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Do models have probabilities or just possibilities?
Andrew says: David:I don’t think it makes sense to talk of the probability of a model. See this paper with Shalizi for much discussion of this point.
David Bickel says: If models do not have probabilities, perhaps they have possibilities in the sense of possibility theory. For example, the possibility of a model might be a function of its adequacy according to a model checking procedure: Appendix B of https://goo.gl/5s7bS3
Inference after checking the prior & sampling model
D. R. Bickel, “Inference after checking multiple Bayesian models for data conflict and applications to mitigating the influence of rejected priors,” International Journal of Approximate Reasoning 66, 53–72 (2015). Simple explanation | Published version | 2014 preprint | Slides
The proposed procedure combines Bayesian model checking with robust Bayes acts to guide inference whether or not the model is found to be inadequate:
- The first stage of the procedure checks each model within a large class of models to determine which models are in conflict with the data and which are adequate for purposes of data analysis.
- The second stage of the procedure applies distribution combination or decision rules developed for imprecise probability.
This proposed procedure is illustrated by the application of a class of hierarchical models to a simple data set.
The link Simple explanation was added on 6 June 2017.
Model fusion & multiple testing in the likelihood paradigm
D. R. Bickel, “Model fusion and multiple testing in the likelihood paradigm: Shrinkage and evidence supporting a point null hypothesis,” Working Paper, University of Ottawa, deposited in uO Research at http://hdl.handle.net/10393/31897 (2014). 2014 preprint | Supplement (link added 10 February 2015)
Errata for Theorem 4:
- The weights of evidence should not be conditional.
- Some of the equal signs should be “is a member of” signs.
Self-consistent frequentism without fiducialism
D. R. Bickel, “Self-consistent confidence sets and tests of composite hypotheses applicable to restricted parameters,” Working Paper, University of Ottawa, deposited in uO Research at http://www.ruor.uottawa.ca/handle/10393/31530 (2014). 2014 preprint
