Gibbs Sampling Methods for Stick-Breaking Priors

By Hemant Ishwaran, Lancelot F. James. 2001

1,816 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/45db16309fbf7e9fc8907047e7e1a9933c4e1b85

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Citations in the corpus

Compound random measures and their use in Bayesian non‐parametrics (2014, methodology): “This usually leads to computationally tractable methods which either extend random truncation methods such as retrospective sampling [38] or slice sampling [24], or develop truncation ideas for Dirichlet process mixtures [22].”
Exact and approximate sum representations for the Dirichlet process (2002, methodology): “In Ishwaran & James (2001,2002), the construction (8) was used to determine the accuracy of almost sure truncations of the form Nwhere VAr = 1 (EN = w) SO that Ck=lpk = 1 (hereafter we use N to denote a finite positive integer).”
A Tutorial on Bayesian Nonparametric Models (2011, methodology): “Gibbs samplers that operate on this representation are also available (Ishwaran and James, 2001).”
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.”
Bayesian Nonparametric Analysis for a Generalized Dirichlet Process Prior (2005, methodology): “Stick–breaking priors, as defined in Ishwaran and James (2001) and further developed in Ishwaran and James (2003), contain, among others, the Dirichlet process (defined in a stick–breaking fashion by Sethuraman (1994)), the two-parameter Poisson–Dirichlet process (Pitman, 1995; Pitman and Yor,…”
Multi-task compressive sensing with Dirichlet process priors (2008, background): “In practice K is chosen as a relatively large integer (e.g., K = M if M is relatively large) which yields a negligible difference compared to the true DP (Ishwaran & James, 2001), while making the computation practical.”
Multiple Imputation of Missing or Faulty Values Under Linear Constraints (2014, methodology): “With specified hyperparameters, the model can be estimated using a Gibbs sampler, as each full conditional distribution is in closed form; see Ishwaran and James (2001).”
A Bayesian Nonparametic Approach for Estimating Individualized Treatment-Response Curves (2016, methodology): “For the infinite-dimensional DPM priors on φi and φid, we use a truncated stick-breaking process that was developed by Ishwaran and James (2001) to approximate. Ishwaran and James (2001)”
Bayesian inference with dependent normalized completely random measures (2014, methodology): “Most contributions to this line of research rely on random probability measures defined by means of a stick-breaking procedure, a popular method set forth in its generality for the first time in [16].”
Nonparametric Bayesian Deep Networks with Local Competition (2018, background): “In this context, they obtain a sparsity-inducing behavior, by imposing appropriate stick-breaking priors (Ishwaran & James, 2001) over the postulated auxiliary latent variables.”
Consistency of mixture models with a prior on the number of components (2022, background): “More generally, for the same reason, Condition 2.2(2) is satisfied if W |k is defined as follows: let Zi ∼ Beta(aki, bki) independently for i ∈ {1, . . . , k − 1} where aki, bki > 0, then set Wi = Zi ∏i−1 j=1(1 − Zj) for i ∈ {1, . . . , k − 1} and Wk = 1 − ∑k−1 i=1 Wi; this is called the generalized”
A Bayesian Semiparametric Approach to Intermediate Variables in Causal Inference (2011, background): “As shown in the article by (Ishwaran and James 2001), an accurate approximation to the infinite limit (i.”
Posterior Analysis for Normalized Random Measures with Independent Increments (2009, methodology): “Moreover, as shown in James (2003), NRMI select almost surely discrete distributions.”
The Matrix Stick-Breaking Process (2008, methodology): “A.1 Proof of Lemma 1 Following an approach closely related to that of Ishwaran and James (2001), we first note that 1 − N−1∑ h=1 πmjh = N−1∏ h=1 (1 − Vmjh).”
A Hierarchical Bayesian Language Model Based On Pitman-Yor Processes (2006, methodology): “, 1995) where each hidden variable is distributed according to a Pitman-Yor process, a nonparametric generalization of the Dirichlet distribution that is widely studied in the statistics and probability theory communities (Pitman and Yor, 1997; Ishwaran and James, 2001; Pitman, 2002).”