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 :
- .
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.
Read more about this topic: Approximate Bayesian Computation
Famous quotes containing the words model and/or comparison:
“... if we look around us in social life and note down who are the faithful wives, the most patient and careful mothers, the most exemplary housekeepers, the model sisters, the wisest philanthropists, and the women of the most social influence, we will have to admit that most frequently they are women of cultivated minds, without which even warm hearts and good intentions are but partial influences.”
—Mrs. H. O. Ward (1824–1899)
“It is comparison than makes people miserable.”
—Chinese proverb.