Bayesian Nonparametric Reliability Analysis Using Dirichlet Process Mixture Model
نویسندگان
چکیده
Cheng, Nan, M.S., August 2011, Industrial and Systems Engineering Bayesian Nonparametric Reliability Analysis Using Dirichlet Process Mixture Model Director of Thesis: Tao Yuan This thesis develops a Bayesian nonparametric method based on Dirichlet Process Mixture Model (DPMM) and Markov chain Monte Carlo (MCMC) simulation algorithms to analyze non-repairable reliability lifetime data. Kernel distributions of the model will be implemented with Weibull, Lognormal and Exponential. The influence of prior distribution on the model parameters is studied. Both simulated and experimental data are used to test the proposed models. Our data analysis results indicate that the Dirichlet Process Lognormal Mixture (DPLNM) model is more flexible than the Dirichlet Process Exponential Mixture (DPEM) model and the Dirichlet Process Weibull Mixture (DPWM) model in terms of capturing different shapes of the life time distribution functions. Typically, when handling the practical data generated from devices with embedded nanocrystals, only the DPLNM model can produce a good fit towards the data. Although the lognormal distribution does not have closed form reliability function, censored data can still be easily handled using modern sampling techniques, such as Slice Sampling. Approved: _____________________________________________________________ Tao Yuan Assistant Professor of Industrial and Systmes Engineering
منابع مشابه
Introducing of Dirichlet process prior in the Nonparametric Bayesian models frame work
Statistical models are utilized to learn about the mechanism that the data are generating from it. Often it is assumed that the random variables y_i,i=1,…,n ,are samples from the probability distribution F which is belong to a parametric distributions class. However, in practice, a parametric model may be inappropriate to describe the data. In this settings, the parametric assumption could be r...
متن کاملFully Bayesian speaker clustering based on hierarchically structured utterance-oriented Dirichlet process mixture model
We have proposed a novel speaker clustering method based on a hierarchically structured utterance-oriented Dirichlet process mixture model. In the proposed method, the number of speakers can be determined from the given data using a nonparametric Bayesian manner and intra-speaker variability is successfully handled by multi-scale mixture modeling. Experimental result showed that the proposed me...
متن کاملDirichlet Process
The Dirichlet process is a prior used in nonparametric Bayesian models of data, particularly in Dirichlet process mixture models (also known as infinite mixture models). It is a distribution over distributions, i.e. each draw from a Dirichlet process is itself a distribution. It is called a Dirichlet process because it has Dirichlet distributed finite dimensional marginal distributions, just as...
متن کاملDirichlet Process Parsimonious Mixtures for clustering
The parsimonious Gaussian mixture models, which exploit an eigenvalue decomposition of the group covariance matrices of the Gaussian mixture, have shown their success in particular in cluster analysis. Their estimation is in general performed by maximum likelihood estimation and has also been considered from a parametric Bayesian prospective. We propose new Dirichlet Process Parsimonious mixtur...
متن کاملCollapsed Variational Dirichlet Process Mixture Models
Nonparametric Bayesian mixture models, in particular Dirichlet process (DP) mixture models, have shown great promise for density estimation and data clustering. Given the size of today’s datasets, computational efficiency becomes an essential ingredient in the applicability of these techniques to real world data. We study and experimentally compare a number of variational Bayesian (VB) approxim...
متن کامل