In this article, we discuss problems with probability theory in representing uncertainties encountered in the "real world" and show how belief functions can overcome these difficulties. Also, we discuss an expected utility approach of decision making under ambiguity using the belief function framework. In particular, we develop a proposition for decision making under ambiguity using the expecte...

Consider the following choice problem, known as “Ellsberg’s three-color urn example”, or simply the “Ellsberg Paradox” (Ellsberg [7]). An urn contains 30 red balls, and 60 green and blue balls, in unspecified proportions; subjects are asked to compare (i) a bet on a red draw vs. a bet on a green draw, and (ii) a bet on a red or blue draw vs. a bet on a green or blue draw. If the subject wins a ...

In his PhD thesis, Ellsberg formulated strong experimental conditions for his proposed tests of subjective expected utility theory. Subjects should have no reason to consider the motives of the urn filler. Standard incentivized experiments do not meet these conditions. Instead of a one-person decision problem, the task can be perceived as a two-player game. One player chooses among the bets. Th...

We derive Cramér–Rao bound (CRB) expressions for the range (time delay), velocity (Doppler shift), and direction of a point target using an active radar or sonar array. First, general CRB expressions are derived for a narrowband signal and array model and a space-time separable noise model that allows both spatial and temporal correlation. We discuss the relationship between the CRB and ambigui...

For a fast moving CROSS-AMBIGUITY FUNCTION Kam W. Lo and Brian G. Ferguson Defence Science and Technology Organisation P.O. Box 44 Pyrmont NSW Australia acoustic source in proximity to a pair of widely spaced sensors, the conventional cross correlation method results in poor time delay estimates because the signal received by each sensor experiences a different degree of time scaling. The corre...

We present maximum likelihood (ML) methods for active estimation of range (time delay), velocity (Doppler shift), and direction of a point target with a radar array in spatially correlated noise with unknown covariance. We consider structured and unstructured array response models and compute the Cram er-Rao bound (CRB) for the time delay, Doppler shift, and direction of arrival. We derive ambi...