#### Robust Bayesian Analysis of Selection Models

M. J. Bayarri and James O. Berger

Selection models arise when the data is selected to enter the
sample only if it occurs in a certain region of the sample
space. When this selection occurs according to some probability
distribution, the resulting model is often instead called a
weighted distribution model. In either case the ``original''
density becomes multiplied by a ``weight function'' $w(x)$. Often
there is considerable uncertainty concerning this weight
function; for instance, it may only be known that $w$ lies
between two specified weight functions. We consider robust
Bayesian analysis for this situation, finding the range of
posterior quantities of interest, such as the posterior mean or
posterior probability of a set, as $w$ ranges over the class of
weight functions. The variational analysis utilizes concepts from
variation diminishing transformations.
PDF File