Nonparametric estimation, bayesian statistics and MCMC

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The project has three themes.1)  In dimension 2 a random the distribution function of a vector (X,Y) can be represented by the marginal distribution of X and Y and the copula which gives a description on how X and Y interact with each other.  For the extrems value distributions the copula depends on a special function A called the Pickands dependance function.  Moreover A is convex ad satisfies the following condition, max(u,1-u)< A(u) < 1 for all u in (0,1).  I want to estimate A with a bayesian approach in a nonparametric setting.2)  I am interested in the problem of estimating a cdf and also a pdf using a nonparametric approach.  I want to develop estimators which take into account a prior information.  These estimators need to be robust if the prior information is not supported by the sample and they have to be smooth.3)  In many cases, it cost almost nothing to rank observations in a large sample but it is expensive to make measurements.  In this situation ranked set sampling is an approachwhere you make measurements on some specific order statistics instead of sampling randomly.  For the estimation of the mean ranked set sampling reduces the variance of the estimator.  I want to improve on ranked set sampling.