Consider a stationary precise hidden Markov model (HMM) with n hidden states Xk, taking values xk in a set {1, . . . ,m} and n observations Ok, taking values ok. Both the marginal model pX1(x1), the emission models pOk|Xk(ok|xk) and the transition models pXk|Xk−1(xk|xk−1) are unknown. We can then use the Baum–Welch algorithm [see, e.g., 4] to get a maximum-likelihood estimate of these models. T...

We do a thorough mathematical study of the notion of full conglomerability, that is, conglomerability with respect to all the partitions of an infinite possibility space, in the sense considered by Peter Walley [1991]. We consider both the cases of precise and imprecise probability (sets of probabilities). We establish relations between conglomerability and countable additivity, continuity, sup...

Rather than having precise preferences consistent with a single utility function over commodity bundles, individuals are assumed to have imprecise preferences with a set of possible utility functions, one of which is the true one. When attention is devoted to the task the set of utility functions contracts, making preferences more precise. This increases the individual’s willingness to pay for ...

The main aim of the paper is to define what the imprecise reliability is, what problems can be solved by means of a framework of the imprecise reliability. From this point of view, various branches of reliability analysis are considered, including analysis of monotone systems, repairable systems, multistate systems, structural reliability, software reliability, human reliability, fault tree ana...

We generalise the optimisation technique of dynamic programming for discretetime systems with an uncertain gain function. We assume that uncertainty about the gain function is described by an imprecise probability model, which generalises the well-known Bayesian, or precise, models. We compare various optimality criteria that can be associated with such a model, and which coincide in the precis...

We generalise the optimisation technique of dynamic programming for discretetime systems with an uncertain gain function. We assume that uncertainty about the gain function is described by an imprecise probability model, which generalises the well-known Bayesian, or precise, models. We compare various optimality criteria that can be associated with such a model, and which coincide in the precis...

A traditional theory of uncertainty says that beliefs come in degrees. Degrees of belief (“credences”) have real number values between  and , where  conventionally represents certain belief,  represents certain disbelief, and values in between represent degrees of uncertainty. We have elegant, well-understood normative theories for credences: norms for how credences should hang together at ...

Let P be a polygonal curve in R of length n, and S be a point set of size k. The Curve/Point Set Matching problem consists of finding a polygonal curve Q on S such that the Fréchet distance from P is less than a given ε. We consider eight variations of the problem based on the distance metric used and the omittability and repeatability of the points. We provide closure to a recent series of com...