Computation Of Optimal Bayesian Credible SetsFor The Binomial And Poisson Distributions
Laxmi P. Gewali, Simeon C. Ntafos, Anupma Singh · WIT transactions on modelling and simulation · 1970
In the classical framework of statistical inference, the unknown parameter of interest is considered to be a constant, and a classical confidence interval for the parameter is a random interval (L, U) that contains the unknown parameter with a specified high probability. Such a confidence interval is usually derived from the probability distribution of a pivotal quantity. The problem of computing a classical confidence interval becomes somewhat intractable in case a pivotal quantity cannot be found. A Bayesian confidence interval, which is called a Bayesian credible set in Bayesian literature, is an alternative that does not have this drawback. In Bayesian inference, the parameter of interest itself is considered to be a random variable with a prior probability distribution. One reason that the Bayesian confidence interval estimation is not as popular as its classical version is that its computation can become quite complicated. We present an algorithm based on computational geometry for