Bayesian nonparametric estimation of the median. I: Computation of the estimates (Q1072290)

Let \(X_ 1,...,X_ n\) be a random sample from a population with distribution function (d.f.) F(x-\(\theta)\), where F(x) has a median equal to zero, but otherwise is assumed unknown or only partially known. The problem of Bayesian estimation of \(\theta\) is considered. Priors are put on the pair (F;\(\theta)\). The priors on F concentrate all their mass on d.f.'s with median equal to zero. These priors include ''Dirichlet-type'' ones. The marginal posterior distribution of \(\theta\) given \(X_ 1,...,X_ n\) is computed, and the mean of the posterior is taken as the estimator of \(\theta\).