Exchangeability and sets of desirable gambles

by   Gert de Cooman, et al.

Sets of desirable gambles constitute a quite general type of uncertainty model with an interesting geometrical interpretation. We give a general discussion of such models and their rationality criteria. We study exchangeability assessments for them, and prove counterparts of de Finetti's finite and infinite representation theorems. We show that the finite representation in terms of count vectors has a very nice geometrical interpretation, and that the representation in terms of frequency vectors is tied up with multivariate Bernstein (basis) polynomials. We also lay bare the relationships between the representations of updated exchangeable models, and discuss conservative inference (natural extension) under exchangeability and the extension of exchangeable sequences.



page 1

page 2

page 3

page 4


A Desirability-Based Axiomatisation for Coherent Choice Functions

Choice functions constitute a simple, direct and very general mathematic...

Geometry of Friston's active inference

We reconstruct Karl Friston's active inference and give a geometrical in...

Coherent and Archimedean choice in general Banach spaces

I introduce and study a new notion of Archimedeanity for binary and non-...

Irrelevant and independent natural extension for sets of desirable gambles

The results in this paper add useful tools to the theory of sets of desi...

Algorithms for Learning Decomposable Models and Chordal Graphs

Decomposable dependency models and their graphical counterparts, i.e., c...

Conservative Extensions for Existential Rules

We study the problem to decide, given sets T1,T2 of tuple-generating dep...

Bayesian Paragraph Vectors

Word2vec (Mikolov et al., 2013) has proven to be successful in natural l...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.