Statistics for Spatial Data.

In network approaches to psychopathology, disorders result from the causal interplay between symptoms (e.g., worry → insomnia → fatigue), possibly involving feedback loops (e.g., a person may engage in substance abuse to forget the problems that arose due to substance abuse). The present review examines methodologies suited to identify such symptom networks and discusses network analysis techniques that may be used to extract clinically and scientifically useful information from such networks (e.g., which symptom is most central in a person's network). The authors also show how network analysis techniques may be used to construct simulation models that mimic symptom dynamics. Network approaches naturally explain the limited success of traditional research strategies, which are typically based on the idea that symptoms are manifestations of some common underlying factor, while offering promising methodological alternatives. In addition, these techniques may offer possibilities to guide and evaluate therape...

http://www.psychosystems.org/files/Literature/borsboomcramerannualreview.pdf

Network Analysis: An Integrative Approach to the Structure of Psychopathology

The huge number of neurons in the human brain are connected to form functionally specialized assemblies. The brain's amazing processing capabilities rest on local communication within and long-range communication between these assemblies. Even simple sensory, motor and cognitive tasks depend on the precise coordination of many brain areas. Recent improvements in the methods of studying long-range communication have allowed us to address several important questions. What are the common mechanisms that govern local and long-range communication and how do they relate to the structure of the brain? How does oscillatory synchronization subserve neural communication? And what are the consequences of abnormal synchronization?

Normal and pathological oscillatory communication in the brain

Nonlinear Programming: A Unified Approach

https://www.lef.wiwi.uni-due.de/fileadmin/fileupload/BWL-LEF/Seminarreihe/RWeron14_Essen.pdf

Electricity price forecasting: A review of the state-of-the-art with a look into the future

https://www.fdm.uni-freiburg.de/publications-preprints/publications/papers/JNeuroScience2006

Testing for directed influences among neural signals using partial directed coherence

https://www.fdm.uni-freiburg.de/publications-preprints/publications/papers/rPDC_printed

Assessing the strength of directed influences among neural signals using renormalized partial directed coherence

Granger-causality and path diagrams for multivariate time series

The identification of effective connectivity from time-series data such as electroencephalogram (EEG) or time-resolved function magnetic resonance imaging (fMRI) recordings is an important problem in brain imaging. One commonly used approach to inference effective connectivity is based on vector autoregressive models and the concept of Granger causality. However, this probabilistic concept of causality can lead to spurious causalities in the presence of latent variables. Recently, graphical models have been used to discuss problems of causal inference for multivariate data. In this paper, we extend these concepts to the case of time-series and present a graphical approach for discussing Granger-causal relationships among multiple time-series. In particular, we propose a new graphical representation that allows the characterization of spurious causality and, thus, can be used to investigate spurious causality. The method is demonstrated with concurrent EEG and fMRI recordings which are used to investigate the interrelations between the alpha rhythm in the EEG and blood oxygenation level dependent (BOLD) responses in the fMRI. The results confirm previous findings on the location of the source of the EEG alpha rhythm.

A graphical approach for evaluating effective connectivity in neural systems

We introduce graphical time series models for the analysis of dynamic relationships among variables in multivariate time series. The modelling approach is based on the notion of strong Granger causality and can be applied to time series with non-linear dependences. The models are derived from ordinary time series models by imposing constraints that are encoded by mixed graphs. In these graphs each component series is represented by a single vertex and directed edges indicate possible Granger-causal relationships between variables while undirected edges are used to map the contemporaneous dependence structure. We introduce various notions of Granger-causal Markov properties and discuss the relationships among them and to other Markov properties that can be applied in this context. Examples for graphical time series models include nonlinear autoregressive models and multivariate ARCH models.

/pdf/graphical-modelling-of-multivariate-time-series-4x7kaj4q4e.pdf

Michael Eichler

Papers

Testing for directed influences among neural signals using partial directed coherence

Assessing the strength of directed influences among neural signals using renormalized partial directed coherence

Granger-causality and path diagrams for multivariate time series

A graphical approach for evaluating effective connectivity in neural systems

Graphical modelling of multivariate time series