  Consider the setting where there are B>1 candidate statistical models, and
one is interested in model selection. Two common approaches to solve this
problem are to select a single model or to combine the candidate models through
model averaging. Instead, we select a subset of the combined parameter space
associated with the models. Specifically, a model averaging perspective is used
to increase the parameter space, and a model selection criterion is used to
select a subset of this expanded parameter space. We account for the
variability of the criterion by adapting Yekutieli (2012)'s method to Bayesian
model averaging (BMA). Yekutieli (2012)'s method treats model selection as a
truncation problem. We truncate the joint support of the data and the parameter
space to only include small values of the covariance penalized error (CPE)
criterion. The CPE is a general expression that contains several information
criteria as special cases. Simulation results show that as long as the
truncated set does not have near zero probability, we tend to obtain lower mean
squared error than BMA. Additional theoretical results are provided that
provide the foundation for these observations. We apply our approach to a
dataset consisting of American Community Survey (ACS) period estimates to
illustrate that this perspective can lead to improvements of a single model.
