Relative Divergence and Maximum Relative Divergence Principle for Grading Functions on Partially Ordered Sets
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918154714742784 |
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| author | Dukhovny, Alexander |
| author_facet | Dukhovny, Alexander |
| contents | Relative Divergence (RD) and Maximum Relative Divergence Principle (MRDP) for grading (order-comonotonic) functions (GF) on posets are used as an expression of Insufficient Reason Principle under the given prior information (IRP+). Classic Probability Theory formulas are presented as IRP+ solutions of MRDP problems on conjoined posets. RD definition principles are analyzed in relation to the poset structure. MRDP techniques are presented for standard posets: power sets, direct products of chains, etc. "Population group-testing" and "Single server of multiple queues" applications are stated and analyzed as "IRP+ by MRDP" problems on conjoined base posets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04314 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Relative Divergence and Maximum Relative Divergence Principle for Grading Functions on Partially Ordered Sets Dukhovny, Alexander Information Theory Primary 94, Secondary 90 Relative Divergence (RD) and Maximum Relative Divergence Principle (MRDP) for grading (order-comonotonic) functions (GF) on posets are used as an expression of Insufficient Reason Principle under the given prior information (IRP+). Classic Probability Theory formulas are presented as IRP+ solutions of MRDP problems on conjoined posets. RD definition principles are analyzed in relation to the poset structure. MRDP techniques are presented for standard posets: power sets, direct products of chains, etc. "Population group-testing" and "Single server of multiple queues" applications are stated and analyzed as "IRP+ by MRDP" problems on conjoined base posets. |
| title | Relative Divergence and Maximum Relative Divergence Principle for Grading Functions on Partially Ordered Sets |
| topic | Information Theory Primary 94, Secondary 90 |
| url | https://arxiv.org/abs/2510.04314 |