# Deviance Information Criteria for Model Selection in Approximate Bayesian Computation

@article{Franois2011DevianceIC, title={Deviance Information Criteria for Model Selection in Approximate Bayesian Computation}, author={Olivier François and Guillaume Laval}, journal={Statistical Applications in Genetics and Molecular Biology}, year={2011}, volume={10} }

Approximate Bayesian computation (ABC) is a class of algorithmic methods in Bayesian inference using statistical summaries and computer simulations. ABC has become popular in evolutionary genetics and in other branches of biology. However, model selection under ABC algorithms has been a subject of intense debate during the recent years. Here, we propose novel approaches to model selection based on posterior predictive distributions and approximations of the deviance. We argue that this…

## 28 Citations

### Approximate Bayesian Computation

- Computer SciencePLoS Comput. Biol.
- 2013

Approximate Bayesian computation (ABC) constitutes a class of computational methods rooted in Bayesian statistics that widen the realm of models for which statistical inference can be considered and exacerbates the challenges of parameter estimation and model selection.

### Monte Carlo algorithms for model assessment via conflicting summaries

- Computer Science
- 2011

A measure-theoretic framework for using the ABC error towards model choice is presented and how easily existing rejection, Metropolis-Hastings and sequential importance sampling ABC algorithms are extended for the purpose of model checking is described.

### Goodness-of-fit statistics for approximate Bayesian computation

- Computer Science
- 2016

One goodness-of-fit statistic indicates a poor fit for both models, and the numerical summaries causing the poor fit were identified using posterior predictive checks.

### Model choice for phylogeographic inference using a large set of models

- BiologyMolecular ecology
- 2014

This investigation demonstrates that the determination of which models to include in ABC model choice experiments is a vital component of model‐based phylogeographic analysis.

### A rare event approach to high-dimensional approximate Bayesian computation

- Computer ScienceStat. Comput.
- 2018

This work proposes a new ABC method for high-dimensional data based on rare event methods which it refers to as RE-ABC, which uses a latent variable representation of the model to estimate the probability of the rare event that the latent variables correspond to data roughly consistent with the observations.

### A transdimensional approximate Bayesian computation using the pseudo-marginal approach for model choice

- Computer ScienceComput. Stat. Data Anal.
- 2014

### An Approximate Likelihood Perspective on ABC Methods

- Computer Science
- 2017

This article provides a unifying review, general representation, and classification of all ABC methods from the view of approximate likelihood theory, which clarifies how ABC methods can be characterized, related, combined, improved, and applied for future research.

### A Guide to General-Purpose Approximate Bayesian Computation Software

- Computer Science
- 2018

This Chapter presents general-purpose software to perform Approximate Bayesian Computation (ABC) as implemented in the R-packages abc and EasyABC and the c++ program ABCtoolbox and demonstrates how to combine ABC with Markov Chain Monte Carlo and describe a realistic population genetics application.

### Approximate Bayesian Computation (ABC) in R: A Vignette

- Computer Science
- 2012

An implementation of Approximate Bayesian Computation methods in the R language with associated example data sets in the abc.data package is provided, with a detailed example of the analysis of real data.

### abc: an R package for approximate Bayesian computation (ABC)

- Computer Science
- 2011

Approximate Bayesian computation (ABC) is devoted to complex models because it bypasses the evaluation of the likelihood function by comparing observed and simulated data.

## References

SHOWING 1-10 OF 52 REFERENCES

### Approximate Bayesian computation in population genetics.

- Computer ScienceGenetics
- 2002

A key advantage of the method is that the nuisance parameters are automatically integrated out in the simulation step, so that the large numbers of nuisance parameters that arise in population genetics problems can be handled without difficulty.

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

- Computer Science, MathematicsJournal of The Royal Society Interface
- 2008

This paper discusses and applies an ABC method based on sequential Monte Carlo (SMC) to estimate parameters of dynamical models and develops ABC SMC as a tool for model selection; given a range of different mathematical descriptions, it is able to choose the best model using the standard Bayesian model selection apparatus.

### Bayesian Computation and Model Selection Without Likelihoods

- Computer ScienceGenetics
- 2010

This work proposes a reformulation of the regression adjustment of population subdivision among western chimpanzees in terms of a general linear model (GLM), which allows the integration into the sound theoretical framework of Bayesian statistics and the use of its methods, including model selection via Bayes factors.

### Lack of confidence in ABC model choice

- Computer Science
- 2011

It is concluded that additional empirical verifications of the performances of the ABC procedure as those available in DIYABC are necessary to conduct model choice, since it depends on an unknown amount of information loss induced by the use of insufficient summary statistics.

### Inferring population history with DIY ABC: a user-friendly approach to approximate Bayesian computation

- Computer ScienceBioinform.
- 2008

Key methods used in DIY ABC, a computer program for inference based on approximate Bayesian computation (ABC), in which scenarios can be customized by the user to fit many complex situations involving any number of populations and samples, are described.

### Approximate Bayesian Computation in Evolution and Ecology

- Biology
- 2011

Although the method arose in population genetics, ABC is increasingly used in other fields, including epidemiology, systems biology, ecology, and agent-based modeling, and many of these applications are briefly described.

### Likelihood-Free Inference of Population Structure and Local Adaptation in a Bayesian Hierarchical Model

- BiologyGenetics
- 2010

A general method for applying ABC to Bayesian hierarchical models is developed and applied to detect microsatellite loci influenced by local selection, and it is demonstrated using receiver operating characteristic (ROC) analysis that this approach has comparable performance to a full-likelihood method and outperforms it when mutation rates are variable across loci.

### ABC likelihood-free methods for model choice in Gibbs random fields

- Computer Science
- 2008

This paper shows in this paper how to implement an ABC algorithm geared towards model choice in the general setting of Gibbs random fields, demonstrating in particular that there exists a sufficient statistic across models.

### Approximate Bayesian Inference Reveals Evidence for a Recent, Severe Bottleneck in a Netherlands Population of Drosophila melanogaster

- BiologyGenetics
- 2006

The results imply that it may be unnecessary to invoke frequent selective sweeps associated with the dispersal of D. melanogaster from Africa to explain patterns of variability in non-African populations.

### Approximate Bayesian computation (ABC) gives exact results under the assumption of model error

- Computer ScienceStatistical applications in genetics and molecular biology
- 2013

Under the assumption of the existence of a uniform additive model error term, ABC algorithms give exact results when sufficient summaries are used, which allows the approximation made in many previous application papers to be understood, and should guide the choice of metric and tolerance in future work.