Approximating Interval hypothesis : p-values and Bayes factors

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Two-sample Bayesian Nonparametric Hypothesis Testing (2009, methodology): “Following the approach of Walker and Mallick (1999); Mallick and Walker (2003) we take common values for the αjs at each level as αj0 = αj1 = cm 2 for an α parameter at level m.”
Bayesian Goodness of Fit Testing with Mixtures of Triangular Distributions (2009, methodology): “Despite this difficulty, Rousseau (2008) has provided a general framework where assumptions A1 and A3 hold.”
On the use of non‐local prior densities in Bayesian hypothesis tests (2010, background): “Members of these classes satisfy the conditions ( ) = 0 for all 2 0, and ( ) > 0 for all 2 1. In contrast to non-local priors that are defined to be 0 on, say, an interval ( 0 ; 0 + ) for some > 0 (e.g., Verdinelli and Wasserman, 1996; Rousseau, 2007 ), the priors proposed here provide substantial ”
Rates of convergence for the posterior distributions of mixtures of betas and adaptive nonparamatric estimation of the density (2010, background): “…also useful in nonparametric density estimation, in particular they can be considered to capture small variations around a speciﬁc parametric model, as typically occurs in robust estimation or in a goodness of ﬁt test of a Parametric family or of a speciﬁc distribution, see for instance [13, 14].”