Modelling Heterogeneity With and Without the Dirichlet Process

By Peter J. Green, Sylvia Richardson. 2001

309 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/ac59a2ec67391bc7dcdd1618a7e9dd95f47b7511

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In Artificial Intelligence

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Citations in the corpus

A method for combining inference across related nonparametric Bayesian models (2004, background): “See Walker and Damien (1998), Neal (2000) and Green and Richardson (2001) for alternative approaches.”
Ontology-Based Semantic Image Segmentation Using Mixture Models and Multiple CRFs (2016, background): “It can be seen as a limit of a parametric mixture model [38], [39].”
An ANOVA Model for Dependent Random Measures (2004, background): “Green and Richardson (2001) argued for the use of more general mixture models and showed appropriate posterior simulation schemes.”
The Nested Dirichlet Process (2008, methodology): “…to methods for computation in finite-mixture models (Ishwaran and Zarepour 2002; Ishwaran and James 2001); and (c) use reversible-jump Markov chain Monte Carlo (RJMCMC) algorithms for finite mixtures with an unknown number of components (Dahl 2003; Green and Richardson 2001; Jain and Neal 2000).”
An Introduction to MCMC for Machine Learning (2004, methodology): “We describe here the “leapfrog” HMC algorithm outlined in Duane et al. (1987) and Neal (1996) focusing on the algorithmic details and not on the statistical mechanics motivation.”
Hierarchical Dirichlet Processes (2006, background): “A DP mixture model can be derived as the limit of a sequence of finite mixture models, where the number of mixture components is taken to infinity (Neal 1992; Rasmussen 2000; Green and Richardson 2001; Ishwaran and Zarepour 2002).”
Inference for Mixtures of Finite Polya Tree Models (2006, methodology): “We consider a Dirichlet multinomial allocation (DMA) model described in Ishwaran and Zarepour (2000) and Green and Richardson (2001). Hierarchically, the model is written as”
Retrospective Markov chain Monte Carlo methods for Dirichlet process hierarchical models (2007, methodology): “…Monte Carlo schemes do exist and include the sequential samplers of Liu (1996) and Ishwaran & James (2003), and referred to as the blocked Gibbs sampler in those papers, the particle ﬁlter of Fearnhead (2004) and the reversible jump method of Green & Richardson (2001) and Jain & Neal (2004).”
The Indian Buffet Process: An Introduction and Review (2011, methodology): “Instead, we will work directly with the distribution over assignment vectors given in Equation 3, considering its limit as the number of classes approaches infinity (cf., Green and Richardson, 2001; Neal, 1992, 2000).”
A Flexible Bayesian Nonparametric Model for Predicting Future Insurance Claims (2017, unknown): “We follow Green and Richardson (2001) and Kalli et al. (2011) and take to be G0 the joint distribution of (μ, σ 2) corresponding to μ ∼ N(m, s2) and (σ 2)−1 ∼ Gamma(a, b), independent, where Gamma(a, b) denotes the gamma distribution with density f (x) = b a (a) xa−1e−bx, x > 0.”
Slice sampling mixture models (2011, methodology): “The simulated data sets are based on the models used in Green and Richardson (2001) and consist of 100 draws from a bimodal and a leptokurtic mixture.”
The Dependent Dirichlet Process and Related Models (2020, methodology): “By choosing κh = κ for all h and (p1, . . . , pk) ∼ Dir(M/k, . . . ,M/k), the resulting RPM G approaches G(·) = ∑∞ h=1whδΘh(·) as k →∞ with DP-style weights (see, e.g. Green and Richardson, 2001).”
Gibbs Sampling Methods for Stick-Breaking Priors (2001, background): “Also see Kingman (1974), Muliere and Secchi (1995), Liu (1996), Walker and Wake eld (1998), Green and Richardson (1999), Neal (2000), and Ishwaran and Zarepour (2000a,c), who discussed this measure in different contexts and under different names. For example, Muliere and Secchi (1995) referred to (”
Methods for the integration of multi-omics data: mathematical aspects (2016, methodology): “The modeling structure of the multi-layer dataset exploits the mathematical connection between mixture models and Dirichelet Processes, a non-trivial problem: for details see [32].”
A Bayesian mixture model for across-site heterogeneities in the amino-acid replacement process. (2004, unknown): “Such mixture models are being introduced in many fields of applied statistics (Escobar and West 1995; Green and Richardson 1998), including bioinformatics (Eskin, Grundy, and Singer 2001; Broet, Richardson, and Radvanyi 2002), but they have not yet been applied to molecular phylogenetics.”
Model choice using reversible jump Markov chain Monte Carlo (2012, background): “See Richardson and Green (1997) and Green and Richardson (2001) for details.”