In experiments and observational studies, scientists gather data to learn more about the world. However, what we can learn from a single data set is always limited, and we are inevitably left with some remaining uncertainty. It is of utmost importance to take this uncertainty into account when drawing conclusions if we want to make real scientific progress. Formalizing and quantifying uncertainty is thus at the heart of statistical methods aiming to obtain insights from data. Numerous research questions in basic science are concerned with comparing multiple scientific theories to understand which of them is more likely to be true, or at least closer to the truth. To compare these theories, scientists translate them into statistical models and then investigate how well the models' predictions match the gathered real-world data. One widely applied approach to compare statistical models is Bayesian model comparison (BMC). Relying on BMC, researchers obtain the probability that each of the competing models is true (or is closest to the truth) given the data. These probabilities are measures of uncertainty and, yet, are also uncertain themselves. This is what we call meta-uncertainty (uncertainty over uncertainties). Meta-uncertainty affects the conclusions we can draw from model comparisons and, consequently, the conclusions we can draw about the underlying scientific theories. However, we have only just begun to unpack and to understand all the implications. This project contributes to this endeavour by developing and evaluating methods for quantifying meta-uncertainty in BMC. Building upon mathematical theory of meta-uncertainty, we will utilize extensive model simulations as an additional source of information, which enable us to quantify so-far implicit yet important assumptions of BMC. What is more, we will be able to differentiate between a closed world, where the true model is assumed to be within the set of considered models, and an open world, where the true model may not be within that set -- a critical distinction in the context of model comparison procedures.
|Project Number||Cyber Valley Project Number: CyVy-RF-2021-16|
|Project Name||Meta Uncertainty in Bayesian Model Comparison|
|Project Duration||December 2021 - November 2024|
|Project Leader||Paul-Christian Bürkner|
|Project Members||Marvin Schmitt, PhD Researcher|
|Project Partners||Stefan Radev, University of Heidelberg|