An Extended Empirical Saddlepoint Approximation for Intractable Likelihoods

Matteo Fasiolo, Simon N Wood, Florian Hartig, Mark V. Bravington

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

The challenges posed by complex stochastic models used in computational ecology, biology and genetics have stimulated the development of approximate approaches to statistical inference. Here we focus on Synthetic Likelihood (SL), a procedure that reduces the observed and simulated data to a set of summary statistics, and quantifies the discrepancy between them through a synthetic likelihood function. SL requires little tuning, but it relies on the approximate normality of the summary statistics. We relax this assumption by proposing a novel, more flexible, density estimator: the Extended Empirical Saddlepoint approximation. In addition to proving the consistency of SL, under either the new or the Gaussian density estimator, we illustrate the method using three examples. One of these is a complex individual-based forest model for which SL offers one of the few practical possibilities for statistical inference. The examples show that the new density estimator is able to capture large departures from normality, while being scalable to high dimensions, and this in turn leads to more accurate parameter estimates, relative to the Gaussian alternative. The new density estimator is implemented by the esaddle R package, which is freely available on the Comprehensive R Archive Network (CRAN).
Original languageEnglish
Pages (from-to)1544-1578
Number of pages35
JournalElectronic Journal of Statistics
Issue number1
Early online date26 May 2018
Publication statusPublished - 30 Jun 2018

Keywords / Materials (for Non-textual outputs)

  • Intractable likelihood
  • saddlepoint approximation
  • synthetic likelihood
  • simulation-based inference
  • implicit statistical model
  • density estimation


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