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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.02777 |
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| _version_ | 1866929614683635712 |
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| author | Hess, Rowan Levine, Lionel |
| author_facet | Hess, Rowan Levine, Lionel |
| contents | Given conflicting probability estimates for a set of events, how can we quantify how much they conflict? How can we find a single probability distribution that best encapsulates the given estimates? One approach is to minimize a loss function such as binary KL-divergence that quantifies the dissimilarity between the given estimates and the candidate probability distribution. Given a set of events, we characterize the facets of the polytope of coherent probability estimates about those events. We explore two applications of these ideas: eliciting the beliefs of large language models, and merging expert forecasts into a single coherent forecast. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_02777 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | How to quantify the coherence of a set of beliefs Hess, Rowan Levine, Lionel Probability Given conflicting probability estimates for a set of events, how can we quantify how much they conflict? How can we find a single probability distribution that best encapsulates the given estimates? One approach is to minimize a loss function such as binary KL-divergence that quantifies the dissimilarity between the given estimates and the candidate probability distribution. Given a set of events, we characterize the facets of the polytope of coherent probability estimates about those events. We explore two applications of these ideas: eliciting the beliefs of large language models, and merging expert forecasts into a single coherent forecast. |
| title | How to quantify the coherence of a set of beliefs |
| topic | Probability |
| url | https://arxiv.org/abs/2412.02777 |