Generalized weighted Chinese restaurant processes for species sampling mixture models

By Hemant Ishwaran, Lancelot F. James. 2003

210 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/c74639a3fc648e19d46b5f52cd40ba8bec936184

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Citations in the corpus

Bayesian Nonparametrics: Models beyond the Dirichlet process (2009, unknown): “See Ishwaran and James (2001). The rationale of the construction is apparent.”
Fast Bayesian Inference in Dirichlet Process Mixture Models (2011, methodology): “For DPM models, a number of alternatives to MCMC have been proposed, including partial predictive recursion (PPR) (Newton and Zhang, 1999), weighted Chinese restaurant (WCR) sampling (Lo, Brunner and Chan 1996; Ishwaran and Takahara 2002; Ishwaran and James 2003), sequential importance sampling (SIS”
The Ubiquitous Ewens Sampling Formula (2016, background): “Others [37, 65] have further contributed to the foundations of Bayesian nonparametrics laid down by Ishawaran and James.”
Large sample asymptotics for the two-parameter Poisson–Dirichlet process (2007, methodology): “However we should point out that Ishwaran and James (18; 17), owing to the attractive results in (35), suggested that one could use Πα,θ in a mixture modeling setting analogous to the case of the Dirichlet process in Lo (29).”
On a preferential attachment and generalized Pólya’s urn model (2012, background): “(See for example [14], [16] or [18] for more on species sampling sequences or for their applications to statistics.”
Adaptor Grammars: A Framework for Specifying Compositional Nonparametric Bayesian Models (2006, methodology): “With a particular choice of adaptor, based on the Pitman-Yor process [1, 2, 3], simple context-free grammars specify distributions commonly used in nonparametric Bayesian statistics, such as Dirichlet processes [4] and hierarchical Dirichlet processes [5].”
Bayesian density regression (2007, methodology): “This is accomplished by using the dependent DP approach of MacEachern (1999, 2000, 2001), which relies on expressing the DP in stick breaking form (Sethuraman, 1994) Gx = ∞ ∑ h=1 πx,hδθx,h , with πx,h / h−1 ∏ l=1 .1−πx,l/ IID ∼ beta.1,α/, where {πx,h} are random weights, δθ is a degenerate distribut”
Inducing Tree-Substitution Grammars (2010, methodology): “…how many elementary trees might be needed to account for the data, we use a nonparametric Bayesian prior, specifically the Pitman-Yor process (PYP) (Pitman, 1995; Pitman and Yor, 1997; Ishwaran and James, 2003), which is a generalization of the more widely known Dirichlet process (Ferguson, 1973).”
Combinatorial Stochastic Processes (2006, background): “The Chinese Restaurant Process and associated computations with random partitions have found applications in Bayesian statistics [109, 287, 210, 212], and in the theory of representations of the infinite symmetric group [243].”
Hierarchical Topic Models and the Nested Chinese Restaurant Process (2003, background): “In a species sampling mixture [6], each table in the Chinese restaurant is associated with a draw from p(β | η) where β is a mixture component parameter.”
Bayesian Poisson process partition calculus with an application to Bayesian Lévy moving averages (2005, methodology): “For brevity, we only sketch out some details, focusing on identifying the relevant probabilities, as one can deduce the operational formalities either from [15, 16] or other relevant cited works.”
Posterior Analysis for Normalized Random Measures with Independent Increments (2009, methodology): “Its role in a Bayesian context, for the homogeneous case, can be deduced from Pitman (1996) and Ishwaran & James (2003), whereas for the nonhomogeneous case one can refer to James (2006).”