A Note on Inferential Decisions, Errors and Path-Dependency
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912912438722560 |
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| author | Wren, Kangda K. |
| author_facet | Wren, Kangda K. |
| contents | Consider the sequential testing of binary outcomes. The a posteriori belief process and its objective conditional-probability counterpart generally differ but converge to the same result in well-defined tests. We show that unless the two processes are 'essentially identical', differing only by an a priori factor, time-homogeneous continuous decisions based on the former are path-dependent with respect to state-variables based on the latter or any other non-essentially-identical processes. Inferential error decomposes into a path-dependent and a path-independent component, whose distinct properties are relevant to error mitigation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_05634 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Note on Inferential Decisions, Errors and Path-Dependency Wren, Kangda K. Statistics Theory 62M, 60G25, 60G35, 93E10 Consider the sequential testing of binary outcomes. The a posteriori belief process and its objective conditional-probability counterpart generally differ but converge to the same result in well-defined tests. We show that unless the two processes are 'essentially identical', differing only by an a priori factor, time-homogeneous continuous decisions based on the former are path-dependent with respect to state-variables based on the latter or any other non-essentially-identical processes. Inferential error decomposes into a path-dependent and a path-independent component, whose distinct properties are relevant to error mitigation. |
| title | A Note on Inferential Decisions, Errors and Path-Dependency |
| topic | Statistics Theory 62M, 60G25, 60G35, 93E10 |
| url | https://arxiv.org/abs/2507.05634 |