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A METHOD FOR TESTING NESTED POINT NULL

HYPOTHESES USING MULTIPLE BAYES FACTOR

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HEA-JUNG KIM

*Department of Statistics, Dongguk University, Seoul 100-715, Korea*
(Received January 17, 1997; revised February 27, 1998)

**Abstract.** As a flexible Bayesian test criterion
for nested point null hypotheses, asymmetric and multiple
Bayes factors are introduced in the form of a modified
Savage-Dickey density ratio. This leads to a simple method
for obtaining pairwise comparisons of hypotheses in a
statistical experiment with a partition on the parameter
space. The method is derived from the fact that in general,
the asymmetric Bayes factor can be written as the product of
the Savage-Dickey ratio and a correction factor where both
terms are easily estimated by means of posterior simulation.
Analyses of a censored data problem and a serial correlation
problem are illustrated for the method. For these cases, the
method is straightforward for specifying distributionally and
to implement computationally, with output readily adapted for
required tests.

*Key words and phrases*:
Asymmetric and multiple
Bayes factors, Savage-Dickey density ratio, Gibbs sampler,
point null hypothesis, censored data, serial correlation.

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