A Scheme for Adaptive Selection of Population
Sizes in Approximate Bayesian Computation -
Sequential Monte CarloEmmanuel Klinger1,2,3and Jan Hasenauer2,3(B)(^1) Department of Connectomics, Max Planck Institute for Brain Research,
60438 Frankfurt, Germany
[email protected]
(^2) Helmholtz Zentrum M ̈unchen - German Research Center for Environmental Health,
Institute of Computational Biology, 85764 Neuherberg, Germany
[email protected], [email protected]
(^3) Center for Mathematics, Chair of Mathematical Modeling of Biological Systems,
Technische Universit ̈at M ̈unchen, 85748 Garching, Germany
Abstract.Parameter inference and model selection in systems biology
often requires likelihood-free methods, such as Approximate Bayesian
Computation (ABC). In recent years, this approach has frequently been
combined with a Sequential Monte Carlo (ABC-SMC) scheme. In this
scheme, the approximation of the posterior distribution through a popu-
lation of particles is iteratively improved by a sequential sampling strat-
egy. However, it has been difficult to give general guidelines on how to
choose the size of these populations. In this manuscript, we propose a
method to adaptively and automatically select these population sizes.
The method exploits the cross-validated approximation error of a kernel
density estimate of the particles in the current population to select the
number of particles for the subsequent population.
We found the proposed method to be robust to the initially chosen
population size and to the number of posterior modes. We demonstrated
that the method is applicable to parameter inference as well as to model
selection. The study of a computationally demanding multiscale model
confirmed the method’s scalability. In conclusion, the proposed method
is applicable to a wide range of parameter and model selection tasks. The
method makes the influence of the population size on the approximation
error explicit simplifying the application of ABC-SMC schemes.
Keywords:Parameter estimation·Likelihood-free inference·Approxi-
mate Bayesian Computation·Model selection·Sequential Monte Carlo·
Population size
1 Introduction
Computer simulations have become an indispensable tool for scientific research.
They facilitate to investigate regimes which are not analytically tractable any-
more. It is often easy to simulate an experimental outcome for a model with given
©cSpringer International Publishing AG 2017
J. Feret and H. Koeppl (Eds.): CMSB 2017, LNBI 10545, pp. 128–144, 2017.
DOI: 10.1007/978-3-319-67471-1 8