This paper presents the link between stochastic approximation and clinical trials based on randomized urn models investigated in [5, 6, 7]. We reformulate the dynamics of both the urn composition and the assigned treatments as standard stochastic approximation (SA) algorithms with remainder. Then, we derive the a.s. convergence and the asymptotic normality (Central Limit Theorem CLT ) of the no...

Motivated by recent studies of big samples, this work aims at constructing a parametric model which is characterized the following features: (i) "local" reinforcement, i.e. reinforcement mechanism mainly based on last observations, (ii) random persistent fluctuation predictive mean, and (iii) long-term convergence empirical mean to deterministic limit, together with chi-squared goodness fit res...

The class of species sampling mixture models is introduced as an extension of semiparametric models based on the Dirichlet process to models based on the general class of species sampling priors, or equivalently the class of all exchangeable urn distributions. Using Fubini calculus in conjunction with Pitman (1995, 1996), we derive characterizations of the posterior distribution in terms of a p...

The sample frequency spectrum is an informative and frequently employed approach for summarizing DNA variation data. Under the standard neutral model the expectation of the sample frequency spectrum has been derived by at least two distinct approaches. One relies on using results from diffusion approximations to the Wright-Fisher Model. The other is based on Pólya urn models that correspond to ...

Key 'words and phrases: Success runs, scan statistics, urn models, Markov clmins, triangular nmltidimensional recurrence relations, distributions of order /,..

Urn models are popular and useful for adaptive designs in clinical studies. Among various urn models, the drop-the-loser rule is an efficient adaptive treatment allocation scheme, recently proposed for comparing different treatments in a clinical trial. This rule is superior to other randomization schemes in terms of variability and power. In this paper, the drop-the-loser rule is generalized t...

Several methods for generating random variables with univariate and multivariate Wallenius' and Fisher's noncentral hypergeometric distributions are developed. Methods for the univariate distributions include: simulation of urn experiments, inversion by binary search, inversion by chop-down search from the mode, ratio-of-uniforms rejection method, and rejection by sampling in the t domain. Meth...