Bayesian model averaging

In the previous chapters, we have seen various types of Bayesian model selection criteria to select the best model among a set of candidate models M1, ...,Mr. However, it is known that this approach ignores the uncertainty in model selection. To treat the model uncertainty, Bayesian model averaging (BMA) provides a coherent mechanism. The idea of BMA was developed by Leamer (1978), and has recently received a lot of attention in the literature, including Madigan and Raftery (1994), Raftery et al. (1997), Hoeting et al. (1999), Fernandez et al. (2001), Clyde and George (2004), Viallefont et al. (2001), Wasserman (2000), Wright (2008). This chapter describes the definition and practical implementations of BMA and related model averaging approaches.