MVEX01-21-19 Estimation through an empirical Bayes method

​The maximum likelihood estimation is by far the most popular method of statistical inference. One of its fundamental properties is its asymptotic efficiency that guarantees the highest possible accuracy of estimation. The main problem with the method is that it requires finding a maximum of the log-likelihood that maybe a challenging/formidable task. Bayesian estimation is an alternative method that also uses likelihood but it does not maximizes but rather averages it, which usually does not cause any major computational problem. The price to be paid is the controversy of subjectively choosing the so-called prior, which is needed for the Bayesian inference. The controversy can be removed by using empirical prior, i.e. a prior that is data driven and thus not subjective.

There is no unique way of deciding for an empirical prior but we choose the one which is based on empirical distribution of a not-so-good estimator. It can be shown the posterior distribution will lead to efficient estimation. The goal is to assess how efficient the method is when compared with the classical maximum likelihood estimation. The comparison will be performed on several parametric classes of univariate and multivariate distributions.
Rapporten skrivs på svenska (men handledning sker på engelska) .

Projektkod MVEX01-21-19
Gruppstorlek 3-6 studenter 
Målgrupp GU- och Chalmersstudenter. För GU-studenter räknas projektet som ett projekt i Matematisk statistik (MSG900/MSG910).
Projektspecifika förkunskapskrav Sannolikhetsteori och matematisk statistik, kunskap om datorsimuleringar.
Se respektive kursplan för allmänna förkunskapskrav. Utöver de allmänna förkunskapskraven i MVEX01 ska Chalmersstudenter ha avklarat kurser i en- och flervariabelanalys, linjär algebra och matematisk statistik.
Handledare Krzysztof Podgorski, krys.podgorski@gmail.com
Examinator Maria Roginskaya, Ulla Dinger
Institution Matematiska vetenskaper

Publicerad: ti 03 nov 2020.