A useful non-parametric class of priors is formed as those probability measures which lie between an upper and a lower measure and it is called a Wand of probability measures Lavine (1991), Moreno and Pericchi (1991), Wasserman and Kadane (1992). This class allows considerable freedom in tail behaviour as long as the upper and lower measures have different tails. This property is inherited from the class of Interval of measures DeRobertis and Hartigan (1981), from which the Band of probability measures class is obtained by restricting attention to those measures that integrate to one, Although the analysis of this restricted class is somewhat more involved, the restriction is quite natural and may lead to robustness in situations in which the larger class is not robust. In fact, it is a generalization of the class implicitly considered by Edwards, Lindman and Savage (1963) in “Precise Measurement Theory”. An empirical analysis is performed with the two classes above. That is, we choose within a class of priors that measure which maximizes the probability of the actual data Good (1983). This “optimal” measure is used in this robust Bayesian context to assess the band of probability m
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