This paper defines statistical consistency, a property that we propose as a necessary characteristic of any calculus for evidence combination. Statistical consistency holds when the combination of repeated observations of a system in a given state leads to the indication that the system is in that state of nature. We show that, for a suitable choice of parameters, Dempster's rule has this desirable property, both for simple systems and for systems composed of a hierarchy of subsystems and described by diagnostic or fault trees, but for other parameter values the rule leads to the wrong conclusion. A necessary and sufficient condition for the existence of simple bpa's being statistically consistent is that p0 + 11 > 1, where p0 and q1 are the reliability (or specificity) and sensitivity of individual sensors detecting malfunctions in components and (sub)systems. A sufficient condition for statistical consistency is that the reliability and sensitivity of each sensor be greater than 0.5. We show that statistical consistency is preserved under diagnostic tree formation. © 1992.
Durham, S. D., Smolka, J. S., & Valtorta, M. (1992). Statistical consistency with Dempster’s rule on diagnostic trees having uncertain performance parameters. International Journal of Approximate Reasoning, 6(1), 67–81. https://doi.org/10.1016/0888-613X(92)90040-7