In Bayesian analysis, empirical and hierarchical methods are two main approaches for the estimation of parameter(s) involved in prior distribution one parameter. But multi-parameter model, e.g., Gamma(α, p), where both parameters unknown, idea ‘Partial Bayes (PB) Estimation’ is introduced. When we do no have proper belief regarding joint variable when estimating parameter presence others, such ...

We consider the problem of inference on one of the two parameters of a probability distribution when we have some prior information on a nuisance parameter. When a prior probability distribution on this nuisance parameter is given, the marginal distribution is the classical tool to account for it. If the prior distribution is not given, but we have partial knowledge such as a fixed number of mo...

PURPOSE Bayesian estimators allow the frequency of visual field progression rates in the population (the prior distribution) to constrain rate estimates for individuals. We examined the benefits of a prior distribution accounting for one of progression's major risk factors--whether intraocular pressure is treated--to gauge the maximum benefit expected from developing priors for other glaucoma r...

Abstract In a Bayesian framework, the Dirichlet distribution is the conjugate distribution to the multinomial likelihood function, and so the analyst is required to develop a Dirichlet prior that incorporates available information. However, as it is a multiparameter distribution, choosing the Dirichlet parameters is less straightforward than choosing a prior distribution for a single parameter,...