Intrinsic test of independence in contingency tables
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A condition needed for testing nested hypotheses from a Bayesian
viewpoint is that the prior for the alternative model concentrates
mass around the small, or null, model. For testing independence
in contingency tables, the intrinsic priors satisfy this requirement.
Further, the degree of concentration of the priors is controlled by
a discrete parameter m, the training sample size, which plays an
important role in the resulting answer regardless of the sample
size.
In this paper we study robustness of the tests of independence
in contingency tables with respect to the intrinsic priors with
different degree of concentration around the null, and compare
with other “robust” results by Good and Crook. Consistency of
the intrinsic Bayesian tests is established.
We also discuss conditioning issues and sampling schemes,
and argue that conditioning should be on either one margin or
the table total, but not on both margins.
Examples using real are simulated data are given
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