Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems

By Tina Toni, David Welch, Natalja Strelkowa, Andreas Ipsen, M. P. Stumpf. 2009

1,655 citations recorded by the source corpus.

Approximate Bayesian computation (ABC) methods can be used to evaluate posterior distributions without having to calculate likelihoods. In this paper, we discuss and apply an ABC method based on sequential Monte Carlo (SMC) to estimate parameters of dynamical models. We show that ABC SMC provides information about the inferability of parameters and model sensitivity to changes in parameters, and tends to perform better than other ABC approaches. The algorithm is applied to several well-known biological systems, for which parameters and their credible intervals are inferred. Moreover, we develop ABC SMC as a tool for model selection; given a range of different mathematical descriptions, ABC SMC is able to choose the best model using the standard Bayesian model selection apparatus.

Subfields: Artificial Intelligence, Spectroscopy, Statistics and Probability

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Citations in the corpus

Generalization in anti-causal learning (2018, methodology): “Simulation of an (approximately) known causal model also lies at the heart of ABC (Rubin et al., 1984), a method for likelihood-free Bayesian inference of the posterior that has proven potent in many areas, see (Beaumont et al., 2002; Toni et al., 2009; Beaumont, 2010).”
Venture: a higher-order probabilistic programming platform with programmable inference (2014, background): “…recognition (Baker, 1979), information extraction (Pasula et al., 2002), multitarget tracking and sensor fusion (Oh et al., 2009; Arora et al., 2010), ecology (Csilléry et al., 2010) and computational biology (Friedman et al., 2000; Yu et al., 2004; Toni et al., 2009; Dowell and Eddy, 2004).”
Likelihood-free MCMC with Amortized Approximate Ratio Estimators (2019, background): “Several procedures have been proposed to improve the acceptance rate by guiding simulations based on previously accepted states (Toni et al., 2008; Marjoram et al., 2003; Wegmann et al., 2009).”
The Controlled Thermodynamic Integral for Bayesian Model Comparison (2014, methodology): “Here too numerous methods have been proposed, including importance sampling (Gelman and Meng, 1998; Chen et al., 2000), ratio importance sampling (Torrie and Valleau, 1977), bridge sampling (Gelman and Meng, 1998; Chen et al., 2000), sequential Monte Carlo (Zhou et al., 2013), annealed importance…”
Approximate Bayesian Computation (2019, background): “Toni et al. , J.Roy.Soc. Interface (2009); Toni & Stumpf, Bioinformatics (2010).”
Approximate Bayesian Computation in Evolution and Ecology (2010, methodology): “Within ecology there have been relatively few applications of ABC methods, although Toni et al. (2009) give an example using a Lotka-Volterra system with time series data on abundances.”
GPS-ABC: Gaussian Process Surrogate Approximate Bayesian Computation (2014, methodology): “Besides the marginal and pseudo-marginal approaches to ABC, there is a large body of work using sequential Monte Carlo sampling to approach this problem [21, 4, 26].”
Likelihood-free Markov chain Monte Carlo (2010, methodology): “, 2007), susceptible-infected-removed (SIR) models (Toni et al., 2009), pathogen transmission (Tanaka et al.”
Automated adaptive inference of phenomenological dynamical models (2015, neutral): “Approaches have been developed using linear dynamic models [10], Bayesian Networks (see Supplementary Information (SI)), recurrent neural networks [11], evolved regulatory networks [12], and symbolic regression [13, 14].”
Bayesian computation: a summary of the current state, and samples backwards and forwards (2015, methodology): “…hypotheses and selecting models, the Bayesian approach relies on modelling hypotheses and model indices as part of the parameter and hence ABC naturally operates as this level as well, as demonstrated in Algorithm 4 following Cornuet et al. (2008), Grelaud et al. (2009) and Toni et al. (2009).”
Dynamic Likelihood-free Inference via Ratio Estimation (DIRE) (2018, methodology): “The manual summary statistics were the x ( t ) 1 and x ( t ) 2 as in previous work where ABC was used for inference (e.g. Toni et al. 2009).”
Parameter Estimation and Model Selection in Computational Biology (2010, methodology): “The repressilator is a synthetic gene regulatory network, whose model is frequently used as an example for numerical algorithms [10,27].”
Identifying Causal Structure in Large-Scale Kinetic Systems (2018, methodology): “mple, combine sparsity regularization with a model selection step based on the information criteria AIC and BIC. Common alternatives are based on approximate Bayesian computation or likelihood ratio [Toni et al., 2009, Vyshemirsky and Girolami, 2007]. Procedures using a Gaussian process prior on the”
Lack of confidence in approximate Bayesian computation model choice (2011, methodology): “• ABC-SysBio, which relies on a sequential Monte Carlo (SMC)based ABC for inference in system biology, including model choice (26).”
Reliable ABC model choice via random forests (2014, methodology): “…1999; Tavaré et al., 1997), the method has found an ever increasing range of applications covering diverse types of complex models in various scientific fields (see, e.g. Arenas et al., 2015; Beaumont, 2008, 2010; Chan et al., 2014; Csillèry et al., 2010; Theunert et al., 2012; Toni et al., 2009).”
Bayesian Optimization for Likelihood-Free Inference of Simulator-Based Statistical Models (2015, methodology): “Related sequential Monte Carlo (SMC) ABC algorithms were proposed by Sisson et al. (2007); Toni et al. (2009).”