Reflections on the Foundations of Probability and Statistics

Thomas Augustin is Professor of Statistics at Ludwig-Maximilians-Universitat Munchen (LMU Munich), where he heads the "Foundations of Statistics and their Applications" Lab. His research interest is to develop set-valued methods for reliable statistical inference, decision making, and machine learning. For this, he utilizes concepts from imprecise probabilities and partial identification to cope with different kinds of complex uncertainty, like non-randomly missing or coarsened data, non-standard measurement error, ambiguity, conflicting information, and structural model indeterminacy. Fabio G. Cozman is Professor of Computer Science at Escola Politecnica, Universidade de Sao Paulo (USP), Director of the Center for Artificial Intelligence at USP, with an interest in machine learning and knowledge/uncertainty representation. Engineer (USP) and PhD (Carnegie Mellon University, USA), he has served as Program and General Chair of the Conference on Uncertainty in Artificial Intelligence, Area Chair of the International Joint Conference on Artificial Intelligence, and Associate Editor of the Artificial Intelligence Journal, the Journal of Artificial Intelligence Research, and the Journal of Approximate Reasoning. Gregory Wheeler is Professor of Philosophy and Computer Science at Frankfurt School of Finance & Management, where he heads the Center for Human & Machine Intelligence and is Academic Director of the Master of Applied Data Science program. His research interests concern the foundations of probability, bounded rationality, and decision-making under uncertainty involving underspecified models, conflicting information, computational resource bounds, and indeterminacy. He also-founded Exaloan AG, a Frankfurt-based financial services software company, where he is Head of Machine Learning.

An Interview with Teddy Seidenfeld.- The Value Provided by a Scientific Explanation.- A Gentle Approach to Imprecise Probability.- Foundations For Temporal Reasoning Using Lower Previsions Without A Possibility Space.- On the Equivalence of Normal and Extensive Form Representations of Games.- Dilation and Informativeness.- Playing with Sets of Lexicographic Probabilities and Sets of Desirable Gambles.- How to Assess Coherent Beliefs: A Comparison of Different Notions of Coherence in Dempster-Shafer Theory of Evidence.- Expected Utility in 3D.- On the Normative Status of Mixed Strategies.- On a Notion of Independence Proposed by Teddy Seidenfeld.- Coherent Choice Functions without Archimedeanity.- Quantifying Degrees of E-admissibility in Decision Making with Imprecise Probabilities.