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Foto: Matthias Friel

Bayesian nonparametric inference - Einzelansicht

Veranstaltungsart Vorlesung/Seminar Veranstaltungsnummer
SWS 6 Semester SoSe 2022
Einrichtung Institut für Mathematik   Sprache englisch
Belegungsfrist 01.04.2022 - 10.05.2022

Belegung über PULS
Gruppe 1:
     jetzt belegen / abmelden
    Tag Zeit Rhythmus Dauer Raum Lehrperson Ausfall-/Ausweichtermine Max. Teilnehmer/-innen
Einzeltermine anzeigen
Vorlesung Mi 08:15 bis 09:45 wöchentlich 20.04.2022 bis 27.07.2022  2.09.0.12 Jun. Prof. Dr. Lie  
Einzeltermine anzeigen
Vorlesung Do 08:15 bis 09:45 wöchentlich 21.04.2022 bis 28.07.2022  2.09.0.12 Jun. Prof. Dr. Lie  
Einzeltermine anzeigen
Seminar Fr 14:15 bis 15:45 wöchentlich 22.04.2022 bis 29.07.2022  2.09.1.10 Jun. Prof. Dr. Lie  
Kurzkommentar

This is an advanced course on mathematical statistics that will focus on the theory of Bayesian nonparametric statistics. It is targeted for students who are strongly interested in proofs.

Kommentar

This is an advanced course that will study some parts of the theory of Bayesian nonparametric inference.

Bayesian nonparametric inference is an important and active research area within mathematical statistics. The main goal is to infer an unknown infinite-dimensional parameter, such as a function, using observations from statistical experiments. The main object of interest is the posterior probability measure, which describes the distribution of the unknown parameter.

The course will be organised around 4-hour lectures and a 2-hour seminar.

Interested participants are required to register on PULS, or if this is not possible, to e-mail the lecturer.

Literatur

Subhashis Ghosal and Aad van der Vaart, "Fundamentals of Nonparametric Bayesian Inference", Cambridge University Press, 2017.

Voraussetzungen

In order to benefit from this course, participants should know the following, or be prepared to learn the material on their own.

Measure-theory: measurable spaces, measures, supports of measures, absolute continuity with respect to a measure, measurable mappings, Borel sigma-algebra, monotone convergence theorem, dominated convergence theorem, Fubini-Tonelli theorem, Fatou's lemma, etc.

Measure-theoretic probability theory: probability measures, random variables, pushforward measure / image measures, conditional expectations, different types of convergence of random variables, limit superior and limit inferior of events, Borel-Cantelli lemmas, Markov's inequality, Markov kernels, etc.

Real analysis: series and sequences, limits, limit inferior and limit superior, Taylor expansions, metric spaces

Functional analysis: function spaces (e.g. Hölder, Sobolev), norms on function spaces

Leistungsnachweis

Participants who take the course for 9 LP must give one seminar presentation of 90 minutes. The seminar topic will be arranged by the lecturer.

Participants who take the course for 6 LP are not required to give a seminar presentation.

All participants who take the course for credit must take a 30-minute oral examination. The examination will be based only on the material from the lectures.

The participant's grade on the exam will be their grade for the course.

Lerninhalte

The lectures of this course will focus on proofs and some analytical examples, most often from regression problems.

-Brief overview of some results from probability theory

-Priors on function spaces

-Posterior consistency

-Posterior contraction rates

 If time permits, we will also cover additional advanced topics in Bayesian nonparametric inference, such as adaptive posterior contraction.

 

This course will not cover the following:

-Dirichlet priors or priors on spaces of probability measures

-Numerical computations

Zielgruppe

The target audience for this course are participants who have the following:

-a very strong foundation in measure-theoretic probability and analysis;

-a strong interest in proofs; and

-a large amount of self-motivation and endurance.


Strukturbaum
Keine Einordnung ins Vorlesungsverzeichnis vorhanden. Veranstaltung ist aus dem Semester SoSe 2022 , Aktuelles Semester: SoSe 2024