On the value of varied evidence for imprecise probabilities

Jürgen Landes, Sébastien Destercke
Proceedings of the Fourteenth International Symposium on Imprecise Probabilities: Theories and Applications, PMLR 290:169-182, 2025.

Abstract

It has long been considered a truism that we can learn more from a variety of sources than from highly correlated sources. This truism is captured by the Variety of Evidence Thesis. To the surprise of many, this thesis turned out to fail in a number of Bayesian settings. In other words, replication can trump variation. Translating the thesis into IP we obtain two distinct, a priori plausible formulations in terms of ‘increased confirmation’ and ‘uncertainty reduction’, respectively. We investigate both formulations, which both fail for different parameters and different reasons, that cannot be predicted prior to formal analysis. The emergence of two distinct formulations distinguishing confirmation increase from uncertainty reduction, which are conflated in the Bayesian picture, highlights fundamental differences between IP and Bayesian reasoning.

Cite this Paper

BibTeX
@InProceedings{pmlr-v290-landes25a, title = {On the value of varied evidence for imprecise probabilities}, author = {Landes, J\"urgen and Destercke, S\'ebastien}, booktitle = {Proceedings of the Fourteenth International Symposium on Imprecise Probabilities: Theories and Applications}, pages = {169--182}, year = {2025}, editor = {Destercke, Sébastien and Erreygers, Alexander and Nendel, Max and Riedel, Frank and Troffaes, Matthias C. M.}, volume = {290}, series = {Proceedings of Machine Learning Research}, month = {15--18 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v290/main/assets/landes25a/landes25a.pdf}, url = {https://proceedings.mlr.press/v290/landes25a.html}, abstract = {It has long been considered a truism that we can learn more from a variety of sources than from highly correlated sources. This truism is captured by the Variety of Evidence Thesis. To the surprise of many, this thesis turned out to fail in a number of Bayesian settings. In other words, replication can trump variation. Translating the thesis into IP we obtain two distinct, a priori plausible formulations in terms of ‘increased confirmation’ and ‘uncertainty reduction’, respectively. We investigate both formulations, which both fail for different parameters and different reasons, that cannot be predicted prior to formal analysis. The emergence of two distinct formulations distinguishing confirmation increase from uncertainty reduction, which are conflated in the Bayesian picture, highlights fundamental differences between IP and Bayesian reasoning.} }
Endnote
%0 Conference Paper %T On the value of varied evidence for imprecise probabilities %A Jürgen Landes %A Sébastien Destercke %B Proceedings of the Fourteenth International Symposium on Imprecise Probabilities: Theories and Applications %C Proceedings of Machine Learning Research %D 2025 %E Sébastien Destercke %E Alexander Erreygers %E Max Nendel %E Frank Riedel %E Matthias C. M. Troffaes %F pmlr-v290-landes25a %I PMLR %P 169--182 %U https://proceedings.mlr.press/v290/landes25a.html %V 290 %X It has long been considered a truism that we can learn more from a variety of sources than from highly correlated sources. This truism is captured by the Variety of Evidence Thesis. To the surprise of many, this thesis turned out to fail in a number of Bayesian settings. In other words, replication can trump variation. Translating the thesis into IP we obtain two distinct, a priori plausible formulations in terms of ‘increased confirmation’ and ‘uncertainty reduction’, respectively. We investigate both formulations, which both fail for different parameters and different reasons, that cannot be predicted prior to formal analysis. The emergence of two distinct formulations distinguishing confirmation increase from uncertainty reduction, which are conflated in the Bayesian picture, highlights fundamental differences between IP and Bayesian reasoning.
APA
Landes, J. & Destercke, S.. (2025). On the value of varied evidence for imprecise probabilities. Proceedings of the Fourteenth International Symposium on Imprecise Probabilities: Theories and Applications, in Proceedings of Machine Learning Research 290:169-182 Available from https://proceedings.mlr.press/v290/landes25a.html.

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