Fakultät für Mathematik, Informatik und Statistik - Digitale Hochschulschriften der LMU - Teil 01/02 Archiv

The conservation of continuous symmetries in two-dimensional systems with interaction is a classical subject of statistical mechanics. Here we establish such a result for internal transformations and spatial translations of Gibbsian systems of marked particles with two body-interaction, where the interesting cases of of singular, hard-core and discontinuous interaction are included.

As measurement of gene expression using microarrays has become a standard high throughput method in molecular biology, the analysis of gene expression data is still a very active area of research in bioinformatics and statistics. Despite some issues in quality and reproducibility of microarray and derived data, they are still considered as one of the most promising experimental techniques for the understanding of complex molecular mechanisms. This work approaches the problem of expression data analysis using contextual information. While all analyses must be based on sound statistical data processing, it is also important to include biological knowledge to arrive at biologically interpretable results. After giving an introduction and some biological background, in chapter 2 some standard methods for the analysis of microarray data including normalization, computation of differentially expressed genes, and clustering are reviewed. The first source of context information that is used to aid in the interpretation of the data, is functional annotation of genes. Such information is often represented using ontologies such as gene ontology. GO annotations are provided by many gene and protein databases and have been used to find functional groups that are significantly enriched in differentially expressed, or otherwise conspicuous genes. In gene clustering approaches, functional annotations have been used to find enriched functional classes within each cluster. In chapter 3, a clustering method for the samples of an expression data set is described that uses GO annotations during the clustering process in order to find functional classes that imply a particularly strong separation of the samples. The resulting clusters can be interpreted more easily in terms of GO classes. The clustering method was developed in joint work with Henning Redestig. More complex biological information that covers interactions between biological objects is contained in networks. Such networks can be obtained from public databases of metabolic pathways, signaling cascades, transcription factor binding sites, or high-throughput measurements for the detection of protein-protein interactions such as yeast two hybrid experiments. Furthermore, networks can be inferred using literature mining approaches or network inference from expression data. The information contained in such networks is very heterogenous with respect to the type, the quality and the completeness of the contained data. ToPNet, a software tool for the interactive analysis of networks and gene expression data has been developed in cooperation with Daniel Hanisch. The basic analysis and visualization methods as well as some important concepts of this tool are described in chapter 4. In order to access the heterogeneous data represented as networks with annotated experimental data and functions, it is important to provide advanced querying functionality. Pathway queries allow the formulation of network templates that can include functional annotations as well as expression data. The pathway search algorithm finds all instances of the template in a given network. In order to do so, a special case of the well known subgraph isomorphism problem has to be solved. Although the algorithm has exponential running time in the worst case, some implementation tricks make it run fast enough for practical purposes. Often, a pathway query has many matching instances, and it is important to assess the statistical significance of the individual instances with respect to expression data or other criteria. In chapter 5 the pathway query language and the pathway search algorithm are described in detail and some theoretical properties are derived. Furthermore, some scoring methods that have been implemented are described. The possibility of combining different scoring schemes for different parts of the query result in very flexible scoring capabilities. In chapter 6, some applications of the methods are described, using public data sets as well as data sets from research projects. On the basis of the well studied public data sets, it is demonstrated that the methods yield biologically meaningful results. The other analyses show how new hypotheses can be generated in more complex biological systems, but the validation of these hypotheses can only be provided by new experiments. Finally, an outlook is given on how the presented methods can contribute to ongoing research efforts in the area of expression data analysis, their applicability to other types of data (such as proteomics data) and their possible extensions.

Many areas of applied statistics have become aware of the problem of measurement error-prone variables and their appropriate analysis. Simply ignoring the error in the analysis usually leads to biased estimates, like e.g. in the regression with error-prone covariates. While this problem has been discussed at length for parametric regression, only few methods exist to handle nonparametric regression under error, which are usually either computer intensive or little effective. This thesis develops new methods achieving the correction quality of state of the art methods while demanding only a trickle of their computing time. These new methods use the so-called relevance vector machine (RVM) for nonparametric regression - now enhanced by correction methods based on the ideas of regression calibration, the so-called SIMEX and Markov Chain Monte Carlo (MCMC) correction. All methods are compared in simulation studies regarding Gaussian, binary and Poisson responses. This thesis also discusses the case of multiple error-prone covariates. Furthermore, a MCMC based correction method for nonparametric regression of binary longitudinal data with covariate measurement error is introduced. This data scenario is often encountered, e.g. in epidemiological applications.

In dieser Arbeit werden Deformationen Riemannscher Flächen auf elementare Weise mittels Integration von Vektorfeldern konstruiert. Diese Deformationen werden zum feinen Modulraum der Riemannschen Flächen mit Teichmüller-Markierung zusammengeklebt. Die Vorgehensweise unterscheidet sich wesentlich von den analytischen Beweisen Teichmüllers und den algebraisch geometrischen Beweisen Grothendiecks.

Die vorliegende Arbeit beschäftigt sich mit der statistischen Modellierung und Inferenz genetischer Netzwerke. Assoziationsstrukturen und wechselseitige Einflüsse sind ein wichtiges Thema in der Systembiologie. Genexpressionsdaten weisen eine hohe Dimensionalität auf, die geringen Stichprobenumfängen gegenübersteht ("small n, large p"). Die Analyse von Interaktionsstrukturen mit Hilfe graphischer Modelle ist demnach ein schlecht gestelltes (inverses) Problem, dessen Lösung Methoden zur Regularisierung erfordert. Ich schlage neuartige Schätzfunktionen für Kovarianzstrukturen und (partielle) Korrelationen vor. Diese basieren entweder auf Resampling-Verfahren oder auf Shrinkage zur Varianzreduktion. In der letzteren Methode wird die optimale Shrinkage Intensität analytisch berechnet. Im Vergleich zur klassischen Stichprobenkovarianzmatrix besitzt speziell diese Schätzfunktion wünschenswerte Eigenschaften im Sinne von gesteigerter Effizienz und von kleinerem mittleren quadratischen Fehler. Außerdem ergeben sich stets positiv definite und gut konditionierte Parameterschätzungen. Zur Bestimmung der Netzwerktopologie wird auf das Konzept graphischer Gaußscher Modelle zurückgegriffen, mit deren Hilfe sich sowohl marginale als auch bedingte Unabhängigkeiten darstellen lassen. Es wird eine Methode zur Modellselektion vorgestellt, die auf einer multiplen Testprozedur mit Kontrolle der False Discovery Rate beruht. Dabei wird die zugrunde liegende Nullverteilung adaptiv geschätzt. Das vorgeschlagene Framework ist rechentechnisch effizient und schneidet im Vergleich mit konkurrierenden Verfahren sowohl in Simulationen als auch in der Anwendung auf molekulare Daten sehr gut ab.

Due to the increasing availability of spatial or spatio-temporal regression data, models that allow to incorporate the special structure of such data sets in an appropriate way are highly desired in practice. A flexible modeling approach should not only be able to account for spatial and temporal correlations, but also to model further covariate effects in a semi- or nonparametric fashion. In addition, regression models for different types of responses are available and extensions require special attention in each of these cases. Within this thesis, numerous possibilities to model non-standard covariate effects such as nonlinear effects of continuous covariates, temporal effects, spatial effects, interaction effects or unobserved heterogeneity are reviewed and embedded in the general framework of structured additive regression. Beginning with exponential family regression, extensions to several types of multicategorical responses and the analysis of continuous survival times are described. A new inferential procedure based on mixed model methodology is introduced, allowing for a unified treatment of the different regression problems. Estimation of the regression coefficients is based on penalized likelihood, whereas smoothing parameters are estimated using restricted maximum likelihood or marginal likelihood. In several applications and simulation studies, the new approach turns out to be a promising alternative to competing methodology, especially estimation based on Markov Chain Monte Carlo simulation techniques.

This thesis discusses a latent variable model (LVM) which is based on a Bayesian approach and is estimated by Markov chain Monte Carlo methods (MCMC). The model extends classic factor analysis by allowing not only for gaussian metric manifest variables, but also for binary and ordinal indicators which are very common in many areas of application (e.g. psychology, sociology). Furthermore, a semiparametric predictor is introduced which describes the influence of covariates on the latent variables. The predictor may contain parametric effects, smooth functions of metric covariates (modeled by random walks and P-splines), spatial effects (modeled by Markov random fields) and interactions of metric and categorical covariates. The integration of temporal effects is easily possible. Consequently, the influence of covariates on the latent variables can be analyzed in much more detail than with currently available methods. One emphasis of this work is the development of an efficient MCMC algorithm with good estimation properties (in particular concerning the cutpoints of ordinal indicators) and its implementation in the standard software package R. Another focus lies on the demonstration of the model's applicability using data from an internet survey. Several models with differently structured predictors are analyzed and first ideas for model selection are presented.

Die Arbeit beschäftigt sich mit (Pseudo)-Likelihood-basierten Schätz-Methoden zur Analyse von marginalen Regressions-Modellen für Longitudinaldaten mit stetigem Response. Es werden drei neuartige Modelle entwickelt, die aufeinander aufbauen. Zunächst wird ein Regressions-Modell entwickelt, das neben einem nichtparametrischen Term auch multiplikative zeitabhängige Parameter und Varying-Coefficients-Terme beinhaltet. Im Anschluss wird das Modell um einen parametrischen Term erweitert, so dass ein semiparametrisches Modell entsteht. Desweiteren wird das Modell auf den Bereich der 'Seemingly-Unrelated-Regression'-Modelle (SUR) ausgeweitet.

Aufgrund der Entwicklung von aggregierten Methoden wurde in den letzten Jahren eine Reihe neuer Verfahren im Forschungsfeld der Klassifikation und Prädiktion eingeführt. Die beiden wichtigsten Entwicklungen, nämlich Bagging und Boosting, wurden sowohl für den Fall von binären Zielvariablen als auch für den Mehrklassenfall ausführlich diskutiert und analysiert. Während diese angeführten Methoden die Klassenvariable jedoch als nominale Größe ohne Ordnungsstruktur betrachten, kann die Zielvariable in vielen Anwendungen als eine geordnete kategoriale Größe angesehen werden. In dieser Arbeit sollen deshalb Varianten für Bagging und Boosting entwickelt und vorgestellt werden, die in der Lage sind, die durch die ordinale Struktur in den Daten gegebene Information zu nutzen. Ferner wird aufgezeigt, wie die Qualität der Vorhersagen durch die Verwendung dieser auf die Problemstellung abgestimmten Aggregationsverfahren verbessert wird. Die dazu nötigen empirischen Vergleiche zwischen diversen Klassifikationstechniken werden nicht nur anhand von Fehlklassifikationsraten durchgeführt; stattdessen sollen auch Kriterien, die die Ordinalität in Vorhersage und Zielgröße zu berücksichtigen vermögen, herangezogen werden. Hier spielen in erster Linie verschiedene Abstandsmaße eine Rolle. Aber auch auf der Basis anderer Techniken und Ansätze kann man versuchen, dem Problem der ordinalen Klassenstruktur zu begegnen: Nächste-Nachbarn-Verfahren, die eine der intuitivsten und einfachsten Methoden zur Klassifikation darstellen, werden in dieser Arbeit durch einige Modifikationen an die besonderen Strukturen von ordinalen Zielgrößen angepaßt. Abschließend können die Resultate dieses zweiten Ansatzes, der ohne großen Rechenaufwand auskommt, mit denjenigen der modernen und rechenintensiven Aggregationstechniken verglichen werden.

The research topic investigated by this thesis is reactivity on the Web. Reactivity on the Web is an emerging research issue covering: updating data on the Web, exchanging information about events (such as executed updates) between Web sites, and reacting to combinations of such events. Following a declarative approach to reactivity on the Web, a novel reactive language called XChange is proposed. Novelties of the language are represented by the proposed data metaphor intended to ease the language understanding and the supported reactive features tailored to the characteristics of the Web. Realising this pressuposed refining, extending, and adapting to a new medium some of the concepts on which active database systems are built upon. Reactivity is specified in XChange by means of reactive rules (or event-condition-action rules) having the following components: the event part is a query against events that occurred on the Web, the condition part is a query against Web resources (expressed in the Web query language Xcerpt), and the action part is a transaction specification (specifying updates to be executed and events to be raised in an all-or-nothing manner). Novel in XChange is its ability to detect composite events on the Web, i.e. possibly time related combinations of events that have occurred at (same or different) Web sites. XChange introduces a novel view over the Web data by stressing a clear separation between persistent data (data of Web resources, such as XML or HTML documents) and volatile data (event data communicated on the Web between XChange programs). Based on the differences between these kinds of data, the data metaphor is that of written text vs. speech. XChange's language design enforces this clear separation and entails new characteristics of event processing on the Web. After motivating the need for a solution to reactivity on the Web, this thesis introduces the design principles and syntax of the language XChange accompanied by use cases for demonstrating the practical applicability of its constructs. Important contributions of the thesis are the specification of the language semantics and the description of an algortihm for evaluating XChange programs.