Conformity and independence with coherent lower previsions
نویسندگان
چکیده
We study the conformity of marginal unconditional and conditional models with a joint model under assumptions of epistemic irrelevance and independence, within Walley’s theory of coherent lower previsions. By doing so, we make a link with a number of prominent models within this theory: the marginal extension, the irrelevant natural extension, the independent natural extension and the strong product.
منابع مشابه
A survey of the theory of coherent lower previsions
This paper presents a summary of Peter Walley’s theory of coherent lower previsions. We introduce three representations of coherent assessments: coherent lower and upper previsions, closed and convex sets of linear previsions, and sets of desirable gambles. We show also how the notion of coherence can be used to update our beliefs with new information, and a number of possibilities to model the...
متن کاملOn Coherent Variability Measures and Conditioning
Coherent upper and lower previsions are becoming more and more popular as a mathematical model for robust valuations under uncertainty. Likewise, the mathematically equivalent class of coherent risk measures is attracting a lot attention in mathematical finance. In this paper, we show that a misinterpretation of upper previsions demands a closer examination of the basis of the theory of impreci...
متن کاملCharacterizing the Set of Coherent Lower Previsions with a Finite Number of Constraints or Vertices
The standard coherence criterion for lower previsions is expressed using an infinite number of linear constraints. For lower previsions that are essentially defined on some finite set of gambles on a finite possibility space, we present a reformulation of this criterion that only uses a finite number of constraints. Any such lower prevision is coherent if it lies within the convex polytope defi...
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 کاملContinuous Linear Representation of Coherent Lower Previsions
This paper studies the possibility of representing lower previsions by continuous linear functionals. We prove the existence of a linear isomorphism between the linear space spanned by the coherent lower previsions and that of an appropriate space of continuous linear functionals. Moreover, we show that a lower prevision is coherent if and only if its transform is monotone. We also discuss the ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Int. J. Approx. Reasoning
دوره 78 شماره
صفحات -
تاریخ انتشار 2016