  Frequentist model averaging has been proposed as a method for incorporating
"model uncertainty" into confidence interval construction. Such proposals have
been of particular interest in the environmental and ecological statistics
communities. A promising method of this type is the model averaged tail area
(MATA) confidence interval put forward by Turek and Fletcher, 2012. The
performance of this interval depends greatly on the data-based model weights on
which it is based. A computationally convenient formula for the coverage
probability of this interval is provided by Kabaila, Welsh and Abeysekera,
2016, in the simple scenario of two nested linear regression models. We
consider the more complicated scenario that there are many (32,768 in the
example considered) linear regression models obtained as follows. For each of a
specified set of components of the regression parameter vector, we either set
the component to zero or let it vary freely. We provide an easily-computed
upper bound on the minimum coverage probability of the MATA confidence
interval. This upper bound provides evidence against the use of a model weight
based on the Bayesian Information Criterion (BIC).
