I describe in this paper an ontological solution to the Sleeping Beauty problem. I begin with describing the Entanglement urn experiment. I restate first the Sleeping Beauty problem from a wider perspective than the usual opposition between halfers and thirders. I also argue that the Sleeping Beauty experiment is best modelled with the Entanglement urn. I draw then the consequences of consideri...

I describe in this paper an ontological solution to the Sleeping Beauty problem. I begin with describing the Entanglement urn experiment. I restate first the Sleeping Beauty problem from a wider perspective than the usual opposition between halfers and thirders. I also argue that the Sleeping Beauty experiment is best modelled with the Entanglement urn. I draw then the consequences of consideri...

We consider a randomized urn model with objects of finitely many colors. The replacement matrices are random, and conditionally independent the color chosen given past. Further, conditional expectations close to an almost surely irreducible matrix. obtain sure $L^1$ convergence configuration vector, proportion vector count vector. show that first moment is sufficient for i.i.d.\ past choices. T...

The URN WG has defined a syntax for Uniform Resource Names (URNs) [RFC2141], as well as some proposed mechanisms for their resolution and use in Internet applications ([RFCXXXX], [RFCYYYY]). The whole rests on the concept of individual "namespaces" within the URN structure. Apart from proof-of-concept namespaces, the use of existing identifiers in URNs has been discussed ([RFC2288]), and this d...

There are three processes associated to a generalized Pólya urn model. First, the process that represents the proportion of balls of each type in the urn. As in each step a ball is drawn from the urn, its type is noted, and it is placed back in the urn, the second process represents the proportion of balls of each type that have been drawn from the urn. As the replacement policy consists in app...

Following the model of Bondesson, Nilsson, and Wikstrand, we consider randomly filled urns, where the probability of falling into urn i is the geometric probability (1− q)qi−1. Assuming n independent random entries, and a fixed parameter k, the interest is in the following parameters: Let T be the smallest index, such that urn T is non-empty, but the following k are empty, then: XT = number of ...

In this paper, I present a solution to the Doomsday argument based on a third type of solution, by contrast to on the one hand, the Carter-Leslie view and on the other hand, the Eckhardt et al. analysis. I begin by strengthening both competing models by highlighting some variations of their ancestors models, which renders them less vulnerable to some objections. I describe then a third line of ...

The behaviour of a Pólya-like urn which generates Ewens' sampling formula in population genetics is investigated. Connections are made with work of Watterson and Kingman and to the Poisson-Dirichlet distribution. The order in which novel types occur in the urn is shown to parallel the age distribution of the infinitely many alleles diffusion model and consequences of this property are explored....

Measure-valued Pólya urn processes (MVPP) are Markov chains with an additive structure that serve as extension of the generalized k-color model towards a continuum possible colors. We prove that, for any MVPP (μn)n≥0 on Polish space X, normalized sequence (μn/μn(X))n≥0 agrees marginal predictive distributions some random process (Xn)n≥1. Moreover, μn=μn−1+RXn, n≥1, where x↦Rx is transition kern...