This paper derives the structure of optimal sequential decision algori
thms for inference from severely uncertain evidence. Uncertainty is re
presented with convex models of uncertainty. We formulate the decision
problem as a selection between competing hypotheses. We define the op
timality of decision in terms of the robustness of the algorithm to th
e associated uncertainties. Binary, N-ary and sequential decisions are
studied. Examples are discussed which deal with tracking an evasive t
arget, and with selecting features for pattern recognition. (C) 1998 A
cademic Press Limited.