📝 SummarXiv

Abstract

Consider the sequential inference of a binary outcome. The process of a posteriori beliefs and its objectively true conditional-probability counterpart generally differ but should lead to the same result eventually in well-defined tests. We show that unless the two are 'essentially identical', differing only by an a priori factor, time-homogeneous continuous decisions based on the former must be path-dependent with respect to state-variables based on the latter or any non-essentially-identical process. Inferential errors decompose into path-dependent and path-independent parts, whose distinct properties are relevant to error mitigation.