popovic, G., Sisson, S. A.
Format: Article
Language:English
Subjects:
Approximation
Bayesian analysis
Computation
Computer simulation
Diagnostic software
Genetics
Kernels
Life Sciences
likelihood-free inference
Mathematical analysis
Mathematical models
Mathematics
model inference
parameter inference
Populations and Evolution
Statistical methods
Statistics
Statistics Theory
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Summary:Summary Approximate Bayesian computation (ABC) is an approach to sampling from an approximate posterior distribution in the presence of a computationally intractable likelihood function. A common implementation is based on simulating model, parameter and dataset triples from the prior, and then accepting as samples from the approximate posterior, those model and parameter pairs for which the corresponding dataset, or a summary of that dataset, is ‘close’ to the observed data. Closeness is typically determined though a distance measure and a kernel scale parameter. Appropriate choice of that parameter is important in producing a good quality approximation. This paper proposes diagnostic tools for the choice of the kernel scale parameter based on assessing the coverage property, which asserts that credible intervals have the correct coverage levels in appropriately designed simulation settings. We provide theoretical results on coverage for both model and parameter inference, and adapt these into diagnostics for the ABC context. We re‐analyse a study on human demographic history to determine whether the adopted posterior approximation was appropriate. Code implementing the proposed methodology is freely available in the R package abctools.
ISSN:1369-1473
1467-842X
DOI:10.1111/anzs.12087