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401-5008-22L 2 Credits DR D-MATH

Bayesian Non-Linear Inverse Problems: Statistical and Computational Guarantees

Lecturers: Prof. Dr. Richard Nickl
Only for ETH D-MATH doctoral students and for doctoral students from the Institute of Mathematics at UZH. The latter need to register the course unit via the Registrar's Office ( ).
VVZ CR n/a

Last Updated: 2026-02-05 16:07:27

Abstract

Nachdiplom lecture

Content

Common examples for non-​linear inverse problems range from parameter identification in PDEs to tomography and data assimilation problems. They naturally involve high-​ or infinite dimensional parameter spaces and appropriate statistical noise models lead to a class of non-​convex inference problems that present substantial challenges in contemporary data science. In influential work, Andrew Stuart (2010) has proposed a unified Bayesian approach to solve such problems. It is computationally feasible via Gaussian process priors and high-​dimensional MCMC algorithms and provides important uncertainty quantification methodology ('error bars' or confidence regions) based on posterior distributions. Despite evident empirical success, the theoretical understanding of the performance of such methods has been limited until recently. Specifically in non-​linear settings Bayesian methods are distinct from optimisation based algorithms and their analysis requires a very different set of mathematical ideas. In these lectures we will summarise recent developments that allow to give rigorous statistical and computational guarantees for the use of these algorithms in high-​dimensional and non-​convex settings. The general theory will be illustrated in two non-​linear model examples arising with elliptic partial differential equations. A standard background in probability and measure, statistics and real analysis will be sufficient to follow this course.

General Information

Language
English
Levels
DR

Examination

Type
ungraded semester performance

Registration & Places

Priority: Registration for the course unit is only possible for the primary target group

Course Components

Type Title Time & Place Hours
lecture Bayesian Non-Linear Inverse Problems: Statistical and Computational Guarantees
  • Wed 10:15-12:00 (HG G 19.1)
  • 16.03 Date 10:15-12:00 (HG E 3)
  • 23.03 Date 10:15-12:00 (HG G 19.1)
2 h weekly

Offered In

  • Doctorate Mathematics (More Information at: )
    • Subject Specialisation (The list of courses (together with the allocated credit points) eligible for doctoral students is published each semester in the newsletter of the ZGSM.)
      • Graduate School (Official website of the Zurich Graduate School in Mathematics: In addition to the 401-....-DRL course units, adapted versions for doctoral students of the following course units: 263-4400-00L Advanced Graph Algorithms and Optimization 401-3902-21L Network & Integer Optimization: From Theory to Application 401-3904-22L Convex Optimization 401-3629-00L Quantitative Risk Management 401-3652-00L Numerical Methods for Hyperbolic Partial Differential Equations 151-0530-00L Nonlinear Dynamics and Chaos II 227-0434-10L Mathematics of Information 401-4490-22L Topology Optimization of Engineering Systems ... (continued ))