Inferential Models
نویسندگان
چکیده
Probability is a useful tool for describing uncertainty, so it is natural to strive for a system of statistical inference based on probabilities for or against various hypotheses. But existing probabilistic inference methods struggle to provide a meaningful interpretation of the probabilities across experiments in sufficient generality. In this paper we further develop a promising new approach based on what are called inferential models (IMs). The fundamental idea behind IMs is that there is an unobservable auxiliary variable that itself describes the inherent uncertainty about the parameter of interest, and that posterior probabilistic inference can be accomplished by predicting this unobserved quantity. We describe a simple and intuitive threestep construction of a random set of candidate parameter values, each being consistent with the model, the observed data, and a auxiliary variable prediction. Then prior-free posterior summaries of the available statistical evidence for and against a hypothesis of interest are obtained by calculating the probability that this random set falls completely in and completely out of the hypothesis, respectively. We prove that these IM-based measures of evidence are calibrated in a frequentist sense, showing that IMs give easily-interpretable results both within and across experiments.
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