Uncertain Evidence in Probabilistic Models and Stochastic Simulators

Andreas Munk, Alexander Mead, Frank Wood
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:25486-25500, 2023.

Abstract

We consider the problem of performing Bayesian inference in probabilistic models where observations are accompanied by uncertainty, referred to as "uncertain evidence.” We explore how to interpret uncertain evidence, and by extension the importance of proper interpretation as it pertains to inference about latent variables. We consider a recently-proposed method "distributional evidence” as well as revisit two older methods: Jeffrey’s rule and virtual evidence. We devise guidelines on how to account for uncertain evidence and we provide new insights, particularly regarding consistency. To showcase the impact of different interpretations of the same uncertain evidence, we carry out experiments in which one interpretation is defined as "correct.” We then compare inference results from each different interpretation illustrating the importance of careful consideration of uncertain evidence.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-munk23a, title = {Uncertain Evidence in Probabilistic Models and Stochastic Simulators}, author = {Munk, Andreas and Mead, Alexander and Wood, Frank}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {25486--25500}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/munk23a/munk23a.pdf}, url = {https://proceedings.mlr.press/v202/munk23a.html}, abstract = {We consider the problem of performing Bayesian inference in probabilistic models where observations are accompanied by uncertainty, referred to as "uncertain evidence.” We explore how to interpret uncertain evidence, and by extension the importance of proper interpretation as it pertains to inference about latent variables. We consider a recently-proposed method "distributional evidence” as well as revisit two older methods: Jeffrey’s rule and virtual evidence. We devise guidelines on how to account for uncertain evidence and we provide new insights, particularly regarding consistency. To showcase the impact of different interpretations of the same uncertain evidence, we carry out experiments in which one interpretation is defined as "correct.” We then compare inference results from each different interpretation illustrating the importance of careful consideration of uncertain evidence.} }
Endnote
%0 Conference Paper %T Uncertain Evidence in Probabilistic Models and Stochastic Simulators %A Andreas Munk %A Alexander Mead %A Frank Wood %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-munk23a %I PMLR %P 25486--25500 %U https://proceedings.mlr.press/v202/munk23a.html %V 202 %X We consider the problem of performing Bayesian inference in probabilistic models where observations are accompanied by uncertainty, referred to as "uncertain evidence.” We explore how to interpret uncertain evidence, and by extension the importance of proper interpretation as it pertains to inference about latent variables. We consider a recently-proposed method "distributional evidence” as well as revisit two older methods: Jeffrey’s rule and virtual evidence. We devise guidelines on how to account for uncertain evidence and we provide new insights, particularly regarding consistency. To showcase the impact of different interpretations of the same uncertain evidence, we carry out experiments in which one interpretation is defined as "correct.” We then compare inference results from each different interpretation illustrating the importance of careful consideration of uncertain evidence.
APA
Munk, A., Mead, A. & Wood, F.. (2023). Uncertain Evidence in Probabilistic Models and Stochastic Simulators. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:25486-25500 Available from https://proceedings.mlr.press/v202/munk23a.html.

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