Nonparametric Bayes Estimation with Incomplete Dirichlet Prior Information.

1977 ◽  
Author(s):  
Gregory Campbell ◽  
Myles Hollander
Keyword(s):  
Prior Information ◽  
Bayes Estimation ◽  
Nonparametric Bayes ◽  
Dirichlet Prior

Nonparametric Bayes estimation in repair models

2009 ◽  
Vol 139 (5) ◽  
pp. 1722-1733 ◽  
Author(s):  
Jayaram Sethuraman ◽  
Myles Hollander
Keyword(s):  
Bayes Estimation ◽  
Nonparametric Bayes ◽  
Repair Models

scholarly journals Nonparametric bayes estimation of the reliability function of a coherent system

2021 ◽  
Vol 54 (2) ◽  
pp. 183-206
Author(s):  
AKM Fazlur Rahman ◽  
Edsel A. Pena
Keyword(s):  
Structure Function ◽  
Dirichlet Process ◽  
Synthetic Data ◽  
Reliability Function ◽  
Bayes Estimation ◽  
Coherent System ◽  
System Failure ◽  
Nonparametric Bayes ◽  
Lifetime Distributions ◽  
Safety Considerations

Complex coherent systems are the engines driving forward our technological world. A coherent system is composed of components, which could be modules or sub-systems, that interact with each other according to some structure function. For purposes of maintenance and safety considerations, it is of critical importance to gain knowledge of the distribution of the system lifetime, with this distribution being a function of the distributions of the components lifetimes. Since the monitoring of a system ceases upon system failure, at system failure some components will be failed, while others, depending on the structure function, will still be functioning with their lifetimes right-censored by the system lifetime. This paper deals with the estimation of the system lifetime distribution. The inferential framework is nonparametric Bayesian, with partition-based Dirichlet processes (PBDP) assigned as priors on the components lifetime distributions. PBDP are more general than the usual Dirichlet process (DP) priors and are particularly suited as priors in settings with censored data. The resulting estimator of the system life distribution, which is a function of the nonparametric Bayes estimators of the components lifetime distributions, is compared in terms of bias and variance with a product-limit type estimator proposed by Doss, et. al. (Ann. Statist., 1989), which can be obtained as a limit of the proposed estimator. These comparisons, which are facilitated through computer simulations, demonstrate that the proposed estimator possesses some robustness. The proposed estimator is illustrated using a synthetic data for a parallel system with five components.

scholarly journals Single-Scan Bayes Estimation of Cerebral Glucose Metabolic Rate: Comparison with Bon-Bades Single-Scan Methods Using DFG Pet Scans in Stroke

1988 ◽  
Vol 8 (3) ◽  
pp. 418-425 ◽  
Author(s):  
P. David Wilson ◽  
Sung-Cheng Huang ◽  
Randall A. Hawkins
Keyword(s):  
Metabolic Rate ◽  
Prior Information ◽  
Normal Population ◽  
Bayes Estimation ◽  
The Other ◽  
Mean Values ◽  
Positron Emission ◽  
Ischemic Tissue ◽  
Monte Carlo Studies ◽  
Pet Scans

Three single-scan (SS) methods are currently available for estimating the local cerebral metabolic rate of glucose (LCMRG) from F-18 deoxyglucose (FDG) positron emission tomography (PET) scan data: SS(SPH), named for Sokoloff, Phelps, and Huang; SS(B), named for Brooks; and SS(H), named for Hutchins and Holden et al. All three of these SS methods make use of prior information in the form of mean values of rate constants from the normal population. We have developed a Bayes estimation (BE) method that uses prior information in the form of rate constant means, variances, and correlations in both the normal and ischemic tissue populations. The BE method selects, based only on the data, whether the LCMRG estimate should be computed using prior information from normal or ischemic tissue. The ability of BE to make this selection gives it an advantage over the other methods. The BE method can be used as a SS method or can use any number of PET scans. We conducted Monte Carlo studies comparing BE as a SS method with the other SS methods, all using a single scan at 60 min. We found SS(H) to be strongly superior to SS(SPH) and SS(B), and we found BE to be definitely superior to SS(H).

scholarly journals Bayes Estimation of Change Point in Discrete Maxwell Distribution

2011 ◽  
Vol 2011 ◽  
pp. 1-8
Author(s):  
Mayuri Pandya ◽  
Hardik Pandya
Keyword(s):  
Change Point ◽  
Prior Information ◽  
Bayes Estimation ◽  
Loss Functions ◽  
Maxwell Distribution ◽  
Bayes Estimators ◽  
Asymmetric Loss ◽  
Bayes Estimates

A sequence of independent lifetimes X1,…,Xm,Xm+1,…,Xn was observed from Maxwell distribution with reliability r1(t) at time t but later, it was found that there was a change in the system at some point of time m and it is reflected in the sequence after Xm by change in reliability r2(t) at time t. The Bayes estimators of m, θ1, θ2 are derived under different asymmetric loss functions. The effects of correct and wrong prior information on the Bayes estimates are studied.

Sign in / Sign up

Export Citation Format

Share Document