Approximate Dirichlet Process Computing in Finite Normal Mixtures

Ishwaran, Hemant; James, Lancelot F.

doi:10.1198/106186002411

Cited by 210 publications

(244 citation statements)

References 28 publications

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“…Since our model is a finite mixture with mixing distribution G x 1 ,...,xm , the following result, a multivariate version of Theorem 2 of Ishwaran and Zarepour (2002), shows that it is fully identified under mild conditions. …”

Section: Model Identifiability and Posterior Consistencymentioning

confidence: 78%

“…Then, we investigate the overall mixture model. We clarify the identifiability of the mixture distribution, building upon results from Ishwaran and Zarepour (2002) which broadens classical work of Teicher (1963). We also discuss consistency of posterior inference under the overall mixture model, extending results in Ishwaran and Zarepour (2002).…”

Section: Introductionmentioning

confidence: 76%

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The Dirichlet labeling process for clustering functional data

Nguyen¹,

Gelfand

2011

STAT. SINICA

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Abstract:We consider problems involving functional data where we have a collection of functions, each viewed as a process realization, e.g., a random curve or surface. For a particular process realization, we assume that the observation at a given location can be allocated to separate groups via a random allocation process, which we name the Dirichlet labeling process. We investigate properties of this process and its use as a prior in a mixture model.We develop exact and approximate representations for the labeling process, analyze the global and local clustering behavior, clarify model identifiability and posterior consistency, and develop efficient inference methods for models using such priors. Performance is demonstrated with synthetic data examples, a public-health application, and an image segmentation task.

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Section: Model Identifiability and Posterior Consistencymentioning

confidence: 78%

Section: Introductionmentioning

confidence: 76%

The Dirichlet labeling process for clustering functional data

Nguyen¹,

Gelfand

2011

STAT. SINICA

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“…We note that we may also specify that k = 1, 2, ..., K where K < ∞, referred to as the finite DP or DP K , and the weights are drawn from a K-dimensional Dirichlet distribution (Ishwaran and Zarepour, 2002).…”

Section: Stochastic Process Models For Random Functionsmentioning

confidence: 99%

Bayesian nonparametric modeling for functional analysis of variance

Nguyen

Gelfand

2013

Ann Inst Stat Math

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Analysis of variance (ANOVA) is a standard statistical modeling approach for comparing populations. The functional analysis setting envisions that mean functions are associated with the populations, customarily modeled using basis representations, and seeks to compare them. More recently, these functions have been modeled as realizations of stochastic processes. Here, we adopt this latter approach, offering several novel contributions. First, we extend the Gaussian process version to allow nonparametric specifications using Dirichlet process mixing. We introduce several useful metrics for comparison of populations under either specification. Then, we introduce a hierarchical Dirichlet process model which compares populations through their distributions. That is, each population has a (random) distribution which generates the functions for each of the individuals sampled within that population. Now, comparison can proceed directly through these distributions or through functions which arise using functionals of interest under these distributions, employing the foregoing metrics. We take the modeling a bit further, introducing a nested hierarchical Dirichlet process to allow us to switch the sampling scheme. There are still population level distributions but now we sample at levels of the functions, obtaining observations from potentially different individuals at different levels. We illustrate with both simulated data as well as a dataset of temperature vs. depth measurements at four different locations in the Atlantic Ocean.

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“…from G, and G is a Dirichlet process with mean probability measure gamma(a, b) and total mass parameter κ. As in Ghosh and Ghosal's paper, we computed the posterior distribution under their model resorting to the N -finite approximation of Dirichlet processes in Ishwaran and Zarepour (2002). In particular, we fixed N = 60, since for a smaller N there were relevant differences between the two posterior distributions of n(π); κ was fixed equal to 2 in order that E(n(π)) = 8.5, a value very close to the actual number of spools.…”

Section: Posterior Distributions and Mcmc Algorithmmentioning

confidence: 99%

Estimation, prediction and interpretation of NGG random effects models: an application to Kevlar fibre failure times

2013

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AperTO -Archivio Istituzionale Open Access dell'Università di TorinoEstimation, prediction and interpretation of NGG random effects models: An application to Kevlar fibre failure times / Argiento, R.; Pievatolo, A.. -55(2014), pp. 805-826. Original Citation:Estimation, prediction and interpretation of NGG random effects models: An application to Kevlar fibre failure times Compared to a previous parametric Bayesian analysis, we obtain narrower credibility intervals and a better fit to the data. We also fit a similar semiparametric model, which can be seen a a special case of ours, where the error is a scale mixture of Weibull densities, mixed by a Dirichlet process, whereas the shape parameter has a parametric prior. The adequacy of the two semiparametric models is comparable, but the more general model provides a different evaluation of the posterior variance of the left tail of the lifetime distribution, which is an effect of assuming a nonparametric prior on both parameters of the Weibull density.

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Approximate Dirichlet Process Computing in Finite Normal Mixtures

Cited by 210 publications

References 28 publications

The Dirichlet labeling process for clustering functional data

The Dirichlet labeling process for clustering functional data

Bayesian nonparametric modeling for functional analysis of variance

Estimation, prediction and interpretation of NGG random effects models: an application to Kevlar fibre failure times

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