Credal model averaging: Dealing robustly with model uncertainty on small data sets

Abstract

Datasets of population dynamics are typically characterized by a short temporal extension. In this condition, several alternative models typically achieve close accuracy, though returning quite different predictions (model uncertainty). Bayesian model averaging (BMA) addresses this issue by averaging the prediction of the different models, using as weights the posterior probability of the models. However, an open problem of BMA is the choice of the prior probability of the models, which can largely impact on the inferences, especially when data are scarce. We present Credal Model Averaging (CMA), which addresses this problem by simultaneously considering a set of prior probability distributions over the models. This allows to represent very weak prior knowledge about the appropriateness of the different models and also to easily accommodate expert judgments, considering that in many cases the expert is not willing to commit himself to a single prior probability distribution. The predictions generated by CMA are intervals whose lengths shows the sensitivity of the predictions on the choice of the prior over the models.