Bayesian density estimation and model selection using nonparametric hierarchical mixtures

Argiento, Raffaele; Guglielmi, Alessandra; Pievatolo, Antonio

doi:10.1016/j.csda.2009.11.002

Cited by 37 publications

(25 citation statements)

References 30 publications

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“…However, in our experiments some mixing problems arose when both η and σ are small. In fact, it is well known (see for instance Argiento et al, 2010, or Lijoi et al, 2007 that small values of these parameters favour samples from the NGG process with few jumps, forcing small values of n(π) and therefore a small number of random effects in model (8). In this case, there are not enough distinct pairs (ϑ 1i , ϑ 2i ) to account for the clustering of the failure times, so that multimodality occurs in the Markov sequence of such pairs.…”

Section: Concluding Remarks and Discussionmentioning

confidence: 99%

“…Then the actual state of the chain will be (G, ψ, π, β, t 108 98 , u). For more explanations and details about the meaning of u, we refer the reader to James et al (2008), Nieto-Barajas and Prünster (2009) and to Argiento et al (2010) and simply describe the steps of our algorithm, with the square brackets notation denoting probability distributions.…”

Section: Posterior Distributions and Mcmc Algorithmmentioning

confidence: 99%

“…For details about the truncation method and the simulation procedure from the Poisson process we refer to Argiento et al (2010).…”

Section: Posterior Distributions and Mcmc Algorithmmentioning

confidence: 99%

“…A sensitivity analysis can then follow by varying (σ, η) on a finite grid. When no such prior information on the number of components in the mixture is available, (σ, η) could be selected based on a Bayes factor, as done by Argiento et al (2010) in the context of mixture density estimation.…”

Section: Random Effects Interpretationmentioning

confidence: 99%

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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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Section: Concluding Remarks and Discussionmentioning

confidence: 99%

Section: Posterior Distributions and Mcmc Algorithmmentioning

confidence: 99%

“…For details about the truncation method and the simulation procedure from the Poisson process we refer to Argiento et al (2010).…”

Section: Posterior Distributions and Mcmc Algorithmmentioning

confidence: 99%

Section: Random Effects Interpretationmentioning

confidence: 99%

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

2013

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“…Barrios et al (2013) propose an a posteriori truncation algorithm for NMRI mixtures using the Ferguson-Klass representation of completely random measures (Ferguson and Klass, 1972). Of course, when using truncation algorithms, the key-point is the choice of the truncation level; Argiento et al (2010) propose a simple adaptive truncation method evaluating an upper bound in probability for the jumps excluded from the summation.…”

Section: Introductionmentioning

confidence: 99%

A blocked Gibbs sampler for NGG-mixture models via a priori truncation

2015

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identically distributed location points, however considering only jumps larger than a threshold ε. Therefore, the number of jumps of the new process, called ε-NGG process, is a.s. finite. A prior distribution for ε can be elicited. We will assume such a process as the mixing measure in a mixture model for density and cluster estimation. We also build an efficient Gibbs sampler scheme to simulate from the posterior. Finally, the performance of our model on two popular datasets will be illustrated.

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A semiparametric Bayesian generalized linear mixed model for the reliability of Kevlar fibers

Argiento

Guglielmi

Soriano

2012

Appl Stoch Models Bus & Ind

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We analyze the reliability of NASA composite pressure vessels by using a new Bayesian semiparametric model. The data set consists of lifetimes of pressure vessels, wrapped with a Kevlar fiber, grouped by spool, subject to different stress levels; 10% of the data are right censored. The model that we consider is a regression on the log-scale for the lifetimes, with fixed (stress) and random (spool) effects. The prior of the spool parameters is nonparametric, namely they are a sample from a normalized generalized gamma process, which encompasses the well-known Dirichlet process. The nonparametric prior is assumed to robustify inferences to misspecification of the parametric prior. Here, this choice of likelihood and prior yields a new Bayesian model in reliability analysis. Via a Bayesian hierarchical approach, it is easy to analyze the reliability of the Kevlar fiber by predicting quantiles of the failure time when a new spool is selected at random from the population of spools. Moreover, for comparative purposes, we review the most interesting frequentist and Bayesian models analyzing this data set. Our credibility intervals of the quantiles of interest for a new random spool are narrower than those derived by previous Bayesian parametric literature, although the predictive goodnessof-fit performances are similar. Finally, as an original feature of our model, by means of the discreteness of the random-effects distribution, we are able to cluster the spools into three different groups.Appl. Stochastic Models Bus. Ind. 2013, 29 410-423 R. ARGIENTO, A. GUGLIELMI AND J. SORIANO and Kunz [2] fitted six separated (frequentist) regression models by using data from six spools only. Glaser [3] and Crowder et al. [4] fitted AFT models for the failure times by using Weibull distributions with both stress and spool as fixed effects. Feiveson and Kulkarni [5] were the first to emphasize the need of assuming the spool effect as random and provided a frequentist estimate of the parameters of the Weibull distribution for each stress level. Recently, Bayesian approaches were proposed to analyze the data set: Leon et al.[6] consider a Bayesian Weibull regression model with the spool random effect, whereas Argiento et al. [7] propose a semiparametric Bayesian Weibull regression model, where the random effect is not induced by the spool classification but is inferred via a discrete nonparametric component. In contrast, our semiparametric model provides new statistical findings, the most relevant being the clustering of the spools into three groups, as heuristically suggested by Crowder et al. [4], but here derived as an inferential result. Indeed, clusterization of the spools into a random partition is intrinsic to our model, thanks to the discreteness of the trajectories of the nonparametric component.As far as the statistical inference of this data set is concerned, the aim of this paper is twofold. On the one hand, we want to predict the reliability of the Kevlar yarn by using a Bayesian hierarchical approach to the problem. Und...

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Bayesian density estimation and model selection using nonparametric hierarchical mixtures

Cited by 37 publications

References 30 publications

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

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

A blocked Gibbs sampler for NGG-mixture models via a priori truncation

A semiparametric Bayesian generalized linear mixed model for the reliability of Kevlar fibers

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