PROTEST: Nonparametric Testing of Hypotheses Enhanced by Experts' Utility Judgements
arxiv(2024)
摘要
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.
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