Instead of testing solely a precise hypothesis, it is often useful to enlarge it with alternatives that are deemed to differ from it negligibly. For instance, in a bioequivalence study one might consider the hypothesis that the concentration of an ingredient is exactly the same in two drugs. In such a context, it might be more relevant to test the enlarged hypothesis that the difference in concentration between the drugs is of no practical significance. While this concept is not alien to Bayesian statistics, applications remain confined to parametric settings and strategies on how to effectively harness experts' intuitions are often scarce or nonexistent. To resolve both issues, we introduce PROTEST, an accessible nonparametric testing framework that seamlessly integrates with Markov Chain Monte Carlo (MCMC) methods. We develop expanded versions of the model adherence, goodness-of-fit, quantile and two-sample tests. To demonstrate how PROTEST operates, we make use of examples, simulated studies - such as testing link functions in a binary regression setting, as well as a comparison between the performance of PROTEST and the PTtest (Holmes et al., 2015) - and an application with data on neuron spikes. Furthermore, we address the crucial issue of selecting the threshold - which controls how much a hypothesis is to be expanded - even when intuitions are limited or challenging to quantify.

翻译：摘要：在假设检验中，除了检验精确假设外，通常更有效的方法是将其扩展为包含那些被认为可忽略差异的备择假设。例如，在生物等效性研究中，可考虑两种药物中某成分浓度完全相同的假设。在此背景下，检验"药物间浓度差异无实际显著性"这一扩展假设往往更具现实意义。尽管该概念在贝叶斯统计中并不陌生，但其应用仍局限于参数化框架，且有效利用专家直觉的策略往往匮乏甚至不存在。为解决这两个问题，我们提出PROTEST——一种与非参数检验框架兼容性强、可无缝衔接马尔可夫链蒙特卡洛（MCMC）方法的简易框架。我们开发了模型符合度检验、拟合优度检验、分位数检验和双样本检验的扩展版本。通过示例分析、模拟研究（如二元回归中链接函数的检验、PROTEST与PTtest法（Holmes等，2015）的性能对比）以及神经元脉冲数据的应用案例，我们展示了PROTEST的操作流程。此外，我们重点探讨了阈值选择这一关键问题——该参数控制假设的扩展程度，即使在直觉信息有限或难以量化的情况下仍可有效实施。