Abstract:
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We show that the prior densities, which assign positive probability around null function in nonparametric Bayesian test, provide exponential accumulation of evidence in favor of alternative hypothesis under a true alternative, but only a polynomical rate of accumulation in favor of null hypothesis under true null. This imbalanced behavior of Bayes factor thus prevents the resulting tests from obtaining strong evidence in favor of a null hypothesis even when a moderate size of samples is available. We propose two new classes of alternative prior densities that ameliorate the asymmetry in the asymptotic rate of Bayes factor. Using the proposed priors, we provide some examples that are applied to hypothesis tests for the nonparametric regression model and the varying coefficient model.
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