Misspecification-robust Sequential Neural Likelihood

Simulation-based inference (SBI) techniques are now an essential tool for the parameter estimation of mechanistic and simulatable models with intractable likelihoods. Statistical approaches to SBI such as approximate Bayesian computation and Bayesian synthetic likelihood have been well studied in the well specified and misspecified settings. However, most implementations are inefficient in that many model simulations are wasted. Neural approaches such as sequential neural likelihood (SNL) have been developed that exploit all model simulations to build a surrogate of the likelihood function. However, SNL approaches have been shown to perform poorly under model misspecification. In this paper, we develop a new method for SNL that is robust to model misspecification and can identify areas where the model is deficient. We demonstrate the usefulness of the new approach on several illustrative examples.

Acceleration of expensive computations in Bayesian statistics using vector operations

Many applications in Bayesian statistics are extremely computationally intensive. However, they are also often inherently parallel, making them prime targets for modern massively parallel central processing unit (CPU) architectures. While the use of multi-core and distributed computing is widely applied in the Bayesian community, very little attention has been given to fine-grain parallelisation using single instruction multiple data (SIMD) operations that are available on most modern commodity CPUs. Rather, most fine-grain tuning in the literature has centred around general purpose graphics processing units (GPGPUs). Since the effective utilisation of GPGPUs typically requires specialised programming languages, such technologies are not ideal for the wider Bayesian community. In this work, we practically demonstrate, using standard programming libraries, the utility of the SIMD approach for several topical Bayesian applications. In particular, we consider sampling of the prior predictive distribution for approximate Bayesian computation (ABC), and the computation of Bayesian $p$-values for testing prior weak informativeness. Through minor code alterations, we show that SIMD operations can improve the floating point arithmetic performance resulting in up to $6\times$ improvement in the overall serial algorithm performance. Furthermore $4$-way parallel versions can lead to almost $19\times$ improvement over a na\"{i}ve serial implementation. We illustrate the potential of SIMD operations for accelerating Bayesian computations and provide the reader with essential implementation techniques required to exploit modern massively parallel processing environments using standard software development tools.