A Bayesian Analysis for Repeated Measurements Adopting a More Informative New Prior for Updating Predicted Mortality Rate After the Cardiac Surgery Activity

Abstract

In this paper, a repeated predicted measurements, using Bayesian approach is considered to filter non appropriate priors from a pool of prior information on (0,1) interval. We used data on mortality rates after the cardiac surgery activity in the UK and Ireland between the years 2003 to 2012. One of a member of this pool is a new proposed unit interval prior (uitp). In repeated Bayesian analysis, the most appropriate prior will be the one which is more informative for mortality rates update and adjustment. The performance of the proposed prior (utip) is found to be the most satisfactory working mechanism prior information, for the particular data set, before observing the data. By using Markov chain Monte Carlo simulation, posterior summaries required for an uncertain parameter are obtained for this particular data set. To show the performance and importance of proposed new prior, we considered Jeffreys' prior (non-informative), Kumaraswamy’s prior (partly informative) and conventional beta prior (informative) and update the prior information with that of proposed new prior under the same conditions. This opens the way to richer, more reliable and consistent inference summaries and avoids the numerical problems that are encountered with non-Bayesian methods.