Bayes computation for reliability estimation

Bayes estimation of complicated functions requires simpler estimation techniques due to the mathematical difficulties involved in the classical Bayes approach. Bayes estimation enjoys many approximation techniques and computational methods like Metropolis, and Gibbs sampler. Bayes estimation of the reliability of a mixture inverse Gaussian distribution requires a numerical approach since the calculations are immensely difficult from the exact Bayes point of view. Lack of full conditional prior distributions for all 3 parameters of this particular case makes the use of Gibbs sampler inefficient. Application of the rejection method, however, is reasonable since it is very simple to implement without any constraints on the prior distributions or on the hyper-parameters.