TY - JOUR
T1 - Estimation, prediction and interpretation of NGG random effects models: An application to Kevlar fibre failure times
AU - Argiento, Raffaele
AU - Guglielmi, Alessandra
AU - Pievatolo, Antonio
PY - 2014
Y1 - 2014
N2 - We propose a class of Bayesian semiparametric mixed-effects models; its
distinctive feature is the randomness of the grouping of observations, which can be
inferred from the data. The model can be viewed under a more natural perspective, as
a Bayesian semiparametric regression model on the log-scale; hence, in the original
scale, the error is a mixture of Weibull densities mixed on both parameters by a
normalized generalized gamma random measure, encompassing the Dirichlet process.
As an estimate of the posterior distribution of the clustering of the random-effects
parameters, we consider the partition minimizing the posterior expectation of a suitable
class of loss functions. As a merely illustrative application of our model we consider
a Kevlar fibre lifetime dataset (with censoring). We implement an MCMC scheme,
obtaining posterior credibility intervals for the predictive distributions and for the
quantiles of the failure times under different stress levels. Compared to a previous
parametric Bayesian analysis, we obtain narrower credibility intervals and a better
fit to the data. We found that there are three main clusters among the random-effects
parameters, in accordance with previous frequentist analysis.
AB - We propose a class of Bayesian semiparametric mixed-effects models; its
distinctive feature is the randomness of the grouping of observations, which can be
inferred from the data. The model can be viewed under a more natural perspective, as
a Bayesian semiparametric regression model on the log-scale; hence, in the original
scale, the error is a mixture of Weibull densities mixed on both parameters by a
normalized generalized gamma random measure, encompassing the Dirichlet process.
As an estimate of the posterior distribution of the clustering of the random-effects
parameters, we consider the partition minimizing the posterior expectation of a suitable
class of loss functions. As a merely illustrative application of our model we consider
a Kevlar fibre lifetime dataset (with censoring). We implement an MCMC scheme,
obtaining posterior credibility intervals for the predictive distributions and for the
quantiles of the failure times under different stress levels. Compared to a previous
parametric Bayesian analysis, we obtain narrower credibility intervals and a better
fit to the data. We found that there are three main clusters among the random-effects
parameters, in accordance with previous frequentist analysis.
KW - Keywords Bayesian nonparametrics, Clustering, Hierarchical models,Mixture models, Nonparametric models, Generalized linear mixed models
KW - Keywords Bayesian nonparametrics, Clustering, Hierarchical models,Mixture models, Nonparametric models, Generalized linear mixed models
UR - http://hdl.handle.net/10807/148068
UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-84903838369&doi=10.1007/s00362-013-0528-8&partnerid=40&md5=b29815bb103ae9eba94e2bb97d1491e6
U2 - 10.1007/s00362-013-0528-8
DO - 10.1007/s00362-013-0528-8
M3 - Article
SN - 0932-5026
VL - 55
SP - 805
EP - 826
JO - Statistical Papers
JF - Statistical Papers
ER -