VVZ API is not affiliated with ETH Zurich. Data might be outdated or incorrect. Please view the official ETHZ Vorlesungsverzeichnis for binding information.
Seminar on Statistics: Inverse Problems in Statistics
Seminar über Statistik: Inverse Problems in Statistics
Last Updated: 2026-02-05 15:18:41
Abstract
Examples of inverse problems are Wicksell's problem,censoring, deconvolution and the indirect regression model.We study minimax lower bounds, plug-in and(nonparametric) maximum likelihood estimators, andalgorithms for computing the maximum likelihood estimator,such as the EM algorithm. Also the asymptotic propertiesof the estimators are examined.
Objective
The seminar is about analyzing the situation where the quantity of interest is indirectly observed, and with moise. An example is when one has noisy observations over time of the speed of a vehicle, and one wants to estimate its location. The seminar will provide a framework for such data, and an overview of modern nonparametric statistics.
Content
A classical inverse problem is Wicksell's corpuscle problem, which basically is on how to estimate the size of holes in a cheese, given some random slice. In the slice, one sees two-dimensional holes. Thus, one has to estimate properties of three-dimensional objects based on two-dimensional observations. Generally, inverse problems are about reconstructions based on indirect observations. This covers the case of censored observations, for example current status data, where one observes at random times whether the mail has arrived, but never its exact arrival time. The statistical problem is to analyze the distribution P(F) of the observations in terms of the unknown distribution F of the unobservable objects. One may then for instance attempt to maximize the likelihood of the observations. Inverse problems are generally ill-posed, that is, the inverse of the map F -> P(F) is unstable. This leads to interesting asymptotic theory as well as interesting computations.
General Information
- Language
- English
- Levels
- BSC , MSC
- Frequency
- Yearly recurring
Examination
- Type
- ungraded semester performance
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| seminar | Seminar über Statistik |
|
2 h weekly |