Computation of posterior distribution in Bayesian analysis – application in an intermittently used reliability system
Author(s) -
Venkata S. Sarma Yadavalli,
Paul Mostert,
Andriëtte Bekker,
M. Botha
Publication year - 2002
Publication title -
suid-afrikaanse tydskrif vir natuurwetenskap en tegnologie/die suid-afrikaanse tydskrif vir natuurwetenskap en tegnologie
Language(s) - English
Resource type - Journals
eISSN - 2222-4173
pISSN - 0254-3486
DOI - 10.4102/satnt.v21i3.231
Subject(s) - bayes' theorem , approximate bayesian computation , posterior probability , bayesian probability , monte carlo method , mathematics , computation , reliability (semiconductor) , statistics , bayesian inference , statistical inference , prior probability , bayesian linear regression , algorithm , inference , computer science , artificial intelligence , physics , power (physics) , quantum mechanics
Bayesian estimation is presented for the stationary rate of disappointments, D∞, for two models (with different specifications) of intermittently used systems. The random variables in the system are considered to be independently exponentially distributed. Jeffreys’ prior is assumed for the unknown parameters in the system. Inference about D∞ is being restrained in both models by the complex and non-linear definition of D∞. Monte Carlo simulation is used to derive the posterior distribution of D∞ and subsequently the highest posterior density (HPD) intervals. A numerical example where Bayes estimates and the HPD intervals are determined illustrates these results. This illustration is extended to determine the frequentistical properties of this Bayes procedure, by calculating covering proportions for each of these HPD intervals, assuming fixed values for the parameters.
Open Access