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 case. This corresponds to a Bernoulli prior on the inclusion indicators with a common parameter inclusion probability , and in turn is assigned a Beta prior distribution with parameters and , . The truncated point is so that .
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.
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