Results 1  10
of
105
On the genealogy of large populations
, 1982
"... Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at ..."
Abstract

Cited by 280 (0 self)
 Add to MetaCart
Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at
Coalescents With Multiple Collisions
 Ann. Probab
, 1999
"... For each finite measure on [0 ..."
(Show Context)
Generalized weighted Chinese restaurant processes for species sampling mixture models
 Statistica Sinica
, 2003
"... Abstract: 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 conj ..."
Abstract

Cited by 85 (10 self)
 Add to MetaCart
Abstract: 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 posterior partition distribution that extend the results of Lo (1984) for the Dirichlet process. These results provide a better understanding of models and have both theoretical and practical applications. To facilitate the use of our models we generalize the work in Brunner, Chan, James and Lo (2001) by extending their weighted Chinese restaurant (WCR) Monte Carlo procedure, an i.i.d. sequential importance sampling (SIS) procedure for approximating posterior mean functionals based on the Dirichlet process, to the case of approximation of mean functionals and additionally their posterior laws in species sampling mixture models. We also discuss collapsed Gibbs sampling, Pólya urn Gibbs sampling and a Pólya urn SIS scheme. Our framework allows for numerous applications, including multiplicative counting process models subject to weighted gamma processes, as well as nonparametric and semiparametric hierarchical models based on the Dirichlet process, its twoparameter extension, the PitmanYor process and finite dimensional Dirichlet priors. Key words and phrases: Dirichlet process, exchangeable partition, finite dimensional Dirichlet prior, twoparameter PoissonDirichlet process, prediction rule, random probability measure, species sampling sequence.
Construction Of Markovian Coalescents
 Ann. Inst. Henri Poincar'e
, 1997
"... Partitionvalued and measurevalued coalescent Markov processes are constructed whose state describes the decomposition of a finite total mass m into a finite or countably infinite number of masses with sum m, and whose evolution is determined by the following intuitive prescription: each pair of ma ..."
Abstract

Cited by 49 (16 self)
 Add to MetaCart
(Show Context)
Partitionvalued and measurevalued coalescent Markov processes are constructed whose state describes the decomposition of a finite total mass m into a finite or countably infinite number of masses with sum m, and whose evolution is determined by the following intuitive prescription: each pair of masses of magnitudes x and y runs the risk of a binary collision to form a single mass of magnitude x+y at rate (x; y), for some nonnegative, symmetric collision rate kernel (x; y). Such processes with finitely many masses have been used to model polymerization, coagulation, condensation, and the evolution of galactic clusters by gravitational attraction. With a suitable choice of state space, and under appropriate restrictions on and the initial distribution of mass, it is shown that such processes can be constructed as Feller or Fellerlike processes. A number of further results are obtained for the additive coalescent with collision kernel (x; y) = x + y. This process, which arises fro...
PoissonDirichlet and GEM invariant distributions for splitandmerge transformations of an interval partition
, 2001
"... This paper introduces a splitandmerge transformation of interval partitions which combines some features of one model studied by Gnedin and Kerov [10, 11] and another studied by Tsilevich [30, 29] and MayerWolf, Zeitouni and Zerner [20]. The invariance under this splitandmerge transformatio ..."
Abstract

Cited by 49 (0 self)
 Add to MetaCart
This paper introduces a splitandmerge transformation of interval partitions which combines some features of one model studied by Gnedin and Kerov [10, 11] and another studied by Tsilevich [30, 29] and MayerWolf, Zeitouni and Zerner [20]. The invariance under this splitandmerge transformation of the interval partition generated by a suitable Poisson process yields a simple proof of the recent result of [20] that a PoissonDirichlet distribution is invariant for a closely related fragmentationcoagulation process. Uniqueness and convergence to the invariant measure are established for the splitandmerge transformation of interval partitions, but the corresponding problems for the fragmentationcoagulation process remain open.
Recent Progress in Coalescent Theory
"... Coalescent theory is the study of random processes where particles may join each other to form clusters as time evolves. These notes provide an introduction to some aspects of the mathematics of coalescent processes and their applications to theoretical population genetics and in other fields such ..."
Abstract

Cited by 48 (3 self)
 Add to MetaCart
Coalescent theory is the study of random processes where particles may join each other to form clusters as time evolves. These notes provide an introduction to some aspects of the mathematics of coalescent processes and their applications to theoretical population genetics and in other fields such as spin glass models. The emphasis is on recent work concerning in particular the connection of these processes to continuum random trees and spatial models such as coalescing random walks.
On exchangeable random variables and the statistics of large graphs and hypergraphs
, 2008
"... ..."
The genealogy of selfsimilar fragmentations with negative index as a continuum random tree
 Electr. J. Prob
, 2004
"... continuum random tree ..."