10.5 Summary

In this chapter, we introduced Bayesian model averaging (BMA) in generalized linear models. For linear Gaussian models, we perform BMA using three approaches: the Bayesian Information Criterion (BIC) approximation with Occam’s window, the Markov Chain Monte Carlo Model Composition (MC3) algorithm, and conditional Bayes factors, which account for endogeneity. Additionally, we show how to perform dynamic Bayesian model averaging in state-space models, where forgetting parameters are used to facilitate computation. For other generalized linear models, such as logit, gamma, and Poisson, we demonstrate how to use the BIC approximation to perform BMA. Finally, we present alternative methods for calculating the marginal likelihood: the Savage-Dickey density ratio, Chib’s method, and the Gelfand-Dey method. These methods are particularly useful when the BIC approximation does not perform well due to small or moderate sample sizes.