Analysis der maximalen a posteriori Schätzwerten: Gemeinsame Konvergenztheorien für Bayes'sche und variationelle inverse Probleme

• Antragsteller: Professor Timothy Sullivan, Ph.D.
• Fachliche Zuordnung: Mathematik
• Förderung: Förderung von 2019 bis 2022
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 415980428

• Erstellungsjahr: 2023

Zusammenfassung der Projektergebnisse

This project aimed to advance the state of the art in the mathematical understanding of Bayesian inverse problems (BIPs), a common framework for statistical learning, by establishing convergence and stability results for maximum a posteriori (MAP) estimators. A single postdoctoral researcher was funded for two years. The research team was able to establish novel stability results using the framework of Γ-convergence of Onsager–Machlup functionals for the Bayesian posterior measures and these results were accepted for publication in the leading international journal for the field of inverse problems. Further lines of research that are still under investigation.

Projektbezogene Publikationen (Auswahl)

• Γ -convergence of Onsager–Machlup functionals: I. With applications to maximum a posteriori estimation in Bayesian inverse problems. Inverse Problems, 38(2), 025005.
  Ayanbayev; Birzhan; Klebanov; Ilja; Lie; Han, Cheng; Sullivan & T. J.
  
• Γ-convergence of Onsager–Machlup functionals: II. Infinite product measures on Banach spaces. Inverse Problems, 38(2), 025006.
  Ayanbayev, Birzhan; Klebanov, Ilja; Lie, Han Cheng & Sullivan, T. J.
  
• An Order-Theoretic Perspective on Modes and Maximum A Posteriori Estimation in Bayesian Inverse Problems. SIAM/ASA Journal on Uncertainty Quantification, 11(4), 1195-1224.
  Lambley, Hefin & Sullivan, T. J.