A Novel Approach for Choosing Summary Statistics in Approximate Bayesian Computation

By S. Aeschbacher, MARK A. Beaumont, Andreas Futschik. 2012

117 citations recorded by the source corpus.

The choice of summary statistics is a crucial step in approximate Bayesian computation (ABC). Since statistics are often not sufficient, this choice involves a trade-off between loss of information and reduction of dimensionality. The latter may increase the efficiency of ABC. Here, we propose an approach for choosing summary statistics based on boosting, a technique from the machine-learning literature. We consider different types of boosting and compare them to partial least-squares regression as an alternative. To mitigate the lack of sufficiency, we also propose an approach for choosing summary statistics locally, in the putative neighborhood of the true parameter value. We study a demographic model motivated by the reintroduction of Alpine ibex (Capra ibex) into the Swiss Alps. The parameters of interest are the mean and standard deviation across microsatellites of the scaled ancestral mutation rate (θanc = 4Neu) and the proportion of males obtaining access to matings per breeding season (ω). By simulation, we assess the properties of the posterior distribution obtained with the various methods. According to our criteria, ABC with summary statistics chosen locally via boosting with the L2-loss performs best. Applying that method to the ibex data, we estimate θ^anc≈1.288 and find that most of the variation across loci of the ancestral mutation rate u is between 7.7 × 10−4 and 3.5 × 10−3 per locus per generation. The proportion of males with access to matings is estimated as ω^≈0.21, which is in good agreement with recent independent estimates.

Subfields: Artificial Intelligence, Statistics and Probability

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Citations in the corpus

K2-ABC: Approximate Bayesian Computation with Infinite Dimensional Summary Statistics via Kernel Embeddings (2015, methodology): “Therefore, selection of the summary statistic is a crucial step in ABC to avoid an unknown loss of information2 due to the use of insufficient summary statistics (Cam, 1964; Abril, 1994; Joyce & Marjoram, 2008; Aeschbacher et al., 2012).”
Likelihood-free inference via classification (2014, methodology): “In previous work, regression with the parameters θ as response variables was used to generate summary statistics from a larger pool of candidates (Aeschbacher et al. 2012; Fearnhead and Prangle 2012; Wegmann et al. 2009).”
Reliable ABC model choice via random forests (2014, methodology): “Fearnhead and Prangle (2012); Aeschbacher et al. (2012). Given the fundamental difficulty in producing reliable tools for model choice based on summary statistics (Robert et al.”
Likelihood-Free Inference by Ratio Estimation (2016, background): “While there are several works on summary statistics selection in the framework of approximate Bayesian computation (Aeschbacher et al., 2012; Fearnhead and Prangle, 2012; Blum et al., 2013; Gutmann et al., 2014; Marin et al., 2016; Gutmann et al., 2018; Jiang et al., 2018), there is comparably littl”
ABC–CDE: Toward Approximate Bayesian Computation With Complex High-Dimensional Data and Limited Simulations (2018, background): “…integrable in L2. estimates of the entire posterior distribution f (θ |xo) rather than surrogates, such as, the regression or posterior mean E[θ |xo] (Aeschbacher, Beaumont, and Futschik 2012; Creel and Kristensen 2016; Faisal et al. 2016), and (ii) it is typically faster than most other…”
Dynamic Likelihood-free Inference via Ratio Estimation (DIRE) (2018, methodology): “In ABC, there has been considerable work on learning or selecting suitable summaries using dimensionality reduction methods and methods from regression and classiﬁcation (see e.g. Aeschbacher et al. 2012; Fearnhead and Prangle 2012; Blum et al. 2013; Gutmann et al. 2018; Jiang et al. 2018).”
Robust Demographic Inference from Genomic and SNP Data (2013, background): “…alternative to the study of complex evolutionary models, which are usually only tackled by ABC approaches [see e.g. 16,70,71], with the additional advantage of not having to choose which summary statistics to use for the inference, which is often a problem in ABC [e.g. 13,72,73,74].”
Supervised Machine Learning for Population Genetics: A New Paradigm (2018, methodology): “Interestingly, several groups have experimented with augmenting ABC by using ML for selecting the optimal combination of summary statistics [60] or even generating them [61].”