A method for combining inference across related nonparametric Bayesian models

By Peter Müller, Fernando A. Quintana, Gary Rosner. 2004

194 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/446dd270e43fb78947a39ea85a9dd79144a42c9e

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Citations in the corpus

Bayesian density regression (2007, background): “Müller et al. (2004) instead induced a hierarchical dependence structure through mixtures of independent DP basis measures.”
Multi-Task Learning for Classification with Dirichlet Process Priors (2007, methodology): “1 DIRICHLET PROCESSES FOR NONPARAMETRIC HIERARCHICAL BAYESIAN MODELING Hierarchical Bayesian modeling is one of the most important methods for meta analysis (Burr and Doss., 2005; Dominici et al., 1997; Hoff, 2003; Müller et al., 2004; Mallick and Walker, 1997).”
Comparing distributions by using dependent normalized random‐measure mixtures (2013, methodology): “Müller et al. (2004) assumed that fg =ψ ∞∑ i=1 wÅg,i k.·|θÅg,i/+ .1−ψ/ ∞∑ i=1 wik.”
Bayesian Selection and Clustering of Polymorphisms in Functionally Related Genes (2008, methodology): “Another possibility for defining dependence in G is to use the mixture approach of Müller, Quintana, and Rosner (2004), letting Gc = πFc + (1 − π)F0, with {F0,F1, . . . ,FC} assigned independent DP priors.”
Order-Based Dependent Dirichlet Processes (2006, background): “Because this implies leaving out a factor in the likelihood, Müller, Quintana, and Rosner (2004) changed the prior on the process to counteract this fact.”
Semi-Supervised Multitask Learning (2007, methodology): “The advantage of applying the DP prior to hierarchical models has been addressed in the statistics literature; see for example [28], [27] and [26].”
Nonparametric Bayesian Kernel Models (2007, methodology): “This Bayesian framework of the model allows for coherent inference, assessment of uncertainty, and access to the posterior distributions via Markov chain Monte Carlo sampling.”
The Matrix Stick-Breaking Process (2008, methodology): “Motivated by borrowing of information across related nonparametric Bayesian models, Müller, Quintana, and Rosner (2004) proposed an approach for incorporating dependence in Gj and Gj ′ by using a mixture specification in which Gj ∼ π0F0 + (1 − π0)Fj with 0 ≤ π ≤ 1 is a mixture probability, F0 ∼…”
Bayesian Nonparametric Calibration and Combination of Predictive Distributions (2015, unknown): “This type of prior, and its multivariate extensions (e.g., see Müller, Quintana, and Rosner 2004 and Griffin and Steel 2006), is now widely used in many fields due to the availability of efficient algorithms for posterior computations (Escobar and West 1995; MacEachern and Müller 1998;…”
Bayesian inference with dependent normalized completely random measures (2014, methodology): “This is close in spirit to the model of Müller, Quintana and Rosner [28], which is based on a vector of dependent random probability measures (p̃1, . . . , p̃n) defined as p̃i = ωpi + (1− ω)p0, (19) where pi and p0 are independent Dirichlet processes and the distribution of ω is a mixture with poin”
Stick-breaking autoregressive processes (2011, background): “…y, the infinite mixture model can be extended by allowing the kernel k to depend on x (Leslie et al., 2007; Chib and Greenberg, 2009), the mixing measure G to depend on x (De Iorio et al., 2004; Müller et al., 2004; Griffin and Steel, 2006; Dunson et al., 2007) or both (Geweke and Keane, 2007).”
The Dependent Dirichlet Process and Related Models (2020, background): “e presented in Section 1, and let G= fG x : x2X g= fG 1;:::;G Jg. Motivated by the need to borrow strength across related studies (a situation also arising in applications of meta-analysis), Muller, Quintana and Rosner (2004) proposed a hierarchical DP model. In this construction, the probability di”
Autoregressive Mixture Models for Dynamic Spatial Poisson Processes: Application to Tracking Intensity of Violent Crime (2010, background): “This defines a discounting of individual elements in successive DP centering measures, and is thus an extension of work that induces correlation through linear combinations of DPs (e.g., Müller, Quintana, and Rosner 2004).”
The matrix stick-breaking process for flexible multi-task learning (2007, methodology): “… increase the probability that .mj' = .m 'j' , for j ' = j. Motivated by borrowing of information across related nonparametric Bayesian models, M¨uller et al. (2004) proposed an approach for incorporating dependence in Gj and Gj ' by using a mixture speci.cation in which Gj ~ p0F0 + (1 -…”