Robust Bayesian synthetic likelihood via a semi-parametric approach

Abstract

Bayesian synthetic likelihood (BSL) is now a well established method for performing approximate Bayesian parameter estimation for simulation-based models that do not possess a tractable likelihood function. BSL approximates an intractable likelihood function of a carefully chosen summary statistic at a parameter value with a multivariate normal distribution. The mean and covariance matrix of this normal distribution are estimated from independent simulations of the model. Due to the parametric assumption implicit in BSL, it can be preferred to its non-parametric competitor, approximate Bayesian computation, in certain applications where a high-dimensional summary statistic is of interest. However, despite several successful applications of BSL, its widespread use in scientific fields may be hindered by the strong normality assumption. In this paper, we develop a semi-parametric approach to relax this assumption to an extent and maintain the computational advantages of BSL without any additional tuning. We test our new method, semiBSL, on several challenging examples involving simulated and real data and demonstrate that semiBSL can be significantly more robust than BSL and another approach in the literature. We also identify an example where semiBSL does not provide sufficient flexibility, promoting further research in robustifying BSL.

Bayesian Inference for Stochastic Differential Equation Mixed Effects Models of a Tumour Xenography Study

“…Similarly to ABC, SL relies on a set of carefully selected summary statistics for the data s := s.y/. However, whereas in ABC no assumption is made for the distribution of s, SL assumes that summary statistics follow a multivariate normal distribution: s ∼ N {μ.θ/, Σ.θ/} (see Fasiolo et al (2018) and An et al (2018) on relaxing this assumption). If this holds true, and if parameters in θ can be identified from μ.θ/ and Σ.θ/, then inference for θ can be based on the Gaussian likelihood of s instead of the intractable likelihood of y.…”

“…() and An et al . () on relaxing this assumption). If this holds true, and if parameters in θ can be identified from μ ( θ ) and Σ ( θ ), then inference for θ can be based on the Gaussian likelihood of s instead of the intractable likelihood of y .…”

A review of approximate Bayesian computation methods via density estimation: Inference for simulator‐models

“…In particular, for small sample size the approximation may be unreliable, see Example 5.2. Recently, a more robust semiparametric version has been proposed to relax the normality assumptions (An, Nott, & Drovandi, ).…”

Composite Surrogate for Likelihood-Free Bayesian Optimisation in High-Dimensional Settings of Activity-Based Transportation Models

“…However, the ABC methods have limited applicability in settings of highdimensional data and costly simulations [16,27,32], constituting a bottleneck for their broader adoption in settings of complex simulation models. Therefore, applicability of the BOLFI method for calibrating the Preday ABM to a new urban environment is limited, and neither of the proposed solutions, such as dimensionality reduction [7,35], or introduction of synthetic parametric/nonparametric likelihoods [2,30,32,37,42], circumvent the obstacle. Namely, the former requires increased number of simulations, while the latter are applicable to problems with low number of parameters.…”