Large sample asymptotics for the two-parameter Poisson--Dirichlet process (2007)
This paper explores large sample properties of the two-parameter $(\alpha,\theta)$ Poisson--Dirichlet Process in two contexts. In a Bayesian context of estimating an unknown probability measure,...
Generalized Gamma Convolutions, Dirichlet means, Thorin measures, with explicit examples (2007)
James, Lancelot F., Roynette, Bernard, Yor, Marc
I. In Section 1, we present a number of classical results concerning the Generalized Gamma Convolution (: GGC) variables, their Wiener-Gamma representations, and relation with the Dirichlet...
New Dirichlet Mean Identities (2007)
An important line of research is the investigation of the laws of random variables known as Dirichlet means as discussed in Cifarelli and Regazzini(1990). However there is not much information on...
Lamperti Type Laws: Positive Linnik, Bessel Bridge Occupation and Mittag-Leffler Functions (2007)
This paper obtains density and cdf formula, and various distributional identities, for random variables defined as the ratio of two independent positive random variables where one variable has an...
Ho, Man-Wai, James, Lancelot F., Lau, John W.
This paper derives explicit results for the infinite Gibbs partitions generated by the jumps of an $\alpha-$stable subordinator, derived in Pitman \cite{Pit02, Pit06}. We first show that for general...
Tilted stable subordinators, Gamma time changes and Occupation Time of rays by Bessel Spiders (2007)
We exhibit, in the form of some identities in law, some connections between tilted stable subordinators, time-changed by independent Gamma processes and the occupation times of Bessel spiders, or...
This paper develops some general calculus for GGC and Dirichlet process means functionals. It then proceeds via an investigation of positive Linnik random variables, and more generally random...
Distributions of linear functionals of two parameter Poisson--Dirichlet random measures (2006)
James, Lancelot F., Lijoi, Antonio, Prünster, Igor
The present paper provides exact expressions for the probability distributions of linear functionals of the two-parameter Poisson--Dirichlet process $\operatorname {PD}(\alpha,\theta)$. We obtain...
Spatial Neutral to the Right Species Sampling Mixture Models (2006)
This paper describes briefly how one may utilize a class of species sampling mixture models derived from Doksum's (1974) neutral to the right processes. For practical implementation we describe an...
In recent years there have been many proposals as flexible alternatives to Gaussian based continuous time stochastic volatility models. A great deal of these models employ positive L\'evy processes....
Poisson calculus for spatial neutral to the right processes (2006)
Neutral to the right (NTR) processes were introduced by Doksum in 1974 as Bayesian priors on the class of distributions on the real line. Since that time there have been numerous applications to...
Ho, Man-Wai, James, Lancelot F., Lau, John W.
Pitman~(1999) describes a duality relationship between fragmentation and coagulation operators. An explicit relationship is described for the two-parameter Poisson-Dirichlet laws, with parameters...
This article develops, and describes how to use, results concerning disintegrations of Poisson random measures. These results are fashioned as simple tools that can be tailor-made to address...
This article develops, and describes how to use, results concerning disintegrations of Poisson random measures. These results are fashioned as simple tools that can be tailor-made to address...
Functionals of Dirichlet processes, the Cifarelli-Regazzini identity and Beta-Gamma processes (2005)
Suppose that P_{\theta}(g) is a linear functional of a Dirichlet process with shape \theta H, where \theta >0 is the total mass and H is a fixed probability measure. This paper describes how one can...
Functionals of Dirichlet processes, the Cifarelli–Regazzini identity and Beta-Gamma processes (2005)
Suppose that Pθ(g) is a linear functional of a Dirichlet process with shape θH, where θ>0 is the total mass and H is a fixed probability measure. This paper describes how one can use the...
Baysian inference via classes of normalized random measures (2005)
James, Lancelot F., Lijoi, Antonio, Pruenster, Igor
One of the main research areas in Bayesian Nonparametrics is the proposal and study of priors which generalize the Dirichlet process. Here we exploit theoretical properties of Poisson random measures...
Recently Carr and Wu (2004, 2005) and also Huang and Wu (2004) show that most stochastic processes used in traditional option pricing models can be cast as special cases of time-changed L\'evy...
In a series of recent papers Barndorff-Nielsen and Shephard introduce an attractive class of continuous time stochastic volatility models for financial assets where the volatility processes are...
James, Lancelot F., Lau, John W.
This paper discusses and analyzes a class of likelihood models which are based on two distributional innovations in financial models for stock returns. That is, the notion that the marginal...
Functionals of Dirichlet processes, the Markov Krein Identity and Beta-Gamma processes (2003)
This paper describes how one can use the well-known Bayesian prior to posterior analysis of the Dirichlet process, and less known results for the gamma process, to address the formidable problem of...
Hemant Ishwaran, Lancelot F. James
INTRODUCTION Consider the nite mixture problem where we wish to estimate Q 0 , an unknown nite mixing distribution with d atoms. We assume that d < 1 is unknown but that a nite upper bound N is known...
Poisson calculus for spatial neutral to the right processes (2003)
Neutral to the right (NTR) processes were introduced by Doksum in 1974 as Bayesian priors on the class of distributions on the real line. Since that time there have been numerous applications to...
Hemant Ishwaran, Lancelot F. James, Jiayang Sun
INTRODUCTION Consider the # nite mixture problem where we wish to estimate Q 0 , an unknown # nite mixing distribution with d atoms. We assume that d < is unknown but that a # nite upper bound N is...
Gibbs Sampling Methods for Stick-Breaking Priors Hemant Ishwaran and Lancelot F. James (2003)
Hemant Ishwaran, Lancelot F. James
this article we present two general types of Gibbs samplers that can be used to # t posteriors of Bayesian hierarchical models based on stick-breaking priors. The # rst type of Gibbs sampler,...
Hemant Ishwaran, Lancelot F. James
this paper will be to develop new surrounding theory for the hierarchical model (7) and show how these may be used to develop computational algorithms for computing posterior quantities. Our...
Approximate Dirichlet Process Computing in (2002)
Hemant Ishwaran, Lancelot F. James
This article looks at the use of a new Gibbs sampling method described by Ishwaran and Zarepour (2000) and Ishwaran and James (2001), which differs from the Gibbs sampling approaches mentioned above,...
This article discusses the usage of a partiton based Fubini calculus for Poisson processes. The approach is an amplification of Bayesian techniques developed in Lo and Weng for gamma/Dirichlet...
Consistent estimation of mixture complexity (2001)
James, Lancelot F., Marchette, David J., Priebe, Carey E.
The consistent estimation of mixture complexity is of fundamental importance in many applications of finite mixture models. An enormous body of literature exists regarding the application,...
Hemant Ishwaran, Lancelot F. James
INTRODUCTION The nite normal mixture model has been the subject of much research interest from a Bayesian perspective. See for example, Ferguson (1983), Escobar (1988, 1994), Diebolt and Robert...
Gibbs Sampling Methods for Stick-Breaking Priors (2000)
Hemant Ishwaran, Lancelot F. James
this paper we present two general types of Gibbs samplers that can be used to fit posteriors of Bayesian hierarchical models based on stick-breaking priors. The first type of Gibbs sampler, referred...
A study of a class of weighted bootstraps for censored data (1997)
Edgeworth expansions are derived for a class of weighted bootstrap methods for the Kaplan-Meier and Nelson-Aalen estimates using the methods contained in the monograph by Barbe and Bertail. Von Mises...
A Study Of A Class Of Weighted Bootstraps For Censored Data (1996)
. Edgeworth expansions are derived for a class of weighted bootstrap methods for the Kaplan-Meier and Nelson-Aalen estimates using the methods contained in the monograph by Barbe and Bertail (1995)....
The bootstrap, Bayesian bootstrap and random weighting methods for censored data models / (1993)
Thesis (Ph. D.)--State University of New York at Buffalo, 1993.
Conjugacy as a Distinctive Feature of the Dirichlet Process
LANCELOT F. JAMES, ANTONIO LIJOI, IGOR PRÜNSTER
Recently the class of normalized random measures with independent increments, which contains the Dirichlet process as a particular case, has been introduced. Here a new technique for deriving moments...
Bayesian Inference via Classes of Normalized Random Measures.
Lancelot F. James, Antonio Lijoi, Igor Pruenster
One of the main research areas in Bayesian Nonparametrics is the proposal and study of priors which generalize the Dirichlet process. Here we exploit theoretical properties of Poisson random measures...