A vital stage in the mathematical modeling 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 characterize the optimal choice of how often to simulate from cheap, low-fidelity models in place of expensive, high-fidelity 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.


  1. Bayesian inference
  2. likelihood-free methods
  3. stochastic simulation
  4. multifidelity methods

MSC codes

  1. 62F15
  2. 65C20
  3. 65C60
  4. 93B30
  5. 92C42

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Supplementary Material

PLEASE NOTE: These supplementary files have not been peer-reviewed.

Index of Supplementary Materials

Title of paper: Multifidelity Approximate Bayesian Computation

Authors: Thomas P. Prescott and Ruth E. Baker

File: supplement.pdf

Type: PDF

Contents: Link between ESS and variance (SM1); Optimising efficiency (SM2); Coupling tau-leap and exact simulations (SM3).


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Information & Authors


Published In

cover image SIAM/ASA Journal on Uncertainty Quantification
SIAM/ASA Journal on Uncertainty Quantification
Pages: 114 - 138
ISSN (online): 2166-2525


Submitted: 29 November 2018
Accepted: 21 October 2019
Published online: 16 January 2020


  1. Bayesian inference
  2. likelihood-free methods
  3. stochastic simulation
  4. multifidelity methods

MSC codes

  1. 62F15
  2. 65C20
  3. 65C60
  4. 93B30
  5. 92C42



Funding Information

Biotechnology and Biological Sciences Research Council https://doi.org/10.13039/501100000268 : BB/R000816/1

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