  Bayesian synthetic likelihood (BSL) is a popular method for estimating the
parameter posterior distribution for complex statistical models and stochastic
processes that possess a computationally intractable likelihood function.
Instead of evaluating the likelihood, BSL approximates the likelihood of a
judiciously chosen summary statistic of the data via model simulation and
density estimation. Compared to alternative methods such as approximate
Bayesian computation (ABC), BSL requires little tuning and requires less model
simulations than ABC when the chosen summary statistic is high-dimensional. The
original synthetic likelihood relies on a multivariate normal approximation of
the intractable likelihood, where the mean and covariance are estimated by
simulation. An extension of BSL considers replacing the sample covariance with
a penalised covariance estimator to reduce the number of required model
simulations. Further, a semi-parametric approach has been developed to relax
the normality assumption. In this paper, we present an R package called BSL
that amalgamates the aforementioned methods and more into a single, easy-to-use
and coherent piece of software. The R package also includes several examples to
illustrate how to use the package and demonstrate the utility of the methods.

Computation;Applications;Machine Learning