Marginal Inferential Models: Prior-Free Probabilistic Inference on Interest Parameters
By Ryan Martin, Chuanhai Liu. 2013
85 citations recorded by the source corpus.
The inferential models (IM) framework provides prior-free, frequency-calibrated, and posterior probabilistic inference. The key is the use of random sets to predict unobservable auxiliary variables connected to the observable data and unknown parameters. When nuisance parameters are present, a marginalization step can reduce the dimension of the auxiliary variable which, in turn, leads to more efficient inference. For regular problems, exact marginalization can be achieved, and we give conditions for marginal IM validity. We show that our approach provides exact and efficient marginal inference in several challenging problems, including a many-normal-means problem. In nonregular problems, we propose a generalized marginalization technique and prove its validity. Details are given for two benchmark examples, namely, the Behrens–Fisher and gamma mean problems.
Subfields: Artificial Intelligence, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/71b89e247809a8c76f1546d57d85b4268158bfb0
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In Artificial Intelligence
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Citations in the corpus
- Generalized Fiducial Inference: A Review and New Results (2016, methodology): “The conditions on the limiting data-generating equation were partially inspired by results for Inferential Models of Martin and Liu (2015a).”
- An imprecise-probabilistic characterization of frequentist statistical inference (2021, methodology): “Moreover, these valid plausibility measures have the additional structure of those derived from the framework of Martin and Liu (2015b).”