Inferring Evidence from Nested Sampling Data via Information Field Theory
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866916495455420416 |
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| author | Westerkamp, Margret Roth, Jakob Frank, Philipp Handley, Will Enßlin, Torsten |
| author_facet | Westerkamp, Margret Roth, Jakob Frank, Philipp Handley, Will Enßlin, Torsten |
| contents | Nested sampling provides an estimate of the evidence of a Bayesian inference problem via probing the likelihood as a function of the enclosed prior volume. However, the lack of precise values of the enclosed prior mass of the samples introduces probing noise, which can hamper high-accuracy determinations of the evidence values as estimated from the likelihood-prior-volume function. We introduce an approach based on information field theory, a framework for non-parametric function reconstruction from data, that infers the likelihood-prior-volume function by exploiting its smoothness and thereby aims to improve the evidence calculation. Our method provides posterior samples of the likelihood-prior-volume function that translate into a quantification of the remaining sampling noise for the evidence estimate, or for any other quantity derived from the likelihood-prior-volume function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_11907 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Inferring Evidence from Nested Sampling Data via Information Field Theory Westerkamp, Margret Roth, Jakob Frank, Philipp Handley, Will Enßlin, Torsten Computational Physics Nested sampling provides an estimate of the evidence of a Bayesian inference problem via probing the likelihood as a function of the enclosed prior volume. However, the lack of precise values of the enclosed prior mass of the samples introduces probing noise, which can hamper high-accuracy determinations of the evidence values as estimated from the likelihood-prior-volume function. We introduce an approach based on information field theory, a framework for non-parametric function reconstruction from data, that infers the likelihood-prior-volume function by exploiting its smoothness and thereby aims to improve the evidence calculation. Our method provides posterior samples of the likelihood-prior-volume function that translate into a quantification of the remaining sampling noise for the evidence estimate, or for any other quantity derived from the likelihood-prior-volume function. |
| title | Inferring Evidence from Nested Sampling Data via Information Field Theory |
| topic | Computational Physics |
| url | https://arxiv.org/abs/2312.11907 |