BSL: An R Package for Efficient Parameter Estimation for Simulation-Based Models via Bayesian Synthetic Likelihood

Abstract

Bayesian synthetic likelihood (BSL) (Price et al., 2018) 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.

Synthetic Likelihood in Misspecified Models: Consequences and Corrections

“…Following the example in Section 2.2, we consider three sample sizes of n = 100, 500, 1000 and obtain the r-BSL posterior via the slice sampling MCMC approach presented in . 10 The procedure is implemented using the BSL package in R (An et al, 2019), with the default prior choice for Γ. We plot the r-BSL posterior across these values in Figure 4, and compare these results with those obtained for the BSL posterior in Figure 2.…”

“…We apply standard BSL with S (1) and S (2) , and r-BSL with S (2) . As above, we use the BSL R package of An et al (2019) for running the BSL methods. We use 100,000 iterations of MCMC for each run of BSL, and use a starting value with good support under each approximate posterior to avoid the need for a burn-in.…”