Optimizing threshold-schedules for sequential approximate Bayesian computation: applications to molecular systems
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Daniel Silk
Abstract
The likelihood–free sequential Approximate Bayesian Computation (ABC) algorithms are increasingly popular inference tools for complex biological models. Such algorithms proceed by constructing a succession of probability distributions over the parameter space conditional upon the simulated data lying in an ε–ball around the observed data, for decreasing values of the threshold ε. While in theory, the distributions (starting from a suitably defined prior) will converge towards the unknown posterior as ε tends to zero, the exact sequence of thresholds can impact upon the computational efficiency and success of a particular application. In particular, we show here that the current preferred method of choosing thresholds as a pre-determined quantile of the distances between simulated and observed data from the previous population, can lead to the inferred posterior distribution being very different to the true posterior. Threshold selection thus remains an important challenge. Here we propose that the threshold–acceptance rate curve may be used to determine threshold schedules that avoid local optima, while balancing the need to minimise the threshold with computational efficiency. Furthermore, we provide an algorithm based upon the unscented transform, that enables the threshold–acceptance rate curve to be efficiently predicted in the case of deterministic and stochastic state space models.
We thank Oliver Ratmann for stimulating discussions on the use of the presented method with different ABC schemes, and we are grateful for the helpful comments received from two anonymous referees. DS is supported by BBSRC grant BB/K003909/1; SF is funded through an MRC Computational Biology Research Fellowship; MPHS is a Royal Society Wolfson Merit Award holder.
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Artikel in diesem Heft
- Masthead
- Masthead
- Research Articles
- Simultaneous inference and clustering of transcriptional dynamics in gene regulatory networks
- Markov chain Monte Carlo sampling of gene genealogies conditional on unphased SNP genotype data
- Performance and estimation of the true error rate of classification rules built with additional information. An application to a cancer trial
- Optimizing threshold-schedules for sequential approximate Bayesian computation: applications to molecular systems
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Artikel in diesem Heft
- Masthead
- Masthead
- Research Articles
- Simultaneous inference and clustering of transcriptional dynamics in gene regulatory networks
- Markov chain Monte Carlo sampling of gene genealogies conditional on unphased SNP genotype data
- Performance and estimation of the true error rate of classification rules built with additional information. An application to a cancer trial
- Optimizing threshold-schedules for sequential approximate Bayesian computation: applications to molecular systems
- Model selection for prognostic time-to-event gene signature discovery with applications in early breast cancer data
- Identifying clusters in genomics data by recursive partitioning
