Bayes factors, practical tools of applied statistics, have been dealt with extensively in the literature in the context of hypothesis testing. The Bayes factor based on parametric likelihoods can be considered both as a pure Bayesian approach as well as a standard technique to compute p-values for hypothesis testing. We employ empirical likelihood methodology to modify Bayes factor type procedures for the nonparametric setting. The paper establishes asymptotic approximations to the proposed procedures. These approximations are shown to be similar to those of the classical parametric Bayes factor approach. The proposed approach is applied towards developing testing methods involving quantiles, which are commonly used to characterize distributions. We present and evaluate one and two sample distribution free Bayes factor type methods for testing quantiles based on indicators and smooth kernel functions. An extensive Monte Carlo study and real data examples show that the developed procedures have excellent operating characteristics for one-sample and two-sample data analysis.

中文翻译：

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用于分位数比较的贝叶斯经验似然方法。

贝叶斯因素，应用统计的实用工具，已经在假设检验的背景下在文献中得到了广泛处理。基于参数似然的贝叶斯因子既可以视为纯贝叶斯方法，也可以视为计算p的标准技术。假设检验的值。我们采用经验似然方法来修改非参数设置的贝叶斯因子类型程序。本文建立了拟议程序的渐近近似。这些近似值显示与经典参数贝叶斯因子方法相似。所提出的方法适用于开发涉及分位数的测试方法，该方法通常用于表征分布。我们提出并评估一种和两种无样本分布的贝叶斯因子类型方法，用于基于指标和平滑核函数测试分位数。广泛的蒙特卡洛研究和实际数据示例表明，所开发的程序具有出色的一样品和两样品数据分析操作特性。