**Dipartimento
di Statistica "Giuseppe Parenti"
**

**A
Course on Mixture Models: Outline **

**Dankmar
Böhning, Free University of Berlin**

**Program**

**Monday, November 29**: Introduction- 09:30 - 12:30
- Population heterogeneity: the natural
genesis of mixture models
- Some examples
- Parametric or nonparametric mixture models?
- 14:00 - 16:30
- Connection to empirical Bayes estimation
- Classification using posterior Bayes
- Missing covariates and mixture models

**Tuesday, November 30**: Theory of nonparametric mixture models- 09:30 - 12:30
- The likelihood and its properties
- The directional derivative and the
gradient function
- The general mixture maximum likelihood
theorem
- Applications of the theorem
- 14:00 - 16:30
- Existence and number of support points
of the NPMLE
- A case study on the Simar's accident
data
- Exercises on real data sets: homogeneity
or heterogeneity? (Tutored by Tan Böhning)
- Diagnostic tests for heterogeneity
- Testing the number of components with
the likelihood ratio

**Wednesday, December 1**: Algorithms- 09.30 - 12.30
- Finding the number of components
- The vertex direction method (VDM)
- The vertex exchange method (VEM)
- Step-length choices
- Introducing C.A.MAN
- 14:00 - 16:30
- Number of components known
- The EM algorithm for mixture models
- Mixing normls with different variance
components
- Exercises with C.A.MAN (Tutored by Tan
Böhning)

**Thursday, December 2**: Applications of Mixtures: Meta-Analysis- 09:30 - 12:30
- The conventional approach
- Strategies of optimal pooling and a
likelihood approach
- Heterogeneity
- Classification of studies using
posterior Bayes
- 14:00 - 16:30
- Introducing META
- Exercises with META (Tutored by Tan
Böhning)
- Adjusting for heterogeneity using
DerSimonian-Laird
- Adjusting for heterogeneity using
Sarol-Böhning

**Friday, December 3**: Applications of Mixtures: Disease Mapping- 09:30 - 12:30
- The conventional approach
- Empirical Bayes estimators and their
maps
- Estimating map heterogeneity -
estimating the prior
- Heterogeneity in perinatal mortality for
the North West Thames Health Region - data: a case study
- 14:00 - 16:30
- Introducing DISMAP
- Exercises with DISMAP (Tutored by Tan
Böhning)
- Adjusting for heterogeneity using
DerSimonian-Laird

The course will give a
state-of-the-art introduction into the area and various field appliactions. The
course will use the book by the author on mixture models:

Dankmar Böhning (1999) *Computer-Assisted Analysis of Mixtures with
Applications: Meta-Analysis, Disease mapping and Others*. Chapman & Hall
/CRC, Boca Raton.

Dipartimento di Statistica Giuseppe
Parenti |
Information: Annibale Biggeri |