Multi Model Inference for dealing with uncertainty in environmental models
This project builds on a previous SNF project titled "Credal Model Averaging for dealing with uncertainty in environmental models". On the basis of the results obtained in that project, we want to address the problem posed when several competing models reasonably intepret the data and nevertheless lead to different conclusions about the quantities of interest. This is a common problem in environmental modelling, and in those disciplines where the role of uncertainty is most relevant.
Mathematical models are inherently approximate descriptions of the reality. Such an inherent imprecision is particularly relevant for models of the environment and of natural processes. In many environmental models uncertainty is overly epistemic, that is, due to the lack of knowledge on certain processes and mechanisms. As epistemic uncertainty becomes more relevant, alternative model formulations can be proposed for describing the same process. In presence of alternative model formulations the problem of model selection arises. Typical criteria for model selection are based on scores provided by BIC (Bayesian Information Criterion) or AIC (Akaike Information Criterion). Often the "winning" model is selected for future use, thus disregarding alternative yet plausible models. Alternatively, model averaging considers several models at the same time, weighting each model proportionally to the support it receives from the data. Model averaging can be thought as a soft model selection: the investigator weighs the model according to how likely they are, without sharply selecting a single candidate. Using model averaging rather than a single model corresponds to ask the opinion of a committee of experts rather than that of a single expert, which is common wisdom when taking critical decisions. A critique of model averaging lies in the strong dependency of the conclusions on the prior probability of the models, especially when the data are scarce. This projects continues a previous SNF funded project aimed at the development of a credal model averaging framework (CMA) to address the problem of the choice of the prior over the models in BMA, by adopting a set of prior distributions over the models. Technically, CMA will constitute an extension of BMA to imprecise probabilities. The prior credal set will express very weak beliefs about the relative credibility a priori of the different models. As a result of the prior credal set, CMA will estimate the posterior probability of each model as belonging to an interval. Moreover, CMA will return predictions in the form of an interval, unlike traditional regressors which return point-wise predictions. In particular, the inferences produces by CMA will encompass those produced by model averaging using both AIC and BIC.