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Ruli, Erlis; Sartori, Nicola; Ventura, Laura

Approximate Bayesian computation with composite score functions. (English) Zbl 1505.62348

Stat. Comput. 26, No. 3, 679-692 (2016).
Summary: Both approximate Bayesian computation (ABC) and composite likelihood methods are useful for Bayesian and frequentist inference, respectively, when the likelihood function is intractable. We propose to use composite likelihood score functions as summary statistics in ABC in order to obtain accurate approximations to the posterior distribution. This is motivated by the use of the score function of the full likelihood, and extended to general unbiased estimating functions in complex models. Moreover, we show that if the composite score is suitably standardised, the resulting ABC procedure is invariant to reparameterisations and automatically adjusts the curvature of the composite likelihood, and of the corresponding posterior distribution. The method is illustrated through examples with simulated data, and an application to modelling of spatial extreme rainfall data is discussed.

Cited in 11 Documents

MSC:

62-08 Computational methods for problems pertaining to statistics
62F15 Bayesian inference
62P12 Applications of statistics to environmental and related topics

Keywords:

complex model; composite marginal likelihood; likelihood-free inference; pairwise likelihood; tangent exponential model; unbiased estimating function

Software:

SpatialExtremes
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Full Text: DOI arXiv

References:

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