Bootstrapped synthetic likelihood
This addresses a bottleneck for researchers using Bayesian inference with computationally expensive simulators, offering an incremental improvement in efficiency.
The paper tackles the computational inefficiency of synthetic likelihood (SL) and approximate Bayesian computation (ABC) methods by using bootstrapping to improve likelihood estimates with fewer simulations, and applies the bag of little bootstraps to handle large datasets, demonstrating examples across i.i.d., temporal, and spatial data.
Approximate Bayesian computation (ABC) and synthetic likelihood (SL) techniques have enabled the use of Bayesian inference for models that may be simulated, but for which the likelihood cannot be evaluated pointwise at values of an unknown parameter $θ$. The main idea in ABC and SL is to, for different values of $θ$ (usually chosen using a Monte Carlo algorithm), build estimates of the likelihood based on simulations from the model conditional on $θ$. The quality of these estimates determines the efficiency of an ABC/SL algorithm. In standard ABC/SL, the only means to improve an estimated likelihood at $θ$ is to simulate more times from the model conditional on $θ$, which is infeasible in cases where the simulator is computationally expensive. In this paper we describe how to use bootstrapping as a means for improving SL estimates whilst using fewer simulations from the model, and also investigate its use in ABC. Further, we investigate the use of the bag of little bootstraps as a means for applying this approach to large datasets, yielding Monte Carlo algorithms that accurately approximate posterior distributions whilst only simulating subsamples of the full data. Examples of the approach applied to i.i.d., temporal and spatial data are given.