Fg. Cozman, Calculation of posterior bounds given convex sets of prior probability measures and likelihood functions, J COMPU G S, 8(4), 1999, pp. 824-838
This article presents alternatives and improvements to Lavine's algorithm,
currently the most popular method for calculation of posterior expectation
bounds induced by sets of probability measures. First, methods from probabi
listic logic and Walley's and White-Snow's algorithms are reviewed and comp
ared to Lavine's algorithm. Second, the calculation of posterior bounds is
reduced to a fractional programming problem. From the unifying perspective
of fractional programming, Lavine's algorithm is derived from Dinkelbach's
algorithm, and the White-Snow algorithm is shown to be similar to the Charn
es-Cooper transformation. From this analysis, a novel algorithm for expecta
tion bounds is derived. This algorithm provides a complete solution for the
calculation of expectation bounds from priors and likelihood functions spe
cified as convex sets of measures. This novel algorithm is then extended to
handle the situation where several independent identically distributed mea
surements are available. Examples are analyzed through a software package t
hat performs robust inferences and that is publicly available.