Model Ensembles: BMC and BMA

In this chapter, we discuss how multiple ‘competing’ models can be used simultaneously. There are advantages to having more than one model, as was already recognised by Chamberlin in the nineteenth century (Chamberlin, Sci 15:92–96, 1890). His still highly readable and important essay on ’The method of multiple working hypotheses’ warned scientists against ’parental affection for a favourite theory’. He worried that inevitable bias in favour of one’s own ideas would lead to ’unconscious pressing of the theory to make it fit the facts, and a pressing of the facts to make them fit the theory’. And that is—or should be—a legitimate concern for modellers nowadays as well. Moreover, different models can have complementary strengths, and we often have no clear idea which of the available models is the best for a given research question. So how can Bayesian thinking help with these issues? Well, as you will expect, the proper Bayesian approach is to quantify our uncertainty about model structure. One way to do that is by following Chamberlin’s advice to use multiple models.