Validity-Preservation Properties of Rules for Combining Inferential Models

Ryan Martin, Nicholas Syring
Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, PMLR 103:286-294, 2019.

Abstract

An inferential model encodes the data analyst’s degrees of belief about an unknown quantity of interest based on the observed data, posited statistical model, etc. Inferences drawn based on these degrees of belief should be reliable in a certain sense, so we require the inferential model to be valid. The construction of valid inferential models based on individual pieces of data is relatively straightforward, but how to combine these so that the validity property is preserved? In this paper we analyze some common combination rules with respect to this question, and we conclude that the best strategy currently available is one that combines via a certain dimension reduction step before the inferential model construction.

Cite this Paper

BibTeX
@InProceedings{pmlr-v103-martin19a, title = {Validity-Preservation Properties of Rules for Combining Inferential Models}, author = {Martin, Ryan and Syring, Nicholas}, booktitle = {Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications}, pages = {286--294}, year = {2019}, editor = {De Bock, Jasper and de Campos, Cassio P. and de Cooman, Gert and Quaeghebeur, Erik and Wheeler, Gregory}, volume = {103}, series = {Proceedings of Machine Learning Research}, month = {03--06 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v103/martin19a/martin19a.pdf}, url = {https://proceedings.mlr.press/v103/martin19a.html}, abstract = {An inferential model encodes the data analyst’s degrees of belief about an unknown quantity of interest based on the observed data, posited statistical model, etc. Inferences drawn based on these degrees of belief should be reliable in a certain sense, so we require the inferential model to be valid. The construction of valid inferential models based on individual pieces of data is relatively straightforward, but how to combine these so that the validity property is preserved? In this paper we analyze some common combination rules with respect to this question, and we conclude that the best strategy currently available is one that combines via a certain dimension reduction step before the inferential model construction.} }
Endnote
%0 Conference Paper %T Validity-Preservation Properties of Rules for Combining Inferential Models %A Ryan Martin %A Nicholas Syring %B Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications %C Proceedings of Machine Learning Research %D 2019 %E Jasper De Bock %E Cassio P. de Campos %E Gert de Cooman %E Erik Quaeghebeur %E Gregory Wheeler %F pmlr-v103-martin19a %I PMLR %P 286--294 %U https://proceedings.mlr.press/v103/martin19a.html %V 103 %X An inferential model encodes the data analyst’s degrees of belief about an unknown quantity of interest based on the observed data, posited statistical model, etc. Inferences drawn based on these degrees of belief should be reliable in a certain sense, so we require the inferential model to be valid. The construction of valid inferential models based on individual pieces of data is relatively straightforward, but how to combine these so that the validity property is preserved? In this paper we analyze some common combination rules with respect to this question, and we conclude that the best strategy currently available is one that combines via a certain dimension reduction step before the inferential model construction.
APA
Martin, R. & Syring, N.. (2019). Validity-Preservation Properties of Rules for Combining Inferential Models. Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, in Proceedings of Machine Learning Research 103:286-294 Available from https://proceedings.mlr.press/v103/martin19a.html.

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