Multifidelity Approximate Bayesian Computation

Abstract

A vital stage in the mathematical modelling of real-world systems is to calibrate a model's parameters to observed data. Likelihood-free parameter inference methods, such as approximate Bayesian computation (ABC), build Monte Carlo samples of the uncertain parameter distribution by comparing the data with large numbers of model simulations. However, the computational expense of generating these simulations forms a significant bottleneck in the practical application of such methods. We identify how simulations of corresponding cheap, low-fidelity models have been used separately in two complementary ways to reduce the computational expense of building these samples, at the cost of introducing additional variance to the resulting parameter estimates. We explore how these approaches can be unified so that cost and benefit are optimally balanced, and we characterise the optimal choice of how often to simulate from cheap, low-fidelity models in place of expensive, highfidelity models in Monte Carlo ABC algorithms. The resulting early accept/reject multifidelity ABC algorithm that we propose is shown to give improved performance over existing multifidelity and high-fidelity approaches.

Quantifying the impact of electric fields on single-cell motility

“…The electrotaxis model in this paper is a starting point for a comprehensive agent-based model that also incorporates phenomena such as volume exclusion, adhesion, elastic collisions, contact inhibition, and so on (13,30,31). Multifidelity approaches (27,32) that can link experiments and information at the single-cell and multicellular level will be vital to identify and quantify the biasing effects of EFs on the collective motility of cell populations (12,14,33).…”

“…Furthermore, there is significant scope for linking the calibrated parameters of the single-cell model described in this work to the construction of lower-level models of the intracellular processes that give rise to electrotaxis. Multifidelity approaches (27, 32) that can link experiments and information at the intracellular, single-cell and multicellular level will be vital to identify and quantify the biasing effects of EFs on the collective motility of cell populations (12, 14, 33).…”

Seven challenges in the multiscale modeling of multicellular tissues

“…Several challenges remain when specifying initial and boundary conditions and estimating parameters of multiscale models. In particular, more tailored and efficient parameter inference techniques are needed that rely less heavily on repeated simulations of computationally expensive models, for example by exploring parameter space more intelligently and by exploiting "low-fidelity" or surrogate modeling (a recent, relevant domain-specific example of this is Prescott & Baker, 2020). Where simulation outputs are intended to inform decision-making, greater use of uncertainty quantification techniques is needed, for which software tools are increasingly available; in this regard, for further discussion of VVUQ and related concepts, see Richardson et al, 2020.…”

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

“…Monte Carlo estimates of the posterior distribution, with respect to the likelihood of the original high-fidelity model, can be constructed using the simulation outputs of the low-fidelity approximation. Prescott and Baker [2020] showed that using the low-fidelity approximation introduces no further bias, so long as, for any parameter proposal, there is a positive probability of simulating the high-fidelity model to check and potentially correct a low-fidelity likelihood estimate. The key to the success of the multifidelity ABC (MF-ABC) approach is to choose this positive probability to be suitably small, thereby simulating the original model as little as possible, while ensuring it is large enough that the variance of the resulting Monte Carlo estimate is suitably small.…”