{"ID":2896864,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.05634","arxiv_id":"2507.05634","title":"A Note on Inferential Decisions, Errors and Path-Dependency","abstract":"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.","short_abstract":"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-...","url_abs":"https://arxiv.org/abs/2507.05634","url_pdf":"https://arxiv.org/pdf/2507.05634v5","authors":"[\"Kangda K. Wren\"]","published":"2025-07-08T03:29:16Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}