Lack of confidence in approximate Bayesian computation model choice

By Christian P. Robert, Jean-Marie Cornuet, Jean-Michel Marin, Natesh S. Pillai. 2011

330 citations recorded by the source corpus.

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): “The key quantity arising from this framework is an easily computable notion of distance between proba- 2This information leak is particularly severe in the context of model selection as described in Robert et al. (2011). bility measures, termed Maximum Mean Discrepancy (MMD).”
Bayesian computation: a summary of the current state, and samples backwards and forwards (2015, background): “This imposed reduction of the statistical information raises many relevant questions, from the choice of summary statistics (Blum et al. 2013) to the consistency of the ensuing inference (Robert et al. 2011).”
Approximate Bayesian computational methods (2011, methodology): “As exposed in Robert et al. (2011), most settings where ABC model choice is implemented do not allow for inter-model sufﬁciency in the selection of the summary statistics, because some models are not within exponential families and because using the whole data is too demanding.”
Representing the acquisition and use of energy by individuals in agent‐based models of animal populations (2013, methodology): “2011); though, implementationmay not be without problems (Robert et al. 2011).”
Complex patterns of global spread in invasive insects: eco-evolutionary and management consequences (2016, background): “There have also been some criticisms of ABC approaches on theoretical grounds that should be considered when using or interpreting these data (Robert et al. 2011).”
Approximate Bayesian computation via regression density estimation (2012, background): “Readers should refer to Blum et al. (2012), Fearnhead and Prangle (2012) and Robert et al. (2011) for further discussion of the use and elicitation of summary statistics in ABC.”
Approximate Bayesian Computation (2013, background): “…[12]: Thus, a summary statistic S ( D ) is sufficient for comparing two models M 1 and M 2 if and only if: It is also clear from the equation above that there might be a huge difference between B 1,2 and B s 1,2 if the condition is not satisfied, as can be demonstrated by toy examples [12,16,18].”
Reliable ABC model choice via random forests (2014, methodology): “…Prangle et al. (2014) show that the Bayes factor itself is an acceptable summary (of dimension one) when comparing two models, but its practical evaluation via a pilot ABC simulation induces a poor approximation 860 P.Pudlo et al. of model evidences (Didelot et al., 2011; Robert et al., 2011).”
The expected demise of the Bayes factor (2015, background): “In a recent work about the validation of ABC model selection (Robert et al., 2011; Marin et al., 2014), we also pointed out the variability of the numerical estimates and in fine the utter dependence of both posterior probabilities and Bayes factors on conditioning statistics, which in turn…”