Approximate Bayesian Computation - Model Comparison With ABC

Model Comparison With ABC

Besides parameter estimation, the ABC-framework can be used to compute the posterior probabilities of different candidate models. In such applications, one possibility is to use the rejection-sampling in a hierarchical manner. First, a model is sampled from the prior distribution for the models; then, given the model sampled, the model parameters are sampled from the prior distribution assigned to that model. Finally, a simulation is performed as in the single-model ABC. The relative acceptance frequencies for the different models now approximate the posterior distribution for these models. Again, computational improvements for ABC in the space of models have been proposed, such as constructing a particle filter in the joint space of models and parameters.

Once the posterior probabilities of models have been estimated, one can make full use of the techniques of Bayesian model comparison. For instance, to compare the relative plausibilities of two models and, one can compute their posterior ratio, which is related to the Bayes factor :

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If the model priors are equal, the Bayes factor equals the posterior ratio.

In practice, as discussed below, these measures can be highly sensitive to the choice of parameter prior distributions and summary statistics, and thus conclusions of model comparison should be drawn with caution.