There is a fundamental tension in empirical analysis in economics between relying on prior beliefs based on theory and empirical evidence - encoded in classical hypotheses or in Bayesian priors - and letting data speak “freely”. To what extent can and should theory be used to impose restrictions on parameterized models? With the availability of ever larger data sets in many areas (financial transactions, medical records, consumer purchase histories etc.), these issues are becoming increasingly important. The panel will discuss new and old methods to meet these challenges.