We take a unified approach to central limit theorems for a class of irreducible urn models with constant replacement matrix. Depending on the eigenvalue, we consider appropriate linear combinations of the number of balls of different colors. Then under appropriate norming the multivariate distribution of the weak limits of these linear combinations is obtained and independence and dependence is...

A famous “curious identity” of Wallis gives a representation of the constant π in terms of a simply structured infinite product of fractions. Sondow and Yi [Amer. Math. Monthly 117 (2010), 912-917] identified a general scheme for evaluating Wallis-type infinite products. The main purpose of this paper is to discuss an interpretation of the scheme by means of Pólya urn models.

We prove a Central Limit Theorem for the sequence of random compositions of a two-color randomly reinforced urn. As a consequence, we are able to show that the distribution of the urn limit composition has no point masses.

Decisions are most effective after collecting sufficient evidence to accurately predict rewarding outcomes. We investigated whether human participants optimally seek evidence and we characterized the brain areas associated with their evidence seeking. Participants viewed sequences of bead colors drawn from hidden urns and attempted to infer the majority bead color in each urn. When viewing each...

We study a new class of time inhomogeneous Pólya-type urn schemes and give optimal rates of convergence for the distribution of the properly scaled number of balls of a given color to nearly the full class of generalized gamma distributions with integer parameters, a class which includes the Rayleigh, half-normal and gamma distributions. Our main tool is Stein’s method combined with characteriz...

We extend a disclosure risk measure defined for population based frequency tables to sample based frequency tables. The disclosure risk measure is based on information theoretical expressions, such as entropy and conditional entropy, that reflect the properties of attribute disclosure. To estimate the disclosure risk of a sample based frequency table we need to take into account the underlying ...

We present an application of Bayesian modeling and inference to topological mapping in robotics. This is a potentially difficult problem due to (a) the combinatorial nature of the state space, and (b) perceptual aliasing by which two different landmarks in the environment can appear similar to the robot’s sensors. Hence, this presents a challenging approximate inference problem, complicated by ...

The essential feature of controlled clinical trials is the random assignment of subjects to two or more treatment groups under investigation. The principle of randomization provides a protection against hidden biases and thus increases the validity of the trial’s findings. Another fundamental aspect of clinical trials is the incorporation into the design and/or analysis those prognostic factors...

We prove a Central Limit Theorem for the sequence of random compositions of a two-color randomly reinforced urn. As a consequence, we are able to show that the distribution of the urn limit composition has no point masses.

The User Requirements Notation (URN) combines the Goaloriented Requirement Language (GRL) with the Use Case Map (UCM) scenario notation. Although tools exist in isolation for both views, they are currently not meant to work together, hence preventing one to exploit URN to its fullest extent. This paper presents jUCMNav, a new Eclipse-based tool that supports both UCM and GRL in an integrated wa...