베이지안 확률 모형을 이용한 위험률 함수의 추론
Hazard Rate Estimation from Bayesian Approach
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Abstract
This paper is intended to compare the hazard rate estimations from Bayesian approach and maximum likelihood estimate(MLE) method. Hazard rate frequently involves unknown parameters and it is common that those parameters are estimated from observed data by using MLE method. Such estimated parameters are appropriate as long as there are sufficient data. Due to various reasons, however, we frequently cannot obtain sufficient data so that the result of MLE method may be unreliable. In order to resolve such a problem we need to rely on the judgement about the unknown parameters. We do this by adopting the Bayesian approach. The first one is to use a predictive distribution and the second one is a method called Bayesian estimate. In addition, in the Bayesian approach, the prior distribution has a critical effect on the result of analysis, so we introduce the method using computerized-simulation to elicit an effective prior distribution. For the simplicity, we use exponential and gamma distributions as a likelihood distribution and its natural conjugate prior distribution, respectively. Finally, numerical examples are given to illustrate the potential benefits of the Bayesian approach.
참고문헌 (20)
- "W. H. Probability Concepts in Engineering Planning and Design" (1975), Inc.
- "Back to Bayesics", 109, pp.179~187 (2003)
- "F. Statistical Theory of Reliability and Life Testing" (1981)
- "A Bayesian model to predict the success of the implementation of health and education innovations in school-centered programs", 22, pp.1~11 (1999)
- "F Using AHP in determining the prior distribution on gas pipeline failures in a robust Bayesian approach", 67, pp.275~284 (2000)
- "Bayesian analysis of reliability and hazard rate function of a mixture model", 37(6), pp.953~941 (1997)
- "On Bayesian reliability analysis with informative priors and censoring", 53, pp.97~98 (1996)
- "bootstrap methods and their application" (1997), CAMBRIDGE UNIVERSITY PRESS
- "R. G. An Introduction to the Bootstrap." (1993), CHAPMAN & HALL[DOI]
- "Bayesian Data Analysis" (2000), Champman&Hall
- "Building prior distributions to support Bayesian reliability growth modeling using expert judgement", 74, pp.117~128 (2001)
- "statistical inference an Integrated Approach" (1999), LONDON
- "Hazard plotting of left truncated life data", 22, pp.230~238 (1990)
- "Bayesian enhanced starategic decision making for reliability", 139, pp.133~145 (2002)
- "Setting preventive maintenance schedules when data are sparse", 51, pp.223~234 (1997)
- "Hazard rate estimation from incomplete and unclean warranty data", 81, pp.79~92 (2003)
- "Bayesian aggregation of experts’ judgements on failure intensity", 70, pp.283~289 (2000)
- "Bayes estimation of the mixture of hazard rate model", 55, pp.9~13 (1997)
- "Bayesian parameter estimation in probabilistic risk assessment", 62, pp.89~116 (1998)
- "Tides of change is Bayesianism the new paradigm in statistics?", 113, pp.371~374 (2003)