BAS version 1.1.0 introduces a truncated Beta-Binomial Prior distribution on the number of predictors included in a model, which is useful for the $p > n$ case. This corresponds to a Bernoulli prior on the inclusion indicators $\gamma_j$ with a common parameter inclusion probability $\pi$, and in turn $\pi$ is assigned a Beta prior distribution with parameters $a$ and $b$, $\pi \sim B(a,b)$. The truncated point $T$ is so that $P(\sum_j \gamma_j > T) = 0$ .

For the example, below the number of predictors is constrained to be less than or equal to 8.

The default method for sampling in “BAS” enumerates all models so that models with size > 8 have zero probability in the above example. Alternatively, we can use the method=”MCMC” to avoid sampling models with prior probability 0.