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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2024
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2401.06177 |
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| _version_ | 1866913193115254784 |
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| author | Lauritzen, Steffen |
| author_facet | Lauritzen, Steffen |
| contents | This note establishes that if a sequence $P_n, n=1,\ldots$ of probability measures converges in total variation to the limiting probability measure $P$, and $σ$-algebras $\mathbb{A}$ and $\mathbb{B}$ are conditionally independent given $\mathbb{H}$ with respect to $P_n$ for all $n$, then they are also conditionally independent with respect to the limiting measure $P$. As a corollary, this also extends to pointwise convergence of densities to a density. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06177 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Total Variation Convergence Preserves Conditional Independence Lauritzen, Steffen Probability This note establishes that if a sequence $P_n, n=1,\ldots$ of probability measures converges in total variation to the limiting probability measure $P$, and $σ$-algebras $\mathbb{A}$ and $\mathbb{B}$ are conditionally independent given $\mathbb{H}$ with respect to $P_n$ for all $n$, then they are also conditionally independent with respect to the limiting measure $P$. As a corollary, this also extends to pointwise convergence of densities to a density. |
| title | Total Variation Convergence Preserves Conditional Independence |
| topic | Probability |
| url | https://arxiv.org/abs/2401.06177 |