EconStor Collection:
http://hdl.handle.net/10419/158
2017-09-26T14:52:49ZA diffusion approximation for an epidemic model
http://hdl.handle.net/10419/31042
Title: A diffusion approximation for an epidemic model
Authors: Dargatz, Christiane
Abstract: Influenza is one of the most common and severe diseases worldwide. Devastating epidemics actuated by a new subtype of the influenza A virus occur again and again with the most important example given by the Spanish Flu in 1918/19 with more than 27 million deaths. For the development of pandemic plans it is essential to understand the character of the dissemination of the disease. We employ an extended SIR model for a probabilistic analysis of the spatio-temporal spread of influenza in Germany. The inhomogeneous mixing of the population is taken into account by the introduction of a network of subregions, connected according to Germany's commuter and domestic air traffic. The infection dynamics is described by a multivariate diffusion process, the discussion of which is a major part of this report. We furthermore present likelihood-based estimates of the model parameters.2007-01-01T00:00:00ZWavelets for diffusion tensor imaging
http://hdl.handle.net/10419/31074
Title: Wavelets for diffusion tensor imaging
Authors: Heim, Susanne
Abstract: In this paper, wavelet basis functions are investigated for their suitability for processing and analysing diffusion tensor imaging (DTI) data. First, wavelet theory is introduced and explained by means of 1d and 2d examples (Section 1.1 - 1.3). General thresholding techniques, which serve as regularization concepts for wavelet based models, are presented in Section 1.4. Regularization of DTI data can be performed at two stages, either immediately after acquisition (Wirestam et al., 2006) or after tensor estimation. The latter stage of denoising is outlined in Section 6 together with the incorporation of the positive definiteness constraint using log-Cholesky parametrization. In Section 3, the procedure is examined in a simulation study and compared to standard processing and the space-varying coefficient model (SVCM) based on B-spines (Heim et al., 2007). In addition, a real data example is presented and discussed. Finally, an approach is proposed how a space-varying coefficient model could fairly be adapted to wavelet basis functions. The theoretical parts are based on books of Gencay et al. (2002, Chap. 1, 4-6), Härdle et al. (1998), Ogden (1997) and Jansen (2001) if not stated otherwise. For an introduction to diffusion tensor imaging refer to Heim et al. (2007, Chap. 2).2007-01-01T00:00:00ZSpatial smoothing techniques for the assessment of habitat suitability
http://hdl.handle.net/10419/31044
Title: Spatial smoothing techniques for the assessment of habitat suitability
Authors: Kneib, Thomas; Müller, Jörg; Hothorn, Torsten
Abstract: Precise knowledge about factors influencing the habitat suitability of a certain species forms the basis for the implementation of effective programs to conserve biological diversity. Such knowledge is frequently gathered from studies relating abundance data to a set of influential variables in a regression setup. In particular, generalised linear models are used to analyse binary presence/absence data or counts of a certain species at locations within an observation area. However, one of the key assumptions of generalised linear models, the independence of the observations is often violated in practice since the points at which the observations are collected are spatially aligned. While several approaches have been developed to analyse and account for spatial correlation in regression models with normally distributed responses, far less work has been done in the context of generalised linear models. In this paper, we describe a general framework for semiparametric spatial generalised linear models that allows for the routine analysis of non-normal spatially aligned regression data. The approach is utilised for the analysis of a data set of synthetic bird species in beech forests, revealing that ignorance of spatial dependence actually may lead to false conclusions in a number of situations.2006-01-01T00:00:00ZStochastic volatility models for ordinal valued time series with application to finance
http://hdl.handle.net/10419/31080
Title: Stochastic volatility models for ordinal valued time series with application to finance
Authors: Müller, Gernot J.; Czado, Claudia
Abstract: In this paper we introduce two stochastic volatility models where the response variable takes on only finite many ordered values. Corresponding time series occur in high-frequency finance when the stocks are traded on a coarse grid. For parameter estimation we develop an efficient Grouped Move Multigrid Monte Carlo (GM-MGMC) sampler. We apply both models to price changes of the IBM stock in January, 2001 at the NYSE. Dependencies of the price change process on covariates are quantified and compared with theoretical considerations on such processes. we also investigate whether this data set requires modeling with a heavy-tailed Student-t distribution.2006-01-01T00:00:00Z