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

Abstract

Bayesian synthetic likelihood (BSL; Price, Drovandi, Lee, and Nott 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 penalized covariance estimator to reduce the number of required model simulations. Further, a semi-parametric approach has been developed to relax the normality assumption. Finally, another extension of BSL aims to develop a more robust synthetic likelihood estimator while acknowledging there might be model misspecification. In this paper, we present the R package BSL that amalgamates the aforementioned methods and more into a single, easy-to-use and coherent piece of software. The package also includes several examples to illustrate use of the package and the utility of the methods.

Approximating Bayes in the 21st Century

“…Pseudo-code for generic MCMC sampling of the BSL posterior in ( 10) is given in Algorithm 3. We refer the interested reader to the R language (R Core Team, 2020) package BSL (An et al, 2019), which can be used to implement BSL and its common variants.…”

ABC of the future

“…Nevertheless, the generic application potential of ABC and other likelihood‐free inference (LFI) methods has been held back by the computational requirements of its standard inference algorithms and the lack of a suitable all‐purpose software implementation. With the advent of more efficient inference strategies adopted from the field of machine learning (Gutmann & Corander, 2016; Gutmann et al , 2018; Lueckmann et al , 2018; Kokko et al , 2019; Papamakarios et al , 2019; Cranmer et al , 2020; Grazian & Fan, 2020; Thomas et al , 2022) and software platforms such as Engine for likelihood‐free inference (ELFI) (Lintusaari et al , 2018), ABCpy (Dutta et al , 2017), BSL (An et al , 2019) and sbi (Tejero‐Cantero et al , 2020), to name a few, the immediate prospect of both using and updating the ABC/LFI toolkits for challenging real‐world applications certainly looks brighter.…”

ABC of the Future

“…Nevertheless, the generic application potential of ABC and other likelihood-free inference (LFI) methods has been held back by the computational requirements of its standard inference algorithms and the lack of a suitable all-purpose software implementation. With the advent of more efficient inference strategies adopted from the field of machine learning [Gutmann and Corander, 2016, Lueckmann et al, 2018, Thomas et al, 2021, Kokko et al, 2019, Cranmer et al, 2020, Grazian and Fan, 2019, Papamakarios et al, 2019 and software platforms such as Engine for likelihood-free inference (ELFI) [Lintusaari et al, 2018], ABCpy , BSL [An et al, 2019a] and sbi [Tejero-Cantero et al, 2020], to name a few, the immediate prospect of both using and updating the ABC/LFI toolkits for challenging real-world applications certainly looks brighter.…”