Bayesian Synthetic Likelihood

Bayesian synthetic likelihood (BSL, Price et al. (2018) ) is an alternative to standard, non-parametric approximate Bayesian computation (ABC). BSL assumes a multivariate normal distribution for the summary statistic likelihood and it is suitable when the distribution of the model summary statistics is sufficiently regular. This package provides a Metropolis Hastings Markov chain Monte Carlo implementation of four methods (BSL, uBSL, semiBSL and BSLmisspec) and two shrinkage estimators (graphical lasso and Warton's estimator). uBSL (Price et al. (2018) ) uses an unbiased estimator to the normal density. A semi-parametric version of BSL (semiBSL, An et al. (2020) ) is more robust to non-normal summary statistics. BSLmisspec (Frazier et al. 2021 ) estimates the Gaussian synthetic likelihood whilst acknowledging that there may be incompatibility between the model and the observed summary statistic. Shrinkage estimation can help to decrease the number of model simulations when the dimension of the summary statistic is high (e.g., BSLasso, An et al. (2019) ). Extensions to this package are planned. For a journal article describing how to use this package, see An et al. (2022) .