Markov chain Monte Carlo in approximate Dirichlet and beta two-parameter process hierarchical models

By Hemant Ishwaran, Mahmoud Zarepour. 2000

324 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/ff57a4a29732183c6e22cfe981d31389630286d2

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Citations in the corpus

Gibbs Sampling Methods for Stick-Breaking Priors (2001, methodology): “These include (a) the Ferguson Dirichlet process (Ferguson 1973, 1974), (b) the two-parameter Poisson‐ Dirichlet process (Pitman and Yor 1997), (c) Dirichletmultinomial processes (Muliere and Secchi 1995), m-spike models (Liu 1996), e nite dimensional Dirichlet priors (Ishwaran and Zarepour 2000b,c)”
Sampling the Dirichlet Mixture Model with Slices (2007, methodology): “Motivated by the work of Ishwaran and Zarepour (2000) and Papaspiliopoulos and Roberts (2005) proposed an exact algorithm based on the notion of retrospective sampling.”
Bayesian Nonparametric Calibration and Combination of Predictive Distributions (2015, methodology): “ion requires the use of simulation methods. Gibbs samplers have been proposed in Escobar (1994) and Ishwaran and James (2001), which make use of the Polya-urn representation of the Dirichlet process. Ishwaran and Zarepour (2000) proposed a sampler based on a truncation of the innite mixture represen”
A General Framework for the Parametrization of Hierarchical Models (2007, methodology): “Approximate centered methods, which impute only an approximation X1: n = {X1,...,Xn},Z1: n = {Z1,...,Zn}, as in [ 18 ], will have O(n) mixing time.”
Stick-breaking autoregressive processes (2011, background): “The form of (3) defines a simple recursion but it also restrict the form of the marginal Gt to a Dirichlet or two-parameter beta process (Ishwaran and Zarepour, 2000).”
Bayesian Nonparametric Modeling for Multivariate Ordinal Regression (2014, background): “The blocked Gibbs sampler (Ishwaran and Zarepour, 2000; Ishwaran and James, 2001) replaces the countable sum with a ﬁnite sum, yielding Here, the ﬁrst N − 1 elements of p are equivalent to those in the countable representation of G , while p N is determined by p 1 , . . . , p N − 1 , so that =1 p l…”
DIRICHLET PRIOR SIEVES IN FINITE NORMAL MIXTURES (2002, methodology): “For 2(a) see Ishwaran and Zarepour (2002), while 2(b) can be proven from the results in Kingman (1975, Section 6) or Kingman (1993, Section 9.”
Order-Based Dependent Dirichlet Processes (2006, background): “Because the weights of the discrete distribution F x are stochastically ordered, Ishwaran and Zarepour (2000) suggested choosing a value of N that bounds the expectation of the error (cid”
A Sticky HDP-HMM With Application to Speaker Diarization (2009, methodology): “Another method is to consider the degree L weak limit approximation to the DP [Ishwaran and Zarepour (2002c)],”
Exact and approximate sum representations for the Dirichlet process (2002, methodology): “See also Ishwaran & Zarepour (2000) where Theorem 2 is discussed (without proof).”
Inference for Mixtures of Finite Polya Tree Models (2006, methodology): “Ishwaran and Zarepour (2000) and Green and Richardson (2001) showed that the DMA model approximates a DPM model as N gets large.”
Joint Species Distribution Modeling: Dimension Reduction Using Dirichlet Processes (2017, background): “As shown in Ishwaran and Zarepour (2000), the sum in (3) can be approximated with a truncated version ∑N l=1 plδθl(·), where ξl ∼ Beta( αN , (N−l) N α) (l N), and ξN = 1 is needed to ensure ∑N l=1 pl = 1.”
Bayesian nonparametric hidden semi-Markov models (2012, background): “The parameter L gives us control over the approximation, with the guarantee that the approximation will become exact as L grows; see Ishwaran and Zarepour (2000), especially Theorem 1, for a discussion of theoretical guarantees.”
Autoregressive Mixture Models for Dynamic Spatial Poisson Processes: Application to Tracking Intensity of Violent Crime (2010, methodology): “In general, the marginal distribution for each Gt is a twoparameter beta process, as described by Ishwaran and Zarepour (2000). However, of particular interest is the special case with Vl ∼ BAR(V ; 1, α, ρ) ∀ l, which implies the vlt are marginally distributed be(1, α) and the prior for each ft = ∫ ”