B0748
Title: How to think about model assumptions
Authors: Christian Hennig - University of Bologna (Italy) [presenting]
Abstract: The starting point is the apparently popular idea that in order to do (frequentist) model-based inference we need to believe that the model is true, and the model assumptions need to be fulfilled. We will argue that this is a misconception. Models are, by their very nature, not ``true'' in reality. Mathematical results secure favourable characteristics of inference in an artificial model world in which the model assumptions are fulfilled. For using a model in reality we need to ask what happens if the model is violated in a ``realistic'' way. One key approach is to model a situation in which certain model assumptions of the method that we want to apply, are violated, in order to find out what happens then. This, somewhat inconveniently, depends strongly on what we assume, how the model assumptions are violated, whether we make an effort to check them, how we do that, and what alternative actions we take if we find them wanting. We will discuss what we know and what we can't know regarding the appropriateness of the models that we ``assume'', and how to interpret them appropriately, including new results on conditions for model assumption checking to work well, and on untestable assumptions.
