Multifidelity multilevel Monte Carlo to accelerate approximate Bayesian parameter inference for partially observed stochastic processes

TL;DR

This paper introduces a novel multifidelity multilevel Monte Carlo method that significantly accelerates likelihood-free Bayesian inference for partially observed stochastic processes, reducing computational costs by over two orders of magnitude.

Contribution

It develops a new algorithm combining multilevel Monte Carlo and multifidelity rejection sampling to improve efficiency in likelihood-free Bayesian inference for complex stochastic models.

Findings

Achieved over 100x reduction in computational effort compared to standard methods.

Demonstrated effectiveness on systems biology models.

Applicable to various sampling schemes beyond rejection sampling.

Abstract

Models of stochastic processes are widely used in almost all fields of science. Theory validation, parameter estimation, and prediction all require model calibration and statistical inference using data. However, data are almost always incomplete observations of reality. This leads to a great challenge for statistical inference because the likelihood function will be intractable for almost all partially observed stochastic processes. This renders many statistical methods, especially within a Bayesian framework, impossible to implement. Therefore, computationally expensive likelihood-free approaches are applied that replace likelihood evaluations with realisations of the model and observation process. For accurate inference, however, likelihood-free techniques may require millions of expensive stochastic simulations. To address this challenge, we develop a new method based on recent advances in multilevel and multifidelity. Our approach combines the multilevel Monte Carlo telescoping summation, applied to a sequence of approximate Bayesian posterior targets, with a multifidelity rejection sampler to minimise the number of computationally expensive exact simulations required for accurate inference. We present the derivation of our new algorithm for likelihood-free Bayesian inference, discuss practical implementation details, and demonstrate substantial performance improvements. Using examples from systems biology, we demonstrate improvements of more than two orders of magnitude over standard rejection sampling techniques. Our approach is generally applicable to accelerate other sampling schemes, such as sequential Monte Carlo, to enable feasible Bayesian analysis for realistic practical applications in physics, chemistry, biology, epidemiology, ecology and economics.