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Research and development in computer science and statistics have producedincreasingly sophisticated software interfaces for interactive and exploratoryanalysis, optimized for easy pattern finding and data exposure. But designphilosophies that emphasize exploration over other phases of analysis riskconfusing a need for flexibility with a conclusion that exploratory visualanalysis is inherently model-free and cannot be formalized. We describe howwithout a grounding in theories of human statistical inference, research inexploratory visual analysis can lead to contradictory interface objectives andrepresentations of uncertainty that can discourage users from drawing validinferences. We discuss how the concept of a model check in a Bayesianstatistical framework unites exploratory and confirmatory analysis, and howthis understanding relates to other proposed theories of graphical inference.Viewing interactive analysis as driven by model checks suggests new directionsfor software and empirical research around exploratory and visual analysis. Forexample, systems should enable specifying and explicitly comparing data to nulland other reference distributions and better representations of uncertainty.Implications of Bayesian and other theories of graphical inference should betested against outcomes of interactive analysis by people to drive theorydevelopment.

To design interfaces for exploratory data analysis, we need theories of graphical inference