The recent spate of theoretical models of behaviour under ambiguity can be partitioned into two sets: those involving multiple priors (in which the probabilities of the various events are not known but probabilities can be attached to the various possible values for the probabilities) and those not involving multiple priors. This paper concentrates on the first set and provides an experimental investigation into recently proposed theories. Using an appropriate experimental interface, in which the probabilities on the various possibilities are explicitly stated, we examine the fitted and predictive power of the various theories. We first estimate subject-by-subject, and then we estimate and predict using a mixture model over the contending theories. The individual estimates suggest that 24% of our 149 subjects have behaviour consistent with Expected Utility, 56% with the Smooth Model (of Klibanoff et al, 2005), 11% with Rank Dependent Expected Utility and 9% with the Alpha Model (of Ghirardato et al 2004); these figures are close to the mixing proportions obtained from the mixture estimates. If we classify our subjects through the posterior probabilities (given all the evidence) of each of them being of the various types: using the estimates we get 25%, 50%, 20% and 5% (for EU, Smooth, Rank Dependent and Alpha); while using the predictions 22%, 53%, 22% and 3%. Interestingly the Smooth model seems to fare the best.