Improving Approximate Bayesian Computation via Quasi-Monte Carlo

ABSTRACT

ABC (approximate Bayesian computation) is a general approach for dealing with models with an intractable likelihood. In this work, we derive ABC algorithms based on QMC (quasi-Monte Carlo) sequences. We show that the resulting ABC estimates have a lower variance than their Monte Carlo counter-parts. We also develop QMC variants of sequential ABC algorithms, which progressively adapt the proposal distribution and the acceptance threshold. We illustrate our QMC approach through several examples taken from the ABC literature.

KEYWORDS:

• Adaptive importance sampling
• Approximate Bayesian computation
• Likelihood-free inference
• Quasi-Monte Carlo
• Randomized quasi-Monte Carlo

Acknowledgments

The authors are thankful to Mathieu Gerber, two anonymous referees, and the editors who made comments that helped them to improve the article.

Additional information

Funding

The research of the first author is funded by a GENES doctoral scholarship. The research of the second author is partially supported by a grant from the French National Research Agency (ANR) as part of the Investissements d’Avenir program (ANR-11-LABEX-0047).