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.
In this package, a Metropolis Hastings Markov chain Monte Carlo (MH-MCMC) implementation of BSL is available. We also include implementations of three methods (BSL, uBSL and semiBSL) and two shrinkage estimations (graphical lasso and Warton's estimation).
Methods: (1) BSL (Price et al., 2018), which is the standard form of Bayesian synthetic likelihood, assumes the summary statistic is roughly multivariate normal; (2) uBSL (Price et al., 2018), which uses an unbiased estimator to the normal density; and (3) semiBSL (An et al. 2018), which relaxes the normality assumption to an extent and maintains the computational advantages of BSL without any tuning.
Shrinkage estimations are designed particularly to reduce the number of simulations if method is BSL or semiBSL: (1) graphical lasso (Friedman et al., 2008) finds a sparse precision matrix with a L1-regularised log-likelihood. (An et al., 2019) use graphical lasso within BSL to bring down the number of simulations significantly when the dimension of the summary statistic is high; and (2) Warton's estimator (Warton 2008) penalises the correlation matrix and is straightforward to compute.
Parallel computing is supported through the foreach package and users can specify their own parallel
backend by using packages like doParallel or doMC. Alternatively a vectorised simulation function
that simultaneously generates n simulation results is also supported.
The main functionality is available through
bsl: The general function to perform BSL, uBSL, and semiBSL (with or without
parallel computing).
selectPenalty: A function to select the penalty for BSL and semiBSL.
Several examples have also been included. These examples can be used to reproduce the results of An et al. (2019), and can help practitioners learn how to use the package.
ma2: The MA(2) example from An et al. (2019).
mgnk: The multivariate G&K example from An et al. (2019).
cell: The cell biology example from Price et al. (2018) and An et al. (2019).
Extensions to this package are planned.
Price, L. F., Drovandi, C. C., Lee, A., & Nott, D. J. (2018). Bayesian synthetic likelihood. Journal of Computational and Graphical Statistics. https://doi.org/10.1080/10618600.2017.1302882
An, Z., South, L. F., Nott, D. J. & Drovandi, C. C. (2019). Accelerating Bayesian synthetic likelihood with the graphical lasso. Journal of Computational and Graphical Statistics. https://doi.org/10.1080/10618600.2018.1537928
An, Z., Nott, D. J. & Drovandi, C. (2018). Robust Bayesian Synthetic Likelihood via a Semi-Parametric Approach. ArXiv Preprint https://arxiv.org/abs/1809.05800
Friedman, J., Hastie, T., Tibshirani, R. (2008). Sparse inverse covariance estimation with the graphical lasso. Biostatistics. https://doi.org/10.1093/biostatistics/kxm045
Warton, D. I. (2008). Penalized Normal Likelihood and Ridge Regularization of Correlation and Covariance Matrices, Journal of the American Statistical Association. https://doi.org/10.1198/016214508000000021