Suesse, Thomas F. Dr.

Estimation for Spatial Auto-regressive Models under the presence of Missing Data

Spatial auto-regressive (SAR) models  are popular models for a finite number of spatially correlated units. Estimation, for example via Maximum likelihood is well established for fully observed units.  However when missing units are present, estimation of model parameters referring to all units is not straightforward. In the project, estimation of a range models including prediction will be considered under the presence of missing units. There are many SAR related models and the same estimation problem applies to all of them.

Estimation of Effects referring to Latent Variables in Poisson Mixed Models

A Poisson Mixed Model is a popular model for counts. When the explanatory variables are not observed for locations of the response variables but for other locations, estimation is complicated. This project will consider various estimation methods to estimate the effects referring to this "unobserved" explanatory variable. 

Variance Estimation in Mixture Models

Mixture models are popular models for classification. The underlying assumption is often that the component distributions are multivariate normal. Estimation of such a mixture is often via maximum likelihood. Then the variance parameters are often underestimated. In this project, you aim at improving upon variance estimates not only for improved efficiency, but also aiming for improved classification rate.

A common model approach to multivariate binary data is to apply a log-linear model. Log-linear models are useful for describing the joint distribution, but not useful for describing the marginal distribution. A simpler and more effective approach is to apply a generalized linear model (GLM), but it does not account for the dependence of the binary observations. A standard approach that accounts for this dependence is to use generalized estimating equations (GEE). Another less widely known approach is to apply a log-linear model and to constrain the model by a GLM. However current fitting techniques using the iterative proportional fitting (IPF) algorithm are infeasible for large cluster-sizes. The PhD project would focus on the use of Markov-Chain-Monte-Carlo (MCMC) techniques to overcome the limitations of the IPF algorithm. The standard assumption for the model approach is to have equal cluster sizes, the project would also focus on overcoming this limitation, considering smaller cluster sizes as clusters with missing data.

Another related topic would focus on the use of a hybrid method combining generalized mixed models (GLMMs) and marginal models (GLMs). The investigator might be interests in a marginal model that still accounts for some of the variations of model parameters, but not to all. For example in a multi-centre clinical trial, multiple observations might be recorded for each patient and the standard treatment would be compared to a new treatment. Then neither the marginal nor the GLMM approach would be suitable. The PhD project would explore effective model fitting techniques and explore usefulness of such an approach in other applications.

Networks, or mathematical graphs, are an important tool for representing relational data, i.e. data on the existence, strength and direction of relationships between interacting actors. Types of actors include individuals, firms and countries. Modeling networks has become more and more important, in particular caused by negative developments in terrorists networks over the past decade, and the currently most widely used class of models are Exponential Random Graph Models (ERGMs). This model approach is useful to explain the underlying generating structure of these data, but is limited in many ways. The PhD project would focus on developing other model approaches that overcome the limitations of ERGMs, for example exploring the use of marginal and transitional models for network data, among others. It also includes theoretical aspects, as consistency of model parameters under non-informative sampling and many more aspects.

Estimation for Spatial Auto-regressive Models under the presence of Missing Data

Spatial auto-regressive (SAR) models  are popular models for a finite number of spatially correlated units. Estimation, for example via Maximum likelihood is well established for fully observed units.  However when missing units are present, estimation of model parameters referring to all units is not straightforward. In the project, estimation of a range models including prediction will be considered under the presence of missing units. There are many SAR related models and the same estimation problem applies to all of them.

Estimation of Effects referring to Latent Variables in Poisson Mixed Models

A Poisson Mixed Model is a popular model for counts. When the explanatory variables are not observed for locations of the response variables but for other locations, estimation is complicated. This project will consider various estimation methods to estimate the effects referring to this "unobserved" explanatory variable. 

Variance Estimation in Mixture Models

Mixture models are popular models for classification. The underlying assumption is often that the component distributions are multivariate normal. Estimation of such a mixture is often via maximum likelihood. Then the variance parameters are often underestimated. In this project, you aim at improving upon variance estimates not only for improved efficiency, but also aiming for improved classification rate.

A common model approach to multivariate binary data is to apply a log-linear model. Log-linear models are useful for describing the joint distribution, but not useful for describing the marginal distribution. A simpler and more effective approach is to apply a generalized linear model (GLM), but it does not account for the dependence of the binary observations. A standard approach that accounts for this dependence is to use generalized estimating equations (GEE). Another less widely known approach is to apply a log-linear model and to constrain the model by a GLM. However current fitting techniques using the iterative proportional fitting (IPF) algorithm are infeasible for large cluster-sizes. The PhD project would focus on the use of Markov-Chain-Monte-Carlo (MCMC) techniques to overcome the limitations of the IPF algorithm. The standard assumption for the model approach is to have equal cluster sizes, the project would also focus on overcoming this limitation, considering smaller cluster sizes as clusters with missing data.

Another related topic would focus on the use of a hybrid method combining generalized mixed models (GLMMs) and marginal models (GLMs). The investigator might be interests in a marginal model that still accounts for some of the variations of model parameters, but not to all. For example in a multi-centre clinical trial, multiple observations might be recorded for each patient and the standard treatment would be compared to a new treatment. Then neither the marginal nor the GLMM approach would be suitable. The PhD project would explore effective model fitting techniques and explore usefulness of such an approach in other applications.

Networks, or mathematical graphs, are an important tool for representing relational data, i.e. data on the existence, strength and direction of relationships between interacting actors. Types of actors include individuals, firms and countries. Modeling networks has become more and more important, in particular caused by negative developments in terrorists networks over the past decade, and the currently most widely used class of models are Exponential Random Graph Models (ERGMs). This model approach is useful to explain the underlying generating structure of these data, but is limited in many ways. The PhD project would focus on developing other model approaches that overcome the limitations of ERGMs, for example exploring the use of marginal and transitional models for network data, among others. It also includes theoretical aspects, as consistency of model parameters under non-informative sampling and many more aspects.