Some robustness issues in predictive sequential elicitation of an exchangeable binary process

Let us consider an exchangeable binary sequence "X_1,...,X_n,...$ and suppose one is only able to partially specify a finite number of features of the process. We investigate the problem of computing ranges of the conditional prediction of a future observations given the outcome of an initial sequence. A solution of the variational problem has been characterized in Tardella (2009) so that the computations is further simplified. We investigate the situation where a full specification of the law of the process is not available and one is only able to specify finitely many features of the law. In fact, this could be accomplished through a sequential elicitation of the finite-dimensional distributions starting from n = 1 up to a finite integer say n = k. her simplified. A pathological and counterintuitive behavior of ranges of predictions is revealed when more and more data are observed and the asymptotic behavior of such ranges can be derived through the previous characterization of the extremal solution.