Abstract: Sketches of an alternative family of indices, for the set of
probability measures of a statistical experiment, that allows for rigorous
numerical decision-making, even in the presence of finite precision in
measurement of the empirical phenomenon of interest, will be given. The
often overlooked "Empirical indiscernibility" of elements of the index set,
usually induced by physical limits on measurement precision, as well as, any
nonidentifiability inherent in the mathematical model itself around the optimal
decision will be rigorously accounted for, in addition to all the usual errors
associated with shadows of real computations confined to a finite screen of
floating-points embedded in the reals. Applications from phylogenetics and
finite mixture problems will be covered.
Key words: rigorous global optimization, interval analysis, automatic
differentiation, Jukes and Cantor model of DNA evolution, efficient M-H
sampling