# What is the connection between Bayesian Model Averaging and SSVS?

What exactly is the difference between Bayesian Model Averaging (BMA) and the Stochastic Search Variable Selection (SSVS) prior when we talk about linear regression models?

The SSVS prior is used for variable selection, which is conceptually different from model averaging, right? However, both result in coefficient estimates and posterior inclusion probabilities and are often mentioned together in literature (see for instance the article on BMA linked above).

Can anyone provide more systematic insights regarding the relationship of SSVS and BMA? Where do they differ? Where are similarities to be found? Do they generally give similar results? Is the model space they explore the same?

Thanks!

SSVS samples from the higher dimensional posterior of all parameters and models. You don’t need to sample models to do BMA, though—you can fit each of the many models separately, and then use their marginal likelihoods to compute a quantity you’re interested in. The authors of the SSVS paper explain that estimating all $$2^p$$ regression models isn’t feasible for a large number of possible predictors $$p$$, and so sampling is preferable.