Bayesian survival and hazard estimates for Weibull regression with censored data using modified Jeffreys prior

In this study, firstly, consideration is given to the traditional maximum likelihood estimator and the Bayesian estimator by employing Jeffreys prior and Extension of Jeffreys prior information on the Weibull distribution with a given shape under right censored data. We have formulated equatio...

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Main Author:	Ahmed, Al Omari Mohammed
Format:	Thesis
Language:	English
Published:	2013
Subjects:	Weibull distribution Bayesian field theory Regression analysis - Mathematical models
Online Access:	http://psasir.upm.edu.my/id/eprint/66635/1/FS%202013%2052%20IR.pdf
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spelling	my-upm-ir.666352019-01-29T06:29:58Z Bayesian survival and hazard estimates for Weibull regression with censored data using modified Jeffreys prior 2013-05 Ahmed, Al Omari Mohammed In this study, firstly, consideration is given to the traditional maximum likelihood estimator and the Bayesian estimator by employing Jeffreys prior and Extension of Jeffreys prior information on the Weibull distribution with a given shape under right censored data. We have formulated equations for the scale parameter, the survival function and the hazard functionunder Bayesian with extension of Jeffreys prior. Next we consider both the scale and shape parameters to be unknown under censored data. It is observed that the estimate of the shape parameter under the maximum likelihood method cannot be obtained in closed form, but can be solved by the application of numerical methods. With the application of the Bayesian estimates for the parameters, the survival function and hazard function, we realised that the posterior distribution from which Bayesian inference is drawn cannot be obtained analytically. Due to this, we have employed Lindley’s approximation technique and then compared it to the maximum likelihood approach. We then incorporate covariates into the Weibull model. Under this regression model with regards to Bayesian, the usual method was not possible. Thus we develop an approach to accommodate the covariate terms in the Jeffreys and Modified of Jeffreys prior by employingGauss quadrature method. Subsequently, we use Markov Chain Monte Carlo (MCMC) method in the Bayesian estimator of the Weibull distributionand Weibull regression model with shape unknown. For the Weibull model with right censoring and unknown shape, the full conditional distribution for the scale and shape parameters are obtained via Gibbs sampling and Metropolis-Hastings algorithm from which the survival function and hazard function are estimated. For Weibull regression model of both Jeffreys priors with covariates, importance sampling technique has been employed. Mean squared error (MSE) and absolute bias are obtained and used to compare the Bayesian and the maximum likelihood estimation through simulation studies. Lastly, we use real data to assess the performance of the developed models based on Gauss quadrature and Markov Chain Monte Carlo (MCMC) methods together with the maximum likelihood approach. The comparisons are done by using standard error and the confidence interval for maximum likelihood method and credible interval for the Bayesian method. Weibull distribution Bayesian field theory Regression analysis - Mathematical models 2013-05 Thesis http://psasir.upm.edu.my/id/eprint/66635/ http://psasir.upm.edu.my/id/eprint/66635/1/FS%202013%2052%20IR.pdf text en public doctoral Universiti Putra Malaysia Weibull distribution Bayesian field theory Regression analysis - Mathematical models
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
topic	Weibull distribution Bayesian field theory Regression analysis - Mathematical models
spellingShingle	Weibull distribution Bayesian field theory Regression analysis - Mathematical models Ahmed, Al Omari Mohammed Bayesian survival and hazard estimates for Weibull regression with censored data using modified Jeffreys prior
description	In this study, firstly, consideration is given to the traditional maximum likelihood estimator and the Bayesian estimator by employing Jeffreys prior and Extension of Jeffreys prior information on the Weibull distribution with a given shape under right censored data. We have formulated equations for the scale parameter, the survival function and the hazard functionunder Bayesian with extension of Jeffreys prior. Next we consider both the scale and shape parameters to be unknown under censored data. It is observed that the estimate of the shape parameter under the maximum likelihood method cannot be obtained in closed form, but can be solved by the application of numerical methods. With the application of the Bayesian estimates for the parameters, the survival function and hazard function, we realised that the posterior distribution from which Bayesian inference is drawn cannot be obtained analytically. Due to this, we have employed Lindley’s approximation technique and then compared it to the maximum likelihood approach. We then incorporate covariates into the Weibull model. Under this regression model with regards to Bayesian, the usual method was not possible. Thus we develop an approach to accommodate the covariate terms in the Jeffreys and Modified of Jeffreys prior by employingGauss quadrature method. Subsequently, we use Markov Chain Monte Carlo (MCMC) method in the Bayesian estimator of the Weibull distributionand Weibull regression model with shape unknown. For the Weibull model with right censoring and unknown shape, the full conditional distribution for the scale and shape parameters are obtained via Gibbs sampling and Metropolis-Hastings algorithm from which the survival function and hazard function are estimated. For Weibull regression model of both Jeffreys priors with covariates, importance sampling technique has been employed. Mean squared error (MSE) and absolute bias are obtained and used to compare the Bayesian and the maximum likelihood estimation through simulation studies. Lastly, we use real data to assess the performance of the developed models based on Gauss quadrature and Markov Chain Monte Carlo (MCMC) methods together with the maximum likelihood approach. The comparisons are done by using standard error and the confidence interval for maximum likelihood method and credible interval for the Bayesian method.
format	Thesis
qualification_level	Doctorate
author	Ahmed, Al Omari Mohammed
author_facet	Ahmed, Al Omari Mohammed
author_sort	Ahmed, Al Omari Mohammed
title	Bayesian survival and hazard estimates for Weibull regression with censored data using modified Jeffreys prior
title_short	Bayesian survival and hazard estimates for Weibull regression with censored data using modified Jeffreys prior
title_full	Bayesian survival and hazard estimates for Weibull regression with censored data using modified Jeffreys prior
title_fullStr	Bayesian survival and hazard estimates for Weibull regression with censored data using modified Jeffreys prior
title_full_unstemmed	Bayesian survival and hazard estimates for Weibull regression with censored data using modified Jeffreys prior
title_sort	bayesian survival and hazard estimates for weibull regression with censored data using modified jeffreys prior
granting_institution	Universiti Putra Malaysia
publishDate	2013
url	http://psasir.upm.edu.my/id/eprint/66635/1/FS%202013%2052%20IR.pdf
_version_	1747812393945137152

Bayesian survival and hazard estimates for Weibull regression with censored data using modified Jeffreys prior

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