ABC methods for model choice in Gibbs random fields

We have resubmitted to Bayesian Analysis a revised version of our paper ” ABC methods for model choice in Gibbs random fields” available on arXiv. The only major change is the addition of a second protein example in the biophysical illustration. The core idea in this paper is that, for Gibbs random fields and in particular for Ising models, when comparing several neighbourhood structures, the computation of the posterior probabilities of the models/structures under competition can be operated by likelihood-free simulation techniques akin to the Approximate Bayesian Computation (ABC) algorithm often discussed here. The point for this resolution is that, due to the specific structure of Gibbs random field distributions, there exists a sufficient statistic across models which allows for an exact (rather than Approximate) simulation from the posterior probabilities of the models. Obviously, when the structures grow more complex, it becomes necessary to introduce a true ABC step with a tolerance threshold$\mathbf{\epsilon}$in order to avoid running the algorithm for too long. Our toy example shows that the accuracy of the approximation of the Bayes factor can be greatly improved by resorting to the original ABC approach, since it allows for the inclusion of many more simulations. In the biophysical application to the choice of a folding structure for two proteins, we also demonstrate that we can implement the ABC solution on realistic datasets and, in the examples processed there, that the Bayes factors allow for a ranking more standard methods (FROST, TM-score) do not.

5 Responses to “ABC methods for model choice in Gibbs random fields”

1. […] but instead the editor asks for a revision clarifying our message and the difference with the Bayesian Analysis paper. This revision should thus be manageable, even though the most negative reviewer considers that ABC […]

2. […] the overwhelming majority of them are not exponential families, with the notable exception of Gibbs random fields where the above agreement graph is derived). There is therefore a strict loss of information in […]

3. […] is highly costly, as in Ising models. However, replacing exact simulation as we did in the model choice paper with a Gibbs sampler cannot be that […]

4. […] while teaching at both Dauphine and ENSAE, which made for a rather diverse environment. Besides the ABC paper for model choice we wrote together, she wrote a very good synthesis on the current state of ABC […]

5. […] while teaching at both Dauphine and ENSAE, which made for a rather diverse environment. Besides the ABC paper for model choice we wrote together, she wrote a very good synthesis on the current state of ABC […]