We consider an individual whose theory of her environment is incomplete

and who therefore is concerned that data are correlated and heterogeneous

in some unknown fashion. We provide a unified normative axiomatic model

of both inference and choice for such an individual. A prime example is an

analyst or policy-maker facing a cross-section of markets in which firms play

an entry game. Her theory is Nash equilibrium and it is incomplete because

there are multiple equilibria and she does not understand how equilibria are

selected. This leads to partial identification of parameters when drawing

inferences from realized outcomes in some markets and to ambiguity when

considering (policy) decisions for other markets. The central component of

the model is a generalization of de Finetti's exchangeable Bayesian model to

accommodate ambiguity. The broad message of the paper is that ambiguity

aversion can be fruitfully applied to partially identified models.