Some Bounds for Conditional Lower Previsions
نویسندگان
چکیده
In this paper we consider some bounds for lower previsions that are either coherent or centered convex. As for coherent conditional previsions, we adopt a structure-free version of Williams’ coherence, which we compare with Williams’ original version and with other coherence concepts. We then focus on bounds concerning the classical product and Bayes’ rules. After discussing some implications of product rule bounds, we generalise a well-known lower bound, which is a (weak) version for coherent lower probabilities of Bayes’ theorem, to the case of (centered) convex previsions. We obtain a family of bounds and show that one of them is undominated in all cases.
منابع مشابه
Envelope Theorems and Dilation with Convex Conditional Previsions
This paper focuses on establishing envelope theorems for convex conditional lower previsions, a recently investigated class of imprecise previsions larger than coherent imprecise conditional previsions. It is in particular discussed how the various theorems can be employed in assessing convex previsions. We also consider the problem of dilation for these kinds of imprecise previsions, and point...
متن کاملNatural extension as a limit of regular extensions
This paper is devoted to the extension of conditional assessments that satisfy some consistency criteria, such as weak or strong coherence, to further domains. In particular, we characterise the natural extension of a number of conditional lower previsions on finite spaces, by showing that it can be calculated as the limit of a sequence of conditional lower previsions defined by regular extensi...
متن کاملCoherent Upper Conditional Previsions Defined by Hausdorff Outer Measures to Forecast in Chaotic Dynamical Systems
Coherent conditional previsions and probabilities are tools to model and quantify uncertainties; they have been investigated in de Finetti [3], [4], Dubins [10] Regazzini [13], [14] and Williams [20]. Separately coherent upper and lower conditional previsions have been introduced in Walley [18], [19] and models of upper and lower conditional previsions have been analysed in Vicig et al. [17] an...
متن کاملMarginal extension in the theory of coherent lower previsions
We generalise Walley’s Marginal Extension Theorem to the case of any finite number of conditional lower previsions. Unlike the procedure of natural extension, our marginal extension always provides the smallest (most conservative) coherent extensions. We show that they can also be calculated as lower envelopes of marginal extensions of conditional linear (precise) previsions. Finally, we use ou...
متن کاملCoherent updating of non-additive measures
The conditions under which a 2-monotone lower prevision can be uniquely updated (in the sense of focusing) to a conditional lower prevision are determined. Then a number of particular cases are investigated: completely monotone lower previsions, for which equivalent conditions in terms of the focal elements of the associated belief function are established; random sets, for which some condition...
متن کامل