Efficient Multifidelity Likelihood-Free Bayesian Inference with Adaptive Computational Resource Allocation

TL;DR

This paper introduces an adaptive multifidelity Bayesian inference method that efficiently allocates computational resources across models of varying fidelity, significantly reducing simulation costs while maintaining accuracy.

Contribution

It extends multifidelity techniques to general likelihood-free Bayesian inference and develops an adaptive algorithm for optimal resource allocation.

Findings

The adaptive method achieves near-optimal efficiency in posterior estimation.

Analytical results guide optimal resource distribution among fidelity levels.

The approach reduces computational costs significantly compared to traditional methods.

Abstract

Likelihood-free Bayesian inference algorithms are popular methods for calibrating the parameters of complex, stochastic models, required when the likelihood of the observed data is intractable. These algorithms characteristically rely heavily on repeated model simulations. However, whenever the computational cost of simulation is even moderately expensive, the significant burden incurred by likelihood-free algorithms leaves them unviable in many practical applications. The multifidelity approach has been introduced (originally in the context of approximate Bayesian computation) to reduce the simulation burden of likelihood-free inference without loss of accuracy, by using the information provided by simulating computationally cheap, approximate models in place of the model of interest. The first contribution of this work is to demonstrate that multifidelity techniques can be applied in the general likelihood-free Bayesian inference setting. Analytical results on the optimal allocation of computational resources to simulations at different levels of fidelity are derived, and subsequently implemented practically. We provide an adaptive multifidelity likelihood-free inference algorithm that learns the relationships between models at different fidelities and adapts resource allocation accordingly, and demonstrate that this algorithm produces posterior estimates with near-optimal efficiency.