**Preface to "The 40th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering"**

#### **40-years anniversary: MaxEnt and Bayesian Inference**

This workshop series was initiated by Myron Tribus and Edwin T. Jaynes, and organised for the first time by C.Ray Smith and Walter T. Grandy in 1981 at the University in Wyoming. Since then, tremendous progress has been made and the number of publications based on Bayesian methods is impressive.

The workshops are a platform for the presentation of new, sometimes highly revolutionary and ambitious ideas, and for lively and controversial discussions. Some of these ideas have proved very fruitful over the years and have also found their way into other disciplines, while others have proved useless. This year's workshop was also a platform for a mix of ideas that are unanimously considered valuable and correct, and ideas that may have very high potential but are still disputed. We believe that it is in the spirit of the workshop and the conference proceedings to give these ideas a forum for further discussion.

Due to the COVID-19 pandemic, the 2020 workshop had to be cancelled and this year's workshop was held online; however, the lively atmosphere was still unbroken.

In agreement with the general framework of the annual workshop, and due to the broad applicability of Bayesian inference, this year's presentations cover many research areas, such as physics (e.g., plasma physics, astro-physics, statistical mechanics, foundations of quantum mechanics), geodesy, biology, medicine, phonetics, ecology, hydrology, measure theory, image reconstruction, computational engineering, machine learning, and, quite appropriately, epidemiology.

We would like to thank TU Graz and Entropy (MDPI) for their institutional and financial support, as well as Brigitte Schwarz, Stefan Schmutzler and Sabine Pucher for their organizational support. Finally, we thank all authors and speakers as well as the reviewers for their invaluable contributions, and all participants for a constructive and inspiring debate.

Wolfgang von der Linden is a full professor and head of the institute of Theoretical and Computational Physics at TU Graz (Austria). His research focuses on strongly correlated many body physics and Bayesian probability theory, which in 30 years has led to more than 100 papers on this topic. He has collected his wealth of experience together with Volker Dose and Udo von Toussaint, both from the IPP in Garching (Germany) in the book "Bayesian probability theory: applications in the physical sciences", Cambridge University Press, 2014.

Sascha Ranftl is a post-doctoral researcher at the Institute of Theoretical and Computational Physics and Graz Center of Computational Engineering at TU Graz (Austria). His research interests are Bayesian probability theory, physics-informed machine learning, uncertainty quantification for computer simulations and their applications to (biomedical) engineering problems such as the mechanics or detection of aortic dissections.

> **Wolfgang von der Linden, Sascha Ranftl** *Editors*
