An improved method of estimating Bayes posterior probability density function in reliability data analysis

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This paper analyses a phenomenon which occurs when a Bayes posterior pdf is used repeatedly as prior pdf to calculate new posterior pdf. The example of conjugate prior beta function and binomial test data is discussed. The discussion shows that in the process of re-using posterior pdf as prior pdf, the variance of the newly obtained posterior pdf may decrease remarkably with the increasing number of re-use times. This phenomenon is not in accord with the observed binomial test data. The discussion reveals a deficiency existing in the above currently used Bayes method. Finally, a modified method is proposed to get a more satisfactory Bayes posterior pdf.