Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6858975 | International Journal of Approximate Reasoning | 2013 | 10 Pages |
Abstract
May the same be said of an infinite hierarchy of higher-order probabilities? Is it consistent to speak of a probability of a probability, and of a probability of a probability of a probability, and so on, ad infinitum? We argue that it is, for it can be shown that there exists an infinite system of probabilities that has a model. In particular, we define a regress of higher-order probabilities that leads to a convergent series which determines an infinite-order probability value. We demonstrate the consistency of the regress by constructing a model based on coin-making machines.
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Artificial Intelligence
Authors
David Atkinson, Jeanne Peijnenburg,