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Semiparametric Bayesian Analysis of Selection Models

Jaeyong Lee and James O. Berger

* July 1999
*

Selection models are appropriate when a datum x enters the sample
only with probability or weight w(x).
It is typically assumed that the weight function w is monotone,
but the precise functional form of the weight function is often unknown.
In this paper, the Dirichlet process prior, centered
on a parametric form, is used as a prior distribution on the weight
function. This allows for incorporation of knowledge about the weight
function, without restricting it to be of some particular functional form.
By introducing latent variables related to the selection mechanism,
computation via Gibbs sampling can be implemented in the case where the
total number of selected and unselected observations, N, is known.
When N is unknown, a reversible jump Markov chain
sampler is needed to carry out the computations.
An important difficulty that can be
thought of as `practical nonidentifiablity' is revealed, even
for selection models in which the weight functions are theoretically
identifiable. The proposed solution to this problem depends
on the existence of prior knowledge concerning the effective range
of the weight function.

The manuscript is available in postscript
format.