2000 character limit reached
Fusing independent inferential models in a black-box manner (2405.07173v1)
Published 12 May 2024 in math.ST and stat.TH
Abstract: Inferential models (IMs) represent a novel possibilistic approach for achieving provably valid statistical inference. This paper introduces a general framework for fusing independent IMs in a "black-box" manner, requiring no knowledge of the original IMs construction details. The underlying logic of this framework mirrors that of the IMs approach. First, a fusing function for the initial IMs' possibility contours is selected. Given the possible lack of guarantee regarding the calibration of this function for valid inferences, a "validification" step is performed. Subsequently, a straightforward normalization step is executed to ensure that the final output conforms to a possibility contour.
- Valid inferential models for prediction in supervised learning problems. International Journal of Approximate Reasoning, 150:1–18.
- Cousins, R. D. (2008). Annotated bibliography of some papers on combining significances or p-values. arXiv:0705.2209.
- The basic principles of uncertain information fusion. An organised review of merging rules in different representation frameworks. Information Fusion, 32:12–39.
- Representation and combination of uncertainty with belief functions and possibility measures. Computational Intelligence, 4(3):244–264.
- Possibility theory in information fusion. In Della Riccia, G., Lenz, H.-J., and Kruse, R., editors, Data Fusion and Perception, pages 53–76, Vienna. Springer Vienna.
- Merging fuzzy information. In Bezdek, J. C., Dubois, D., and Prade, H., editors, Fuzzy Sets in Approximate Reasoning and Information Systems, pages 335–401, Boston, MA. Springer US.
- Fisher, R. A. (1932). Statistical Methods for Research Workers. 4th ed. Oliver and Boyd, Edinburgh.
- Martin, R. (2021). An imprecise-probabilistic characterization of frequentist statistical inference. arXiv:2112.10904.
- Martin, R. (2022a). Valid and efficient imprecise-probabilistic inference with partial priors, i. first results. arXiv:2203.06703.
- Martin, R. (2022b). Valid and efficient imprecise-probabilistic inference with partial priors, ii. general framework. arXiv:2211.14567.
- Inferential Models: Reasoning with Uncertainty. Monographs in Statistics and Applied Probability Series. Chapman & Hall/CRC Press.
- Validity-preservation properties of rules for combining inferential models. In De Bock, J., de Campos, C. P., de Cooman, G., Quaeghebeur, E., and Wheeler, G., editors, Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, volume 103 of Proceedings of Machine Learning Research, pages 286–294. PMLR.
- Oosterhoff, J. (1976). Combination of one-sided statistical tests. MC Tracts.
- Owen, A. B. (2009). Karl pearson’s meta-analysis revisited. The Annals of Statistics, 37(6B):3867–3892.