title: Likelihood-Free Inference in High-Dimensional Models.
abstract: Methods that bypass analytical evaluations of the likelihood function have become an indispensable tool for statistical inference in many fields of science. These so-called likelihood-free methods rely on accepting and rejecting simulations based on summary statistics, which limits them to low-dimensional models for which the value of the likelihood is large enough to result in manageable acceptance rates. To get around these issues, we introduce a novel, likelihood-free Markov chain Monte Carlo (MCMC) method combining two key innovations: updating only one parameter per iteration and accepting or rejecting this update based on subsets of statistics approximately sufficient for this parameter. This increases acceptance rates dramatically, rendering this approach suitable even for models of very high dimensionality. We further derive that for linear models, a one-dimensional combination of statistics per parameter is sufficient and can be found empirically with simulations. Finally, we demonstrate that our method readily scales to models of very high dimensionality, using toy models as well as by jointly inferring the effective population size, the distribution of fitness effects (DFE) of segregating mutations, and selection coefficients for each locus from data of a recent experiment on the evolution of drug resistance in influenza.
authors.affiliation: Department of Biology and Biochemistry, University of Fribourg, 1700 Fribourg, Switzerland Swiss Institute of Bioinformatics, 1700 Fribourg, Switzerland.
authors.forename: Athanasios
authors.initials: A
authors.lastname: Kousathanas
authors.affiliation: Department of Mathematics, University of Fribourg, 1700 Fribourg, Switzerland.
authors.forename: Christoph
authors.initials: C
authors.lastname: Leuenberger
authors.affiliation: Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge Massachusetts 02139.
authors.forename: Jonas
authors.initials: J
authors.lastname: Helfer
authors.affiliation: Department of Computational Biology, University of Lausanne, 1200 Lausanne, Switzerland.
authors.forename: Mathieu
authors.initials: M
authors.lastname: Quinodoz
authors.affiliation: International Agency for Research on Cancer, 69372 Lyon, France.
authors.forename: Matthieu
authors.initials: M
authors.lastname: Foll
authors.affiliation: Department of Biology and Biochemistry, University of Fribourg, 1700 Fribourg, Switzerland Swiss Institute of Bioinformatics, 1700 Fribourg, Switzerland daniel.wegmann@unifr.ch.
authors.forename: Daniel
authors.initials: D
authors.lastname: Wegmann
mesh_terms: D024882:Drug Resistance, Viral / Q000235:genetics*; D056084:Genetic Fitness; D056426:Genetic Loci; D008957:Models, Genetic; D009154:Mutation; D009975:Orthomyxoviridae / Q000187:drug effects / Q000235:genetics; D011336:Probability; D012641:Selection, Genetic
keywords: Markov chain Monte Carlo; approximate Bayesian computation; distribution of fitness effects; hierarchical models; high dimensions